Rezolvari fizica mecanica subiectul II

Ministerul Educaţiei Cercetării şi Tineretului Centrul Naţional pentru Curriculum şi Evaluare icircn Icircnvăţămacircntul Preuniversitar

Varianta 001

Subiectul A MECANICĂ

IIa reprezentarea corectă a greutăţilor tensiunii icircn fir forţei de frecare şi reacţiunii planului b NFgmGgmG f micro=== 2211 amTG 22 =minus amFT f 1=minus 01 =minusGN Rezultat final 22 sma = c amGT 22 minus= Rezultat final NT 80= d

tv

a∆∆=

Rezultat final st 2=∆ e 02 =minusminus GFF f sau orice relaţie echivalentă

Rezultat final NF 41=


Varianta 002


II a ct FG = αmicroα cossin mgmg = microα arctg= Rezultat final 030=α b dFL cf sdotminus= Rezultat final JLf 4minus=

c reprezentarea corectă a forţei de tracţiune greutăţii forţei de frecare reacţiunii planului d maFGF ct =minusminus ( )αsin2gamF += Rezultat final NF 26=


Varianta 003


Nr Item Soluţie rezolvare IIa Figurarea componentelor greutăţii Figurarea forţei de frecare b Gp = 15 kN Gn = 20 kN Ff = 4 kN c N = 16 kN Ff = microN micro = 025 d Figura corectă Frsquof = 200 N e Grsquop minus Frsquof = mrsquoa a = 4 ms2


Varianta 004


IIa reprezentarea corectă a greutăţii corpurilor forţelor de tensiune forţei care acţionează asupra scripetelui b Tgmam minus= 22

gmTam 11 minus=

g

mm

mma

12

12

+minus

=

Rezultat final 2

310

sma =

c

gmm

mmT

21

212

+=

Rezultat final N 403T = d TF 2=

Rezultat final NT380=


Varianta 005 Subiectul A MECANICĂ

IIa

t

va

∆∆=

Rezultat final 22 sma =

b reprezentarea corectă a forţelor

de greutate de apăsare pe normală

de frecare c

mgN = Rezultat final NN 20= d

amGFNF f =+++

mamgF =minus micro

Rezultat final 30=micro e

11 tg

v

∆=micro

Rezultat final 501 =micro


Varianta 006


IIa gmG AA =

Rezultat final kgg

Gm A

A 30==

b reprezentarea corectă a greutăţilor corpurilor şi componentelor greutăţii pe plan icircnclinat tensiunii din fir reacţiunii planului icircnclinat c

=minus=minus

0sin

0

αA

B

GT

Tgm

Rezultat final kg

gG

m AB 150sin == α

d αsinAGT = Rezultat final NT 51=

e amG AA =αsin Rezultat final 25sin smga == α



IIa mgG = Rezultat final NG 1000= b ( )gamF micro+= Rezultat final NF 300= c

F

F12sin =α

21 90 αα minusdeg= Rezultat final deg=deg= 3060 21 αα

d ga microminus= Rezultat final 22 sma minus=


Varianta 008


IIa reprezentarea corectă a greutăţii reacţiunii planului forţei de frecare b cosnG G ϕ= sdot

sintG G ϕ= sdot

tgmicro ϕ=

Rezultat final 3

3micro =

c 0N = sinF Gαsdot =

sinG

Fα =

Rezultat final

2sin

3α =

d

xm a F Nmicrosdot = minus sdot

yN m g F= sdot minus

(cos sin )Fa g

m

α micro α micro+= minus

Rezultat final

2577

ma

s=



IIa FG =αsin Rezultat final deg= 30α b reprezentarea corectă a greutatăţii forţei de frecare reacţiunii planului c αcosmgN = Rezultat final αmicromicro cosmgNFf =sdot=

d amFGF f =++ maFGF ft =minusminus ( ) mamgF ++= αmicroα cossin Rezultat final NF 100=


Varianta 010


IIa reprezentarea corectă a tuturor forţelor ce acţionează asupra sistemului b legea a II-a a dinamicii amTgmF 11 =-- micro şi amgmgmT 222 cossin =αmicroα -- expresia acceleraţiei )(])cos(sin[ 2121 mmgmmFa +++= αmicroαmicro- Rezultat final 270 sma cong c expresia tensiunii din fir amgmFT 11 -- micro= Rezultat final NT 64= d expresia forţei de apăsare icircn scripete TTF += 2TF =

Rezultate finale NF 561 cong


Varianta 011

Subiectul A MECANICĂ IIa mgG = Rezultat final NG 200= b reprezentarea corectă a greutatăţii forţei de frecare forţei F cu componentele sale reacţiunii planului c )( αmicro sinFmgFf minus=

Rezultat final )(

gm

Fa microαmicroα minus+= sincos

d

Rezultat final 2

872s

ma =

e tav ∆=

Rezultat final sm

v 745=


Varianta 012


IIa 0vtt 1 =rarr= Rezultat final s3t1 =

b tva ∆∆= cacircnd 0t rarr∆ )t(v)tt(vv minus+= ∆∆ Rezultat final 2sm2a minus= c fFma minus= NFf micro= mgGN == Rezultat final 20=micro

d 1mtvd = 2)vv(v fim += (variaţie liniară) 0vsm6vv f0i === Rezultat final m9d =


Varianta 013


Nr Item Soluţie rezolvare IIa Componenta paralelă cu planul a greutăţii Componenta normală pe plan a greutăţii Forţa de frecare b Gp = G sin α Gn = G cos α (unde G = mg = 20 000 N sau 20 kN) Gp = 06 G = 12 kN Gn = 08 G = 16 kN Ff = T minus Gp Ff = 4 kN c Figurarea corectă a forţei de frecare d

fF N= micro

4 kN025

16 kNmicro = =

Ff = 125 N e Trsquo = Gp minus Frsquof Ff = 375 N



IIa reprezentare corecta a tensiunilor din fir Reprezentare corecta a normalei si a greutatilor b R= 2T T=G2 Rezultat final R = 80N c NTGF +=+ 1 N = F + G1 ndash G2 Rezultat final N = 40 N d G2gtG1

Rezultat final La eliberarea sistemului corpul 1 va urca accelerat e 11 2TR = ( ) 1221 GGamm minus=+ )(21 agmT minus= Rezultat final R1 = 32 N


Varianta 015


IIa αcos22 FF x = Rezultat final 12 FF x lt deci corpul se deplasează spre stacircnga

b lkF ∆=1 Rezultat final ml 030=∆

c maFF x =minus 21 GFN y =+ 2

αsin22 FF y =

Rezultat final 21 sma = d

yFGN 2minus=

Rezultat final NN 511= e 0=N αsin

2FG =

Rezultat final NF 6222 =


Varianta 016


II a reprezentarea corectă a reacţiunii normale a peretelui greutăţii forţei de frecare b αcosFdL = Rezultat final JL 18=

c maFmgF c =minusminusαcos Rezultat final NFc 36=

d NFc micro= αsinFN = Rezultat final 290321 cong=micro e răspuns corect - acceleraţia corpului creşte justificarea răspunsului


Varianta 017


IIa reprezentarea corectă a greutăţilor reacţiunii corpului de masă m tensiunii b

1 2G G Mg= =

3G mg=

Rezultat final

1 2

3

2

0 2

G G N

G N

= ==

c Ma Mg f T

Ma T Mg

ma mg f

= + minus= minus= minus

2

mga

m M=

+

Rezultat final

2048

ma

s

d 2

2

mMf g

m M=

+

Rezultat final 019f N e ( )2

2

M M mT g

M m

+=

+

Rezultat final 209T N


Varianta 018


IIa Reprezentarea forţelor de greutate forţelor de tensiune forţei indicate de dinamometru b gmG sdot= 11 şi gmG sdot= 22 gmTam sdotminus=sdot 11 Tgmam minussdot=sdot 22

21

12

mm

mmga

+minus

=

Rezultat final 25 sma = c

Tgm

gmT

m

m

minusminus

=2

1

2

1

( )Tmmgmm 21212 +=

gmm

mmT sdot

+=

21

212

Rezultat final NT 15= d TF sdot= 2 Rezultat final NT 30=



IIa reprezentarea corectă a forţelor 0=+ eFT lkT prime∆= Rezultat final NT 40= b lkFe ∆= lkT ∆=1 Rezultat final ml 40=∆ c mgG = Rezultat final NG 10= d 0=++ GFN e lkmgN ∆minus= Rezultat final NN 2= e GFT e =Prime=1 Rezultat final NT 101 =


Varianta 020


IIa reprezentarea corectă a tuturor forţelor componentele forţei F greutatea reacţiunea normală frecarea b amFNGF f =+++

=minus+=minus

0sin

cos

mgFN

maFF f

αα

( )αmicromicro sinFmgNFf minus== ( )

αmicroαmicrosincos +

+= gamF

NF 556=

c 0sin leminus= αFmgN

αsinmg

F ge

Rezultat final NF 40min =

d precizarea că icircn absenţa apăsării dispare frecarea αcosFma =

Rezultat final 2

317310coss

mtgg

mF

a cong===α

α


Varianta 021


IIa Reprezentarea corectă a forţelor ce acţionează asupra corpului A forţelor ce acţionează asupra corpului B

forţelor ce acţionează asupra corpului C b amTgm AB 22 =minus

amgmTT ACAB 11 =minusminus micro

amgmTAC 33 =minus

321

132

mmm

mmmga

++minusminus

=micro

Rezultat final 253 sma = c ( )agmTAB minus= 2 Rezultat final NTAB 532=

d 0=a

1

32

m

mm minus=micro



Varianta 022


IIa

tva ∆

∆=

Rezultat final st 20=∆ b F minus Ff = m a F = n m a (nminus1) rezultat final F = 30 N c grafic corect Rezultat final atg =α

d vvv crel minus=

TL

vrel =

relvL

T =

Rezultat final T= 5s e

vvL

Tc +

=1

Rezultat final sT 521 =


Varianta 023


Nr Item Soluţie rezolvare IIa G = mg R = 25103 N sau 25 kN b T = R T = 25103 N sau 25 kN c Reprezentarea corectă a forţelor sau altă justificare corectă Ft = 2 R sau 2 mg Ft = 5103 N sau 5 kN d P = F v v = 20 ms v = 72 kmh e T = m(025 g + a) T = 4103 N sau 4 kN


Varianta 024


IIa G mg=

Rezultat final 5G N= b reprezentarea corectă a greutăţii reacţiunii corpului de masă m forţei elastice c

0

0

cosl

l lα =

+ ∆

0

11

cos

l

l α∆ = minus

Rezultat final

0

1l

l

∆ =

d coseN G F α= minus sdot

eF k l= ∆

Rezultat final 45N N=

e

x

y

f e

e

f

F F

N mg F

F Nmicro

=

= minus

=

sin

cosx

y

e e

e e

F F

F F

αα

= sdot

= sdot

x

y

e

e

F

G Fmicro =

minus

Rezultat final 019micro =


Varianta 025

Subiectul A MECANICĂ IIa mgG = Rezultat final NG 10= b reprezentarea corectă a greutatăţii forţei elastice c GFma minus= )( gamF += Rezultat final NF 810= d lkF ∆=

lF

k∆

=

Rezultat final

mN

k 540=

e GF = Rezultat final NF 10=


Varianta 026


II a reprezentarea forţelor ce acţionează asupra sistemului principiul II al dinamicii pentru sac mamgT =minus pentru muncitor FT =

mmgF

aminus=

Rezultat final 2521 sma = b Reprezentarea forţelor ce acţionează asupra omului Observaţia că forţa de apăsare este egală cu reacţiunea planului asupra omului TNG += FGN minus= Rezultat numeric NN 50=

c amgmT =minus

)( agmT += Rezultat numeric NT 450 =


Varianta 027


IIa αsinFgmN 11 minus= gmN 22 = NNN 21 == Rezultat final 030=α b NFf micro= Rezultat final N6FFF f2f1f ===

c f21 F2cosFa)mm( minus=+ α Rezultat final 2sm761a cong d amFcosFFamT 1ff2 minusminus=+= α Rezultat final N767T cong



IIa Reprezentare corecta a greutatilor si a normalelor Reprezentare corecta a tensiunilor si a fortelor de frecare b RC = 0 rarr TBC = FfC TBC = microGC

Rezultat final TBC = 10 N c BfB NF micro= deg= 30cosBfB GF micro Rezultat final NNFfB 66835 ==

d fBBCtBAB FTGT ++=

ABA TG =

Rezultat final kgmA 873=

e AfBtB GFG lt=+ 6628 sistemul se misca accelerat ammFGG BAfBtBA )( +=minusminus amGT AAAB minus= Rezultat final NTAB 7633 =


Varianta 029


IIa reprezentarea corectă a greutăţilor tensiuniii icircn fir reacţiunii planului b amTG t 22 =minus 022 =minus nGN amGT t 11 =minus 011 =minus nGN αβ sinsin 1122 gmGgmG tt == Rezultat final 2460 sma = c

tv

a∆∆=

Rezultat final smv 32= d ( )agmT minus= βsin2 2TF = Rezultat final NF 123=


Varianta 030


II a mgG = Rezultat final kgm 80=

b reprezentarea corectă a greutăţii reacţiunii normale forţei de frecare c ecuaţia principiului fundamental al dinamicii maFF c =minusαcos mişcare rectilinie uniformă 0=rArr a Rezultat final NNFc 46332 cong=

d NFc micro= αsinFGN minus=

Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==

b ( )2 1 0m g k l l= minus

( )1 0 2m g k l l= minus

1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+

Rezultat final 0 25l cm=


Varianta 032


IIa reprezentarea forţelor de greutate tG nG descompunerea lui F icircn xF şi yF

reacţiunii la plan N forţei de frecare fF

b αcossdot= FFx şi αsinsdot= FFy

αsinsdotsdot= gmGt şi αcossdotsdot= gmGn αα sincos sdot+sdotsdot=+= FgmFGN yn

Rezultat final NN 35= c tfx GFF += txf GFF minus= αα sincos sdotsdotminussdot= gmFFf Rezultat final NFf 35=

d

NFf sdot= micro sau ααααmicro

sincossincos

sdot+sdotsdotsdotsdotminussdot==

FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033


Nr Item Soluţie rezolvare IIa diagrama forţelor care acţionează asupra paraşutistului b amR =

makvmg =minus

c

0vkmg sdot=

0vmgk =

Rezultat final skg120k =

d gmkva +minus=

Rezultat final 2ms2a minus=



IIa mgG = Rezultat final NG 619= b reprezentarea corectă a forţei de greutate reprezentarea corectă a forţei de frecare la alunecare reprezentarea corectă a forţei de apăsare pe normală c amFNFG f =+++

maFG =minus maGFf minus=

Rezultat final NFf 617=

d FN = FFf micro=

Rezultat final 240congmicro


Varianta 035


IIa αsinmgGt = αcosmgGn = NGt 5= NGn 7835 cong=

b amFNG f =++

=minus=minus

0n

ft

GN

maFG

αmicromicro cosmgNFf == ( )αmicroα cossin minus= ga Rezultat final 282 sma =

c Condiţia de echilibru 0=minus+ tf GFF ( )αmicroα cossinmin minus= mgF Rezultat final NF 82min =

d Condiţia de echilibru 0=minusminus tf GFF ( )αmicroα cossinmax += mgF Rezultat final NF 27min =


Varianta 036


IIa Reprezentarea forţelor ce acţionează asupra corpurilor b amTF 111 cos =minusα amFT 222 cos =minus α

21

2211 coscos

mm

FFa

+minus

=αα

Rezultat final 2212 sma = c 0sin 1

111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F

Rezultat final 221 1

2 =FF


Varianta 037


Nr Item Soluţie rezolvare II a maxTF =

1001010 =+t Rezultat final st 9= b [ ]st 90isin tensiunea creşte liniar de la valoarea zero la maxT

Grafic corect c NFf micro=

mgN = Rezultat final NFf 100=

d maFF f =minus

maNt =minus+ micro1010

mmgt

amicrominus+= 1010

unde st 10=




IIa reprezentarea corectă a greutatăţii a componentelor forţei F b reprezentarea corectă a componentelor forţei F a reacţiunii planului a forţei de frecare c αsin11 FGN minus= αsin22 FGN +=

d maFF f =minus 11 cosα maNF =minus 1cos microα ( ) ( )gamF microαmicroα +=minus sincos1 ( ) ( )gamF microαmicroα +=+ sincos2 Rezultat final 2F mai mare decacirct 1F

e ESFl0=∆ Rezultat final m510113 minussdotcong∆



IIa mgG = Rezultat final NG 20= b reprezentarea corectă a greutăţilor forţei de frecare tensiunii icircn fir reacţiunii planului c αsinMgGt = αmicro cosMgFf =

Mm

Mgmga

++minus= )cos(sin αmicroα

Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+

++= )cossin1( αmicroα

Rezultat final NT 18=


Varianta 040


II a legea a doua a dinamicii 11

sin maFG f =minusα şi αcos1 GN =

)cos(sin1 αmicroα minus= ga Rezultat final 2

1 24 sma =

b 22

maFf =minus şi GN =2

ga micro22 minus= Rezultat final 2

2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=

21 ttt ∆+∆=∆ Rezultat final st 2674=∆ d Teorema variaţiei energiei cinetice cop Emgd minus=minus 02micro

gvdop micro42=

Rezultat final mdop 512=



IIa Reprezentarea corecta a componentelor greutatilor Reprezentarea normalelor si a fortelor de frecare Reprezentarea corecta a tensiunii in fir b gmGgmG 2211 == Rezultat final NGNG 8040 21 ==

c ( )ammR 21 += ( )ammFFGG fftt 212121 +=minusminus+ αmicroαmicro coscos gmFgmF ff 222111 == αα sinsin gmGgmG tt 2211 ==

Rezultat final 22

83065

s

m

s

ma cong=

d amFGT ft 222 =minus+ sau echivalent


e rarr= 0fF fortele exterioare care actioneaza asupra sistemului sunt 21 tt GG 12 tt GG gt Rezultat final T=0 firul este netensionat


Varianta 042


Nr Item Soluţie rezolvare IIa

1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s

c legea mişcării rectilinii uniforme

12D

tv

∆ =

6 mint∆ = hhmm = 1201 d 9 kmMd =

45 kmNd =

45 kmPd =

e Alura corectă a graficelor Precizarea valorilor numerice


Varianta 043


IIa amTFG ft 22 =minusminus 0=minus nGN amGT 11 =minus αsin22 gmG t = cos2 αmicro gmFf = gmG 11 =

Rezultat final 202

1 =m

m

b amTG 11 =minus amFGT ft 22 =minusminus 0=minus nGN

Rezultat final 2

484s

ma =

c ( )agmT minus= 1 Rezultat final NT 525= d

tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=

Rezultat final mx 51=∆


Varianta 044



b reprezentarea corectă a greutăţii reacţiunii normale tensiunii din fir c αsinGGt = TGF t =+αcos Rezultat final NT 35=

d αα sincos FGN minus= 0=N cacircnd maxFF = Rezultat final NF 269max cong


Varianta 045


IIa 11 GN0 minus= 11f NF micro= Rezultat final N2F 1f =

b 1f1 FTam minus= TGam 22 minus= Rezultat final 2sm251a = c )ga(m)ag(mT 12 micro+=minus= Rezultat final N6252T = d 2TF = Rezultat final N703F cong e tva ∆∆= atv = ( 0v0t 00 =rarr= ) Rezultat final sm5v =


Varianta 046


IIa reprezentarea corectă a greutatăţii normalei la plan forţei de frecare proiecţiilor lui F pe axe b αcossdot= FFx αsinsdot= FFy

fx FF = αtgFF fy sdot=

Rezultat final NFx 310= NFy 10=

c GFN y =+

yFGN minus=

Rezultat final NN 30= d NFf sdot= micro

N

Ff=micro

Rezultat final

3

1=micro

e fx FFam minus=sdot

1



Varianta 047


Nr Item Soluţie rezolvare IIa reprezentarea corectă forţa de greutate forţa de reacţiune normală

forţa rarr

1F

forţa de frecare b ft FFG += 1

ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=

Rezultat final 170=micro

c maFG ft =minus

( )αmicroα cossin minus= ga


d tav ∆sdot= Rezultat final smv 517=



IIa reprezentarea corectă a forţelor 0=minus fFF


b NFf micro=

GN = Rezultat final 50=micro c maFF f =primeminus

g

a

mg

F minus=primemicro

Rezultat final 30=primemicro d maFF f =minusprime

Rezultat final NF 7=prime


Varianta 049


IIa mgG = NG 1=

b Precizarea că panta graficului este numeric egală cu constanta elastică

yF

k∆∆=

Rezultat final mNk 50=

c Condiţia de echilibru 0=+ eFG kymg =

kmg

y =

Rezultat final my 020=

d Condiţia de echilibru 0=++ inertiee FFG mamgky =minus

kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=

Rezultat final 25 sma = b ( )gamT += 1 Rezultat final NT 51= c TF 2=

∆= kF Rezultat final cm51=∆ d ( )ascagmF minus= 1 Rezultat final NF 90=


Varianta 051


IIa 0=minus rFT 0=minus mgN

NFr micro=

0=minusTF mgF micro=


b 02 =minus FT Rezultat final NT 80=

c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR

Rezultat final NR 96203=


Varianta 052


IIa ( )01 llkgm minus=sdot ( )01 llgmk minussdot= Rezultat final mNk 100=

b reprezentarea corectă a greutatăţii tensiunii din resort (forţei elastice) reacţiunii planului c

021 llkT minus=

Rezultat final NT 501 =

d tGT =1 αsdotsdot=minus sin02 gmllk

gmllk sdotminus=α sin 02

Rezultat final 030=α


Varianta 053


II a Legea a doua a dinamicii maFmg f =minusαsin

)( alh

gmFf minus=


b Legea a doua a frecării NFf sdot= micro αcosmgN = Rezultat final 3460=micro

c

)cos(sin αmicroα minus= ga acceleraţia e independentă de masa corpurilor Rezultat final 22 sma = d 0sin)( =+minusminus αgmMFF f

αcos)( gmMN += gmMF )cos)(sin( αmicroα ++=



Varianta 054

Subiectul A MECANICĂ IIa mgG = Rezultat final kNG 5= b

)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===

c atv = Rezultat final

sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv



IIa Reprezentarea corecta a componentelor greutatilor Reprezentarea corecta a normalelor Reprezentarea corecta a tensiunii in fir si a fortei elastice b αcosgmN AA = αcosgmN BB = Rezultat final NNNN BA 35310 ==

c TGtA = αsingmG AtA =

2

gmT A=

Rezultat final NT 10= d etB FTG =+ kxTgmB =+αsin Rezultat final mx 10=

e etBtA FGG =+ Rezultat final ctxctGG tBtA =rArr=+



Nr Item Soluţie rezolvare IIa bull Determinarea din grafic a vitezelor la deplasările ArarrB şi BrarrA

ABas tvvd sdot+= )( BAas tvvd sdotminus= )( min72=ABt min40=BAt kmd 12= Rezultat final smhkmv s 88314 cong=

b bull calculul duratei parcursului ArarrBrarrA BAAB ttt += Rezultat final min112=t c bull aplicarea legilor de mişcare la mişcările celor două şalupe

ias tvvxd sdotminus=minus )( ias tvvx sdot+= )( Rezultat final kmx 77cong d bull

ABs tvd sdot=

bull min451 cong= BAAB tt

bull min86102 congABAt

bull reprezentarea grafică


Varianta 057


IIa 11 maF = Rezultat final 2

1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=

212 vvv ∆+= Rezultat final smv 302 =

c

21

1v

v m =

Rezultat final smv m 51 =

d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058


II a reprezentarea corectă a greutăţii reacţiunii normale forţei de frecare b αcosmgN = Rezultat final NN 317cong

c ecuaţia principiului fundamental al dinamicii maFG ct =minus αsinmgGt = NFc micro= Rezultat final 252 sma =

d mişcare rectilinie uniformă 0=rArr a ct FGF += Rezultat final NF 15=


Varianta 059


IIa 02 =yR şi 222 GNR +=y

22 GN =

Rezultat final N= 122N b forţa de tracţiune trebuie să fie mai mică decacirct forţa de frecare la alunecare fcosα FF lt 1NF micro=f

αsin11 FgmN -= Rezultat final N870ltF c 01 =N şi FGN prime+= 11 0sin1 =prime αFG - rezultat final N676ЎЦFprime d

++++=

+=

ff 2121

21 )(

NNFFFR

ammR

1NF micro=f1 şi 2NF micro=f2

rezultat final 28750 sma =


Varianta 060


IIa mgG = Rezultat final kgm 303 =

b reprezentarea corectă a forţelor care acţionează asupra lui 1m forţelor care acţionează asupra lui 2m forţelor care acţionează asupra lui 3m

c 23 GTN =+ NGT minus= 23 Rezultat final NT 2003 =

d

23

21T

TT ==

213 TTT += Rezultat final NTT 10021 ==

e 11 TG = gmG sdot= 11

g

Tm 1

1 =

g

Tmm

sdot==

23

21

Rezultat final kgmm 1021 ==


Varianta 061

Subiectul A MECANICĂ IIa amMgmMF )()( +=+minus

gmM

Fa minus

+=

Rezultat final 22 sma = b mamgN =minus )( agmN += Rezultat final NN 36= c

tv

a∆∆=

av

t∆=∆

Rezultat final 10st =∆ d

SF=σ

4

2dS

π=

2

4

d

F

πσ =

Rezultat final 26 10384 mNsdot=σ



IIa 0)sin(cos 2222 =minusminus αmicroα FmgF

22

2

sin

cos

αmicro

Fmg

F

minus=

Rezultat final 10congmicro b mgFmgF microαmicroαmicroαα =+=+ )sin(cos)sin(cos 111222

211

121 sincos

sincosFF

αmicroααmicroα

++

=

Rezultat final NF 461 cong c 0sin0sin 222111 =+minus=+minus αα FmgNFmgN

22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos

11111 αmicroα FmgF

ma primeminusminusprime=

Rezultat final 2520 sma cong


Varianta 063


IIa amFNG f =++ mamgmg =minus αmicroα cossin ( )αmicroα cossin gga minus=


315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12

Rezultat final 2882310 smv congminus=

c Condiţia de echilibru αmicroα cossinmin mgmgF minus=

Rezultat final NNF 4010

3150min cong

minus=

d Condiţia de echilibru αmicroα cossinmin mgmgF +=


3150min cong

+=


Varianta 064

Subiectul A MECANICA

IIa gmFf 11

micro=

Rezultat final NFf 8521

=

b ( ) 01 =+minus gmmT micro 02 =minusTgm

12 m

mm minus=

micro

Rezultat final kgm 6= c ( )

21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro

Rezultat final 4 21 =aa

d ( )12 agmT minus= Rezultat final NT 578=


Varianta 065


IIa reprezentarea corectă a greutatăţilor celor două corpuri tensiunii din fir reacţiunii planului b GGt lt corpul A urcă şi corpul B coboară αsdotsdotminussdot=sdotsdot sin2 gmgmam Rezultat final 252 sma =

c ( ) αsdotsdotminussdot=primesdot+ sin22 gmgmamm 0=primea αsdot= sin2 mm Rezultat final kgm 12 =

d gmT sdot=prime 2 Rezultat final NT 10=prime



Nr Item Soluţie rezolvare IIa Determinarea din grafic a acceleraţiei

t

vv

tv

a if

∆minus

=∆∆=


b rFgmam minussdot=sdot

Rezultat final NagmFr 10)( =minussdot=

c bull 2)()( 1221 ttvvtvd m minussdot+=∆sdot=

bull Determinarea din grafic a vitezelor 1v şi 2v smv 541 = smv 5132 = Orice altă variantă de calcul corectă se va puncta integral

Rezultat final md 9= d 0=a rArr gmvk sdot=sdot

Rezultat final smv 20=


Varianta 067


II a Legea a doua a dinamicii amFF f 1=minus gmFf 1micro= Rezultat final NF 12= b

22 amTgm =minus 11 amgmT =minus micro

Rezultat final 2 52 sma = c

)()1( 2121 mmgmmT ++= micro Rezultat final NT 522= d

2 Tgm = 0)( 01 =+minus gmmT micro

120 mmm minus= micro

Rezultat final kgm 100 =

e 1NFap = gmN 00 =

Corpul 1m gmNN 101 += Rezultat final NFap 150=


Varianta 068


IIa 1∆= kmg 12 2 ∆=+ kFmg

Rezultat final m = 05 kg b

0kpmg = Rezultat final k = 500 Nm

c reprezentarea corectă a sistemului mecanic reprezentarea corectă a greutăţii reprezentarea corectă a forţei 3F reprezentarea corectă a forţei elastice 3eF

d

GF3βtg =

rezultat final 1βtg =

e

33 ∆kFe = 2

32

3 FGFe +=

rezultat final cm23 =∆



IIa mgG = Rezultat final NG 70= b reprezentarea corectă a greutăţii si componentelor fortei F si a componentelor sale fortei de frecare reacţiunii planului c 0=rArr= Rctv αcosFGF tf minus= αα cossin FGFf minus= Rezultat final NFf 20=

d NFf micro= αα sincos FGN +=

Rezultat final 288032

1 asymp=micro


Varianta 070


IIa nGN = αcosmgGn = Rezultat final N52N = b tva ∆∆= Rezultat final 2sm5a = c ft FGma minus= αsinmgGt = NFf micro= Rezultat final 730=micro

d ft FGF += Rezultat final N665F =


Varianta 071

Subiectul A MECANICĂ IIa gmG 11 = Rezultat final kgm 11 =

b reprezentarea corectă a greutatăţilor forţei de frecare reacţiunii planului tensiunii icircn fir c

amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072


IIa reprezentarea corectă a greutăţii şi reacţiunii planului tensiunii din resort (forţei elastice) şi forţei de frecare b

125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆

NkFT e 62=∆sdot== NmgG 10== NTmgN 67cos =minus= α NTFf 1sin == α

c

ααmicrocos

sinTmg

Tminus

=

Rezultat final 130asympmicro d

43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020

2 =minusminusprime+=prime∆

NkFT e 87=prime∆sdot=prime=prime şi NTmgN 763cos =primeprimeminus=prime α

mNT

aprimeminusprimeprime

= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus

Rezultat final NF 1000= c enunţul corect αcosmgN =

Rezultat final NN 8660cong d NFf micro=



Varianta 074


Nr Item Soluţie rezolvare IIa gmMG )( += Rezultat final NG 300= b reprezentarea corectă a fiecărei forţe forţa de tracţiune forţa de frecare corp-sanie forţa de greutate forţa de reacţiune normală c enunţul corect NFf 1micro=

gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075


IIa intervalul de timp s10 rarr tconstFt sdot= şi [ ]gmFf sdotsdotmicroisin 0 NgmFf 10max =sdotsdotmicro= 00 =rArr=+= RFFR ft corpul este icircn repaus Rezultat final 0=v b intervalul de timp s32 rarr NconstFt 20== şi gmFf sdotsdotmicro= ft FFam minus=sdot şi ( ) mgmFa t sdotsdotmicrominus= Rezultat final 21 sma =

c intervalul de timp s61rarr constgmFf =sdotsdotmicro= Rezultat final NFf 10=

d din grafic rArr tF scade de la 10 N pacircnă la zero icircn intervalul de timp s65 rarr Rezultat final intervalul de timp este s65 rarr

e intervalul de timp s54 rarr NFt 10= şi NgmFf 10=sdotsdotmicro= ft FFR minus= Rezultat final 0=R



Nr Item Soluţie rezolvare IIa Reprezentarea forţelor ce acţionează asupra celor două corpuri

b bull Aplicarea principiului fundamental al dinamicii fiecărui corp

Tgmam minussdot=sdot 11 gmFf sdotsdot= 2micro gmTam sdotsdotminus=sdot 22 micro

Rezultat final NgmT 62)1(1 =+sdotsdot= micro

c bull Exprimarea acceleraţiei 1 mTga minus=


d bull Exprimarea acceleraţiei medii ( maa = deoarece acceleraţia este constantă)

tvtvva fininfin ∆=∆minus= )(

Rezultat final smv fin 4=

e bull Scrierea condiţiei de mişcare uniformă 0 =a (sau condiţia de echilibru a forţelor)

bull Aplicarea principiului II al mecanicii icircn noile condiţii

1

1 Tgmam minussdot=sdot gMTaM sdotsdotminus=sdot micro

Rezultat final kgmM 51 == micro


Varianta 077


IIa gmTFe 111 == 11 ∆= kFe

Rezultat final cmk

gm31

1 ==∆

b amTgm 11 =minus amgmT 22 =minus

Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=

∆== kFT e Rezultat final cm42=∆ d TR 2=

Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078


IIa mgG = Rezultat final G = 20 N b icircn punctul A

0=R TFR += Rezultat final T = 152 N c

NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=

αsinmgG =t NF microf =

αcosmgN =

Rezultat final 20=micro d

212 amR = NFGR ++= f12 )cos(sin2 αmicroα -ga =

Rezultat final 2ms= 442a


Varianta 079


Nr Item Soluţie rezolvare IIa [ ]min500isint

1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=

Rezultat final 22 50 sma minus=

b 0=minus ft FF

GFf 10

1=

Rezultat final NFt 700= c tvd ∆sdot= Rezultat final md 2700= d

2

2mvEc =

Rezultat final kJEc 7578=


Varianta 080


III a observaţia că mişcarea corpului este rectilinie uniformă icircn intervalul s62 minus Rezultat final st 4=∆

b

tx

v∆∆=


c observaţia că mişcarea corpului este uniform icircncetinită icircn intervalul s106 minus

tv

a∆∆=

Rezultat final 2251 sma minus=

d

2

2mvEc =

viteza corpului la momentul st 8= este smv 52= Rezultat final JEc 512=

e

2106 vv

v med+

=

Rezultat final smv med 52=



IIa maf = Rezultat final f =173 N b a)mM(cosF sdot+=α αsdot+= cosa)mM(F Rezultat final N10F = c α+= sinFMgN1 Rezultat final N1= 45 N d 2rFSF sdotπ==σ

)ag(MF +sdot= Rezultat final 26 mN10315 sdotasympσ


Varianta 082


IIa αcosMgN = Rezultat final NN 317310 cong=

b maTmg =minus MaMgMgT =minusminus αmicroα cossin

Rezultat final ( ) 33

cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα

Rezultat final NT 21= b forţa de frecare orientată icircn sus de-a lungul planului gmMgMg 1cossin += αmicroα )cos(sin1 αmicroα minus= Mm Rezultat final kgm 501 =


Varianta 083


IIa Fortele corect marcate gmgmgm 211 cossin += αmicroα

α

αmicrocos1

2

mm

tg minus=


b Fortele corect marcate amgmT 22 =minus amgmTgm 111 cossin =minusminus αmicroα

)(2 agmT += 2

370

sma minus=

Rezultat final NT 3103195 minussdotcong c Fortele corect marcate 0

2 =minusTgm 0cossin 11

=minusminus αmicroα gmgmT Rezultat final gm 249

2 =


Varianta 084


IIa 1m se deplasează uniform vertical icircn jos gmgmgmgm sdot+αsdotsdotsdotmicro=αsdotsdot+sdot 21 cossin 1m se deplasează uniform vertical icircn sus gmgmgmgm sdot=αsdotsdotsdotmicro+αsdotsdot+sdot 21 cossin Rezultat final Kgm im 692max1 cong şi Kgm im 301min1 cong

b ( ) gmgmgmgmammm sdotminusαsdotsdotsdotmicrominusαsdotsdot+sdot=sdot++ 2121 cossin Rezultat final 2091 sma cong

c 111 Tgmam minussdot=sdot rArr ( )agmT minussdot= 11 Rezultat final NT 64351 =

d d gmTam sdotminus=sdot 222 rArr ( )agmT +sdot= 22 0

222

22

22 60cos2 sdotsdotsdot++= TTTTR rArr 32 sdot= TR unde 7313 =

Rezultat final NR 7476cong


Varianta 085


IIa αsinFGN minus= Rezultat final N3511N cong b fFcosFma minus= α NFf micro= Rezultat final 2sm80a cong c tva ∆∆= atv = ( 0v0t 00 =rarr= ) Rezultat final sm12v cong d 0f0 Fma minus= ga0 microminus= 00 tvtva minus== ∆∆ Rezultat final s4t0 cong


Varianta 086


Nr Item Soluţie rezolvare IIa observaţia că la momentul st 2= NF 20=rArr 1maF =

Rezultat final 21 2 sma =

b

tv

a∆∆=1

tav ∆= 11

Rezultat final smv 81 =

c tvs m∆=

210

1vv

v+

=

Rezultat final ms 16= d 2 maF =

FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a



Nr Item Soluţie rezolvare IIa bull Reprezentarea corectă a forţelor ce acţionează asupra celor două corpuri greutate tensiune

icircn fir forţă de frecare la alunecare reacţiune normală

b bull Aplicarea principiului II al mecanicii corpului de masă m

Tgmam minussdot=sdot

bull Aplicarea principiului II al mecanicii corpului de masă M

fFTaM minus=sdot gMN sdot=

bull Exprimarea forţei de frecare NFf sdot= micro

Rezultat final 252

)(sm

MmMm

ga =+

sdotminussdot= micro

c )( agmT minussdot=


d lkT ∆sdot= Rezultat final cml 252=∆


Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr

Rezultat final m22A =r c desen r∆

d

t

=DA

m ∆∆

rarrr

v

22 yxr ∆∆∆ +=DArarr

AD= xxx -∆ şi AD y-y=y∆ Rezultat final ms170m ЎЦv

e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089


Nr Item Soluţie rezolvare IIa 0=minusminus ft FGF

nGN =

NFf micro=

0cossin =minusminus αmicroα mgmgF


b maFG ft =minus

)cos(sin αmicroα minus= ga


c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=

)cos(sin2 αmicroα minus= gLv


d θmicro tg=

Rezultat final 30arctg=θ


Varianta 090


IIa Forte corect marcate amTgm sdot=minussdotsdot 11 sinα amT sdot= 2

gmm

mmT sdot

+sdotsdot=

21

21 cosα

Rezultat final NT 57= b

gmm

ma sdot

+sdot=

21

1 sinα


c Forte corect marcate NFf sdot= micro 0cossin 111 =sdotsdotsdotminusminussdotsdot αmicroα gmTgm 021 =sdotsdotminus gmT micro Rezultat final 4170=micro


Varianta 091


IIa tva ∆∆= Rezultat final v = 03 ms b reprezentarea corectă a greutatăţilor forţelor de tensiune din fir forţei de tensiune din firul de care este suspendat scripetele c amgmT 22 =minus amgmT 11 =+minus ( )

( )21

21mm

mmga +minussdot=

Rezultat final sm6a = d

)mm(gmm4T2F

21

21+==

Rezultat final N32F =


Varianta 092


IIa reprezentarea forţelor G şi rezistentaF

b kvGFGma rez minus=minus=

Rezultat final

minus=Gkv

ga 1

c dacă constvv == 0 rArr 0=a mgkv =0

Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093


IIa ( )βsdotminussdotmicrominusβsdot=sdot sincos0 FGFam ( )[ ] gmFa sdotmicrominusβsdotmicro+βsdot= sincos0 Rezultat final 2

0 872 sma =

b fptxp FGFam minusminus=sdot unde 0=pa

( )ynfp FGF minussdotmicro=

( ) 0sincossincos =βsdotminusαsdotsdotsdotmicrominusαsdotsdotminusβsdot FgmgmF ( ) ( )βsdotmicro+βαsdotmicro+αsdotsdot= sincoscossingmF Rezultat final NF 25151=

c 0=pN rArr 0=minus yn FG

0sincos min =βsdotminusαsdot FG βαsdotsdot= sincosmin gmF Rezultat final NF 39245min =


Varianta 094


IIa Reprezentarea corecta a greutatilor

tensiunii din fir reactiunii planului fortei de frecare

b amTgm 22 =minus amFT f 1=minus NFf micro= Rezultatul final 25 sma =

c )(2 agmT minus= Rezultat final NT 51= d 2TF = Rezultat final NF 112cong


Varianta 095


IIa Fortele corect reprezentate ammTgmm )()( 22 +=minus+ amgmT 11 =minus

gmmm

ma

++=

21


b mafmg =minus )( agmf minus= Rezultat final Nf 862cong c )(1 agmT += Rezultat final NT 4131= d TF 2= Rezultat final NF 8262=


Varianta 096

Orice altă rezolvare care conduce la rezultate corecte se va puncta corespunzător

Subiectul A MECANICĂ Nr Item Soluţie rezolvare IIa

tv

a∆∆=


b

bull Reprezentarea forţelor (rarr

1F rarr

2F rarrG

rarrN

rarr

rF )


rFFFaM minus+=sdot 21

Rezultat final NFr 450=

c tvd m ∆sdot=

smvv

v infinm 60

2=

+=

Rezultat final md 42=

d 2

11 30 smaaMFr minus=rArrsdotminus=

1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097


Nr Item Soluţie rezolvare IIa mgN =

Rezultat final NN 50= b maFF f =minus

NFf micro=

g

mF

a microminus=


c

tv

a∆∆=


d observaţia că forţa F trebuie să acţioneze sub un unghi α icircn sus αsinFGN minus= 0=N

FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen

b enunţ este valabilă pentru valori ale forţei deformatoare mai mici decacirct 20 N c ∆kF = cm6=siN= 05 ∆F Rezultat final Nm833ЎЦk d 00const === Rav rarrrarr

fe1x FFR += şi NGR +=y

1∆kF =e1 NF micro=f Rezultat final cm= 601∆

06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099


IIa MaMgT =minusminus micro maTmg =+minus

gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1

Rezultat final NT 84= c ( )aMmMgmg prime+=minus micro

gmMMm

a+

minus=prime micro

Rezultat final 282 sma =prime

d aMMg primeprime=minusmicro Rezultat final 22 smga minus=minus=primeprime micro


Varianta 100


Nr Item Soluţie rezolvare IIa maFG ft =minus

nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆

Rezultat final st 2=∆ c τav =

2

2mvEc =

Rezultat final JEc 150=

d αmicro tg=


e_f_mecanica_bii_001





































































































Varianta 002


II a ct FG = αmicroα cossin mgmg = microα arctg= Rezultat final 030=α b dFL cf sdotminus= Rezultat final JLf 4minus=

c reprezentarea corectă a forţei de tracţiune greutăţii forţei de frecare reacţiunii planului d maFGF ct =minusminus ( )αsin2gamF += Rezultat final NF 26=


Varianta 003




Varianta 004



gmTam 11 minus=

g

mm

mma

12

12

+minus

=

Rezultat final 2

310

sma =

c

gmm

mmT

21

212

+=





IIa

t

va

∆∆=




de frecare c


amGFNF f =+++

mamgF =minus micro


11 tg

v

∆=micro



Varianta 006


IIa gmG AA =

Rezultat final kgg

Gm A

A 30==


=minus=minus

0sin

0

αA

B

GT

Tgm

Rezultat final kg

gG

m AB 150sin == α






F

F12sin =α




Varianta 008



sintG G ϕ= sdot

tgmicro ϕ=

Rezultat final 3

3micro =


sinG

Fα =

Rezultat final

2sin

3α =

d



(cos sin )Fa g

m


Rezultat final

2577

ma

s=






Varianta 010





Varianta 011


Rezultat final )(

gm


d

Rezultat final 2

872s

ma =

e tav ∆=

Rezultat final sm

v 745=


Varianta 012






Varianta 013



fF N= micro

4 kN025

16 kNmicro = =







Varianta 015





αsin22 FF y =


yFGN 2minus=


2FG =



Varianta 016






Varianta 017



1 2G G Mg= =

3G mg=

Rezultat final

1 2

3

2

0 2

G G N

G N

= ==

c Ma Mg f T

Ma T Mg

ma mg f


2

mga

m M=

+

Rezultat final

2048

ma

s

d 2

2

mMf g

m M=

+


2

M M mT g

M m

+=

+



Varianta 018



21

12

mm

mmga

+minus

=


Tgm

gmT

m

m

minusminus

=2

1

2

1

( )Tmmgmm 21212 +=

gmm

mmT sdot

+=

21

212






Varianta 020



=minus+=minus

0sin

cos

mgFN

maFF f

αα



+= gamF

NF 556=


αsinmg

F ge



Rezultat final 2

317310coss

mtgg

mF

a cong===α

α


Varianta 021





amgmTAC 33 =minus

321

132

mmm

mmmga

++minusminus

=micro


d 0=a

1

32

m

mm minus=micro



Varianta 022


IIa

tva ∆

∆=


d vvv crel minus=

TL

vrel =

relvL

T =


vvL

Tc +

=1



Varianta 023




Varianta 024


IIa G mg=


0

0

cosl

l lα =

+ ∆

0

11

cos

l

l α∆ = minus

Rezultat final

0

1l

l

∆ =


eF k l= ∆


e

x

y

f e

e

f

F F

N mg F

F Nmicro

=

= minus

=

sin

cosx

y

e e

e e

F F

F F

αα

= sdot

= sdot

x

y

e

e

F

G Fmicro =

minus



Varianta 025


lF

k∆

=

Rezultat final

mN

k 540=



Varianta 026



mmgF

aminus=


c amgmT =minus



Varianta 027








d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 003




Varianta 004



gmTam 11 minus=

g

mm

mma

12

12

+minus

=

Rezultat final 2

310

sma =

c

gmm

mmT

21

212

+=





IIa

t

va

∆∆=




de frecare c


amGFNF f =+++

mamgF =minus micro


11 tg

v

∆=micro



Varianta 006


IIa gmG AA =

Rezultat final kgg

Gm A

A 30==


=minus=minus

0sin

0

αA

B

GT

Tgm

Rezultat final kg

gG

m AB 150sin == α






F

F12sin =α




Varianta 008



sintG G ϕ= sdot

tgmicro ϕ=

Rezultat final 3

3micro =


sinG

Fα =

Rezultat final

2sin

3α =

d



(cos sin )Fa g

m


Rezultat final

2577

ma

s=






Varianta 010





Varianta 011


Rezultat final )(

gm


d

Rezultat final 2

872s

ma =

e tav ∆=

Rezultat final sm

v 745=


Varianta 012






Varianta 013



fF N= micro

4 kN025

16 kNmicro = =







Varianta 015





αsin22 FF y =


yFGN 2minus=


2FG =



Varianta 016






Varianta 017



1 2G G Mg= =

3G mg=

Rezultat final

1 2

3

2

0 2

G G N

G N

= ==

c Ma Mg f T

Ma T Mg

ma mg f


2

mga

m M=

+

Rezultat final

2048

ma

s

d 2

2

mMf g

m M=

+


2

M M mT g

M m

+=

+



Varianta 018



21

12

mm

mmga

+minus

=


Tgm

gmT

m

m

minusminus

=2

1

2

1

( )Tmmgmm 21212 +=

gmm

mmT sdot

+=

21

212






Varianta 020



=minus+=minus

0sin

cos

mgFN

maFF f

αα



+= gamF

NF 556=


αsinmg

F ge



Rezultat final 2

317310coss

mtgg

mF

a cong===α

α


Varianta 021





amgmTAC 33 =minus

321

132

mmm

mmmga

++minusminus

=micro


d 0=a

1

32

m

mm minus=micro



Varianta 022


IIa

tva ∆

∆=


d vvv crel minus=

TL

vrel =

relvL

T =


vvL

Tc +

=1



Varianta 023




Varianta 024


IIa G mg=


0

0

cosl

l lα =

+ ∆

0

11

cos

l

l α∆ = minus

Rezultat final

0

1l

l

∆ =


eF k l= ∆


e

x

y

f e

e

f

F F

N mg F

F Nmicro

=

= minus

=

sin

cosx

y

e e

e e

F F

F F

αα

= sdot

= sdot

x

y

e

e

F

G Fmicro =

minus



Varianta 025


lF

k∆

=

Rezultat final

mN

k 540=



Varianta 026



mmgF

aminus=


c amgmT =minus



Varianta 027








d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 004



gmTam 11 minus=

g

mm

mma

12

12

+minus

=

Rezultat final 2

310

sma =

c

gmm

mmT

21

212

+=





IIa

t

va

∆∆=




de frecare c


amGFNF f =+++

mamgF =minus micro


11 tg

v

∆=micro



Varianta 006


IIa gmG AA =

Rezultat final kgg

Gm A

A 30==


=minus=minus

0sin

0

αA

B

GT

Tgm

Rezultat final kg

gG

m AB 150sin == α






F

F12sin =α




Varianta 008



sintG G ϕ= sdot

tgmicro ϕ=

Rezultat final 3

3micro =


sinG

Fα =

Rezultat final

2sin

3α =

d



(cos sin )Fa g

m


Rezultat final

2577

ma

s=






Varianta 010





Varianta 011


Rezultat final )(

gm


d

Rezultat final 2

872s

ma =

e tav ∆=

Rezultat final sm

v 745=


Varianta 012






Varianta 013



fF N= micro

4 kN025

16 kNmicro = =







Varianta 015





αsin22 FF y =


yFGN 2minus=


2FG =



Varianta 016






Varianta 017



1 2G G Mg= =

3G mg=

Rezultat final

1 2

3

2

0 2

G G N

G N

= ==

c Ma Mg f T

Ma T Mg

ma mg f


2

mga

m M=

+

Rezultat final

2048

ma

s

d 2

2

mMf g

m M=

+


2

M M mT g

M m

+=

+



Varianta 018



21

12

mm

mmga

+minus

=


Tgm

gmT

m

m

minusminus

=2

1

2

1

( )Tmmgmm 21212 +=

gmm

mmT sdot

+=

21

212






Varianta 020



=minus+=minus

0sin

cos

mgFN

maFF f

αα



+= gamF

NF 556=


αsinmg

F ge



Rezultat final 2

317310coss

mtgg

mF

a cong===α

α


Varianta 021





amgmTAC 33 =minus

321

132

mmm

mmmga

++minusminus

=micro


d 0=a

1

32

m

mm minus=micro



Varianta 022


IIa

tva ∆

∆=


d vvv crel minus=

TL

vrel =

relvL

T =


vvL

Tc +

=1



Varianta 023




Varianta 024


IIa G mg=


0

0

cosl

l lα =

+ ∆

0

11

cos

l

l α∆ = minus

Rezultat final

0

1l

l

∆ =


eF k l= ∆


e

x

y

f e

e

f

F F

N mg F

F Nmicro

=

= minus

=

sin

cosx

y

e e

e e

F F

F F

αα

= sdot

= sdot

x

y

e

e

F

G Fmicro =

minus



Varianta 025


lF

k∆

=

Rezultat final

mN

k 540=



Varianta 026



mmgF

aminus=


c amgmT =minus



Varianta 027








d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=








































































































IIa

t

va

∆∆=




de frecare c


amGFNF f =+++

mamgF =minus micro


11 tg

v

∆=micro



Varianta 006


IIa gmG AA =

Rezultat final kgg

Gm A

A 30==


=minus=minus

0sin

0

αA

B

GT

Tgm

Rezultat final kg

gG

m AB 150sin == α






F

F12sin =α




Varianta 008



sintG G ϕ= sdot

tgmicro ϕ=

Rezultat final 3

3micro =


sinG

Fα =

Rezultat final

2sin

3α =

d



(cos sin )Fa g

m


Rezultat final

2577

ma

s=






Varianta 010





Varianta 011


Rezultat final )(

gm


d

Rezultat final 2

872s

ma =

e tav ∆=

Rezultat final sm

v 745=


Varianta 012






Varianta 013



fF N= micro

4 kN025

16 kNmicro = =







Varianta 015





αsin22 FF y =


yFGN 2minus=


2FG =



Varianta 016






Varianta 017



1 2G G Mg= =

3G mg=

Rezultat final

1 2

3

2

0 2

G G N

G N

= ==

c Ma Mg f T

Ma T Mg

ma mg f


2

mga

m M=

+

Rezultat final

2048

ma

s

d 2

2

mMf g

m M=

+


2

M M mT g

M m

+=

+



Varianta 018



21

12

mm

mmga

+minus

=


Tgm

gmT

m

m

minusminus

=2

1

2

1

( )Tmmgmm 21212 +=

gmm

mmT sdot

+=

21

212






Varianta 020



=minus+=minus

0sin

cos

mgFN

maFF f

αα



+= gamF

NF 556=


αsinmg

F ge



Rezultat final 2

317310coss

mtgg

mF

a cong===α

α


Varianta 021





amgmTAC 33 =minus

321

132

mmm

mmmga

++minusminus

=micro


d 0=a

1

32

m

mm minus=micro



Varianta 022


IIa

tva ∆

∆=


d vvv crel minus=

TL

vrel =

relvL

T =


vvL

Tc +

=1



Varianta 023




Varianta 024


IIa G mg=


0

0

cosl

l lα =

+ ∆

0

11

cos

l

l α∆ = minus

Rezultat final

0

1l

l

∆ =


eF k l= ∆


e

x

y

f e

e

f

F F

N mg F

F Nmicro

=

= minus

=

sin

cosx

y

e e

e e

F F

F F

αα

= sdot

= sdot

x

y

e

e

F

G Fmicro =

minus



Varianta 025


lF

k∆

=

Rezultat final

mN

k 540=



Varianta 026



mmgF

aminus=


c amgmT =minus



Varianta 027








d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 006


IIa gmG AA =

Rezultat final kgg

Gm A

A 30==


=minus=minus

0sin

0

αA

B

GT

Tgm

Rezultat final kg

gG

m AB 150sin == α






F

F12sin =α




Varianta 008



sintG G ϕ= sdot

tgmicro ϕ=

Rezultat final 3

3micro =


sinG

Fα =

Rezultat final

2sin

3α =

d



(cos sin )Fa g

m


Rezultat final

2577

ma

s=






Varianta 010





Varianta 011


Rezultat final )(

gm


d

Rezultat final 2

872s

ma =

e tav ∆=

Rezultat final sm

v 745=


Varianta 012






Varianta 013



fF N= micro

4 kN025

16 kNmicro = =







Varianta 015





αsin22 FF y =


yFGN 2minus=


2FG =



Varianta 016






Varianta 017



1 2G G Mg= =

3G mg=

Rezultat final

1 2

3

2

0 2

G G N

G N

= ==

c Ma Mg f T

Ma T Mg

ma mg f


2

mga

m M=

+

Rezultat final

2048

ma

s

d 2

2

mMf g

m M=

+


2

M M mT g

M m

+=

+



Varianta 018



21

12

mm

mmga

+minus

=


Tgm

gmT

m

m

minusminus

=2

1

2

1

( )Tmmgmm 21212 +=

gmm

mmT sdot

+=

21

212






Varianta 020



=minus+=minus

0sin

cos

mgFN

maFF f

αα



+= gamF

NF 556=


αsinmg

F ge



Rezultat final 2

317310coss

mtgg

mF

a cong===α

α


Varianta 021





amgmTAC 33 =minus

321

132

mmm

mmmga

++minusminus

=micro


d 0=a

1

32

m

mm minus=micro



Varianta 022


IIa

tva ∆

∆=


d vvv crel minus=

TL

vrel =

relvL

T =


vvL

Tc +

=1



Varianta 023




Varianta 024


IIa G mg=


0

0

cosl

l lα =

+ ∆

0

11

cos

l

l α∆ = minus

Rezultat final

0

1l

l

∆ =


eF k l= ∆


e

x

y

f e

e

f

F F

N mg F

F Nmicro

=

= minus

=

sin

cosx

y

e e

e e

F F

F F

αα

= sdot

= sdot

x

y

e

e

F

G Fmicro =

minus



Varianta 025


lF

k∆

=

Rezultat final

mN

k 540=



Varianta 026



mmgF

aminus=


c amgmT =minus



Varianta 027








d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=









































































































F

F12sin =α




Varianta 008



sintG G ϕ= sdot

tgmicro ϕ=

Rezultat final 3

3micro =


sinG

Fα =

Rezultat final

2sin

3α =

d



(cos sin )Fa g

m


Rezultat final

2577

ma

s=






Varianta 010





Varianta 011


Rezultat final )(

gm


d

Rezultat final 2

872s

ma =

e tav ∆=

Rezultat final sm

v 745=


Varianta 012






Varianta 013



fF N= micro

4 kN025

16 kNmicro = =







Varianta 015





αsin22 FF y =


yFGN 2minus=


2FG =



Varianta 016






Varianta 017



1 2G G Mg= =

3G mg=

Rezultat final

1 2

3

2

0 2

G G N

G N

= ==

c Ma Mg f T

Ma T Mg

ma mg f


2

mga

m M=

+

Rezultat final

2048

ma

s

d 2

2

mMf g

m M=

+


2

M M mT g

M m

+=

+



Varianta 018



21

12

mm

mmga

+minus

=


Tgm

gmT

m

m

minusminus

=2

1

2

1

( )Tmmgmm 21212 +=

gmm

mmT sdot

+=

21

212






Varianta 020



=minus+=minus

0sin

cos

mgFN

maFF f

αα



+= gamF

NF 556=


αsinmg

F ge



Rezultat final 2

317310coss

mtgg

mF

a cong===α

α


Varianta 021





amgmTAC 33 =minus

321

132

mmm

mmmga

++minusminus

=micro


d 0=a

1

32

m

mm minus=micro



Varianta 022


IIa

tva ∆

∆=


d vvv crel minus=

TL

vrel =

relvL

T =


vvL

Tc +

=1



Varianta 023




Varianta 024


IIa G mg=


0

0

cosl

l lα =

+ ∆

0

11

cos

l

l α∆ = minus

Rezultat final

0

1l

l

∆ =


eF k l= ∆


e

x

y

f e

e

f

F F

N mg F

F Nmicro

=

= minus

=

sin

cosx

y

e e

e e

F F

F F

αα

= sdot

= sdot

x

y

e

e

F

G Fmicro =

minus



Varianta 025


lF

k∆

=

Rezultat final

mN

k 540=



Varianta 026



mmgF

aminus=


c amgmT =minus



Varianta 027








d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 008



sintG G ϕ= sdot

tgmicro ϕ=

Rezultat final 3

3micro =


sinG

Fα =

Rezultat final

2sin

3α =

d



(cos sin )Fa g

m


Rezultat final

2577

ma

s=






Varianta 010





Varianta 011


Rezultat final )(

gm


d

Rezultat final 2

872s

ma =

e tav ∆=

Rezultat final sm

v 745=


Varianta 012






Varianta 013



fF N= micro

4 kN025

16 kNmicro = =







Varianta 015





αsin22 FF y =


yFGN 2minus=


2FG =



Varianta 016






Varianta 017



1 2G G Mg= =

3G mg=

Rezultat final

1 2

3

2

0 2

G G N

G N

= ==

c Ma Mg f T

Ma T Mg

ma mg f


2

mga

m M=

+

Rezultat final

2048

ma

s

d 2

2

mMf g

m M=

+


2

M M mT g

M m

+=

+



Varianta 018



21

12

mm

mmga

+minus

=


Tgm

gmT

m

m

minusminus

=2

1

2

1

( )Tmmgmm 21212 +=

gmm

mmT sdot

+=

21

212






Varianta 020



=minus+=minus

0sin

cos

mgFN

maFF f

αα



+= gamF

NF 556=


αsinmg

F ge



Rezultat final 2

317310coss

mtgg

mF

a cong===α

α


Varianta 021





amgmTAC 33 =minus

321

132

mmm

mmmga

++minusminus

=micro


d 0=a

1

32

m

mm minus=micro



Varianta 022


IIa

tva ∆

∆=


d vvv crel minus=

TL

vrel =

relvL

T =


vvL

Tc +

=1



Varianta 023




Varianta 024


IIa G mg=


0

0

cosl

l lα =

+ ∆

0

11

cos

l

l α∆ = minus

Rezultat final

0

1l

l

∆ =


eF k l= ∆


e

x

y

f e

e

f

F F

N mg F

F Nmicro

=

= minus

=

sin

cosx

y

e e

e e

F F

F F

αα

= sdot

= sdot

x

y

e

e

F

G Fmicro =

minus



Varianta 025


lF

k∆

=

Rezultat final

mN

k 540=



Varianta 026



mmgF

aminus=


c amgmT =minus



Varianta 027








d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=











































































































Varianta 010





Varianta 011


Rezultat final )(

gm


d

Rezultat final 2

872s

ma =

e tav ∆=

Rezultat final sm

v 745=


Varianta 012






Varianta 013



fF N= micro

4 kN025

16 kNmicro = =







Varianta 015





αsin22 FF y =


yFGN 2minus=


2FG =



Varianta 016






Varianta 017



1 2G G Mg= =

3G mg=

Rezultat final

1 2

3

2

0 2

G G N

G N

= ==

c Ma Mg f T

Ma T Mg

ma mg f


2

mga

m M=

+

Rezultat final

2048

ma

s

d 2

2

mMf g

m M=

+


2

M M mT g

M m

+=

+



Varianta 018



21

12

mm

mmga

+minus

=


Tgm

gmT

m

m

minusminus

=2

1

2

1

( )Tmmgmm 21212 +=

gmm

mmT sdot

+=

21

212






Varianta 020



=minus+=minus

0sin

cos

mgFN

maFF f

αα



+= gamF

NF 556=


αsinmg

F ge



Rezultat final 2

317310coss

mtgg

mF

a cong===α

α


Varianta 021





amgmTAC 33 =minus

321

132

mmm

mmmga

++minusminus

=micro


d 0=a

1

32

m

mm minus=micro



Varianta 022


IIa

tva ∆

∆=


d vvv crel minus=

TL

vrel =

relvL

T =


vvL

Tc +

=1



Varianta 023




Varianta 024


IIa G mg=


0

0

cosl

l lα =

+ ∆

0

11

cos

l

l α∆ = minus

Rezultat final

0

1l

l

∆ =


eF k l= ∆


e

x

y

f e

e

f

F F

N mg F

F Nmicro

=

= minus

=

sin

cosx

y

e e

e e

F F

F F

αα

= sdot

= sdot

x

y

e

e

F

G Fmicro =

minus



Varianta 025


lF

k∆

=

Rezultat final

mN

k 540=



Varianta 026



mmgF

aminus=


c amgmT =minus



Varianta 027








d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 011


Rezultat final )(

gm


d

Rezultat final 2

872s

ma =

e tav ∆=

Rezultat final sm

v 745=


Varianta 012






Varianta 013



fF N= micro

4 kN025

16 kNmicro = =







Varianta 015





αsin22 FF y =


yFGN 2minus=


2FG =



Varianta 016






Varianta 017



1 2G G Mg= =

3G mg=

Rezultat final

1 2

3

2

0 2

G G N

G N

= ==

c Ma Mg f T

Ma T Mg

ma mg f


2

mga

m M=

+

Rezultat final

2048

ma

s

d 2

2

mMf g

m M=

+


2

M M mT g

M m

+=

+



Varianta 018



21

12

mm

mmga

+minus

=


Tgm

gmT

m

m

minusminus

=2

1

2

1

( )Tmmgmm 21212 +=

gmm

mmT sdot

+=

21

212






Varianta 020



=minus+=minus

0sin

cos

mgFN

maFF f

αα



+= gamF

NF 556=


αsinmg

F ge



Rezultat final 2

317310coss

mtgg

mF

a cong===α

α


Varianta 021





amgmTAC 33 =minus

321

132

mmm

mmmga

++minusminus

=micro


d 0=a

1

32

m

mm minus=micro



Varianta 022


IIa

tva ∆

∆=


d vvv crel minus=

TL

vrel =

relvL

T =


vvL

Tc +

=1



Varianta 023




Varianta 024


IIa G mg=


0

0

cosl

l lα =

+ ∆

0

11

cos

l

l α∆ = minus

Rezultat final

0

1l

l

∆ =


eF k l= ∆


e

x

y

f e

e

f

F F

N mg F

F Nmicro

=

= minus

=

sin

cosx

y

e e

e e

F F

F F

αα

= sdot

= sdot

x

y

e

e

F

G Fmicro =

minus



Varianta 025


lF

k∆

=

Rezultat final

mN

k 540=



Varianta 026



mmgF

aminus=


c amgmT =minus



Varianta 027








d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 012






Varianta 013



fF N= micro

4 kN025

16 kNmicro = =







Varianta 015





αsin22 FF y =


yFGN 2minus=


2FG =



Varianta 016






Varianta 017



1 2G G Mg= =

3G mg=

Rezultat final

1 2

3

2

0 2

G G N

G N

= ==

c Ma Mg f T

Ma T Mg

ma mg f


2

mga

m M=

+

Rezultat final

2048

ma

s

d 2

2

mMf g

m M=

+


2

M M mT g

M m

+=

+



Varianta 018



21

12

mm

mmga

+minus

=


Tgm

gmT

m

m

minusminus

=2

1

2

1

( )Tmmgmm 21212 +=

gmm

mmT sdot

+=

21

212






Varianta 020



=minus+=minus

0sin

cos

mgFN

maFF f

αα



+= gamF

NF 556=


αsinmg

F ge



Rezultat final 2

317310coss

mtgg

mF

a cong===α

α


Varianta 021





amgmTAC 33 =minus

321

132

mmm

mmmga

++minusminus

=micro


d 0=a

1

32

m

mm minus=micro



Varianta 022


IIa

tva ∆

∆=


d vvv crel minus=

TL

vrel =

relvL

T =


vvL

Tc +

=1



Varianta 023




Varianta 024


IIa G mg=


0

0

cosl

l lα =

+ ∆

0

11

cos

l

l α∆ = minus

Rezultat final

0

1l

l

∆ =


eF k l= ∆


e

x

y

f e

e

f

F F

N mg F

F Nmicro

=

= minus

=

sin

cosx

y

e e

e e

F F

F F

αα

= sdot

= sdot

x

y

e

e

F

G Fmicro =

minus



Varianta 025


lF

k∆

=

Rezultat final

mN

k 540=



Varianta 026



mmgF

aminus=


c amgmT =minus



Varianta 027








d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 013



fF N= micro

4 kN025

16 kNmicro = =







Varianta 015





αsin22 FF y =


yFGN 2minus=


2FG =



Varianta 016






Varianta 017



1 2G G Mg= =

3G mg=

Rezultat final

1 2

3

2

0 2

G G N

G N

= ==

c Ma Mg f T

Ma T Mg

ma mg f


2

mga

m M=

+

Rezultat final

2048

ma

s

d 2

2

mMf g

m M=

+


2

M M mT g

M m

+=

+



Varianta 018



21

12

mm

mmga

+minus

=


Tgm

gmT

m

m

minusminus

=2

1

2

1

( )Tmmgmm 21212 +=

gmm

mmT sdot

+=

21

212






Varianta 020



=minus+=minus

0sin

cos

mgFN

maFF f

αα



+= gamF

NF 556=


αsinmg

F ge



Rezultat final 2

317310coss

mtgg

mF

a cong===α

α


Varianta 021





amgmTAC 33 =minus

321

132

mmm

mmmga

++minusminus

=micro


d 0=a

1

32

m

mm minus=micro



Varianta 022


IIa

tva ∆

∆=


d vvv crel minus=

TL

vrel =

relvL

T =


vvL

Tc +

=1



Varianta 023




Varianta 024


IIa G mg=


0

0

cosl

l lα =

+ ∆

0

11

cos

l

l α∆ = minus

Rezultat final

0

1l

l

∆ =


eF k l= ∆


e

x

y

f e

e

f

F F

N mg F

F Nmicro

=

= minus

=

sin

cosx

y

e e

e e

F F

F F

αα

= sdot

= sdot

x

y

e

e

F

G Fmicro =

minus



Varianta 025


lF

k∆

=

Rezultat final

mN

k 540=



Varianta 026



mmgF

aminus=


c amgmT =minus



Varianta 027








d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=











































































































Varianta 015





αsin22 FF y =


yFGN 2minus=


2FG =



Varianta 016






Varianta 017



1 2G G Mg= =

3G mg=

Rezultat final

1 2

3

2

0 2

G G N

G N

= ==

c Ma Mg f T

Ma T Mg

ma mg f


2

mga

m M=

+

Rezultat final

2048

ma

s

d 2

2

mMf g

m M=

+


2

M M mT g

M m

+=

+



Varianta 018



21

12

mm

mmga

+minus

=


Tgm

gmT

m

m

minusminus

=2

1

2

1

( )Tmmgmm 21212 +=

gmm

mmT sdot

+=

21

212






Varianta 020



=minus+=minus

0sin

cos

mgFN

maFF f

αα



+= gamF

NF 556=


αsinmg

F ge



Rezultat final 2

317310coss

mtgg

mF

a cong===α

α


Varianta 021





amgmTAC 33 =minus

321

132

mmm

mmmga

++minusminus

=micro


d 0=a

1

32

m

mm minus=micro



Varianta 022


IIa

tva ∆

∆=


d vvv crel minus=

TL

vrel =

relvL

T =


vvL

Tc +

=1



Varianta 023




Varianta 024


IIa G mg=


0

0

cosl

l lα =

+ ∆

0

11

cos

l

l α∆ = minus

Rezultat final

0

1l

l

∆ =


eF k l= ∆


e

x

y

f e

e

f

F F

N mg F

F Nmicro

=

= minus

=

sin

cosx

y

e e

e e

F F

F F

αα

= sdot

= sdot

x

y

e

e

F

G Fmicro =

minus



Varianta 025


lF

k∆

=

Rezultat final

mN

k 540=



Varianta 026



mmgF

aminus=


c amgmT =minus



Varianta 027








d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 016






Varianta 017



1 2G G Mg= =

3G mg=

Rezultat final

1 2

3

2

0 2

G G N

G N

= ==

c Ma Mg f T

Ma T Mg

ma mg f


2

mga

m M=

+

Rezultat final

2048

ma

s

d 2

2

mMf g

m M=

+


2

M M mT g

M m

+=

+



Varianta 018



21

12

mm

mmga

+minus

=


Tgm

gmT

m

m

minusminus

=2

1

2

1

( )Tmmgmm 21212 +=

gmm

mmT sdot

+=

21

212






Varianta 020



=minus+=minus

0sin

cos

mgFN

maFF f

αα



+= gamF

NF 556=


αsinmg

F ge



Rezultat final 2

317310coss

mtgg

mF

a cong===α

α


Varianta 021





amgmTAC 33 =minus

321

132

mmm

mmmga

++minusminus

=micro


d 0=a

1

32

m

mm minus=micro



Varianta 022


IIa

tva ∆

∆=


d vvv crel minus=

TL

vrel =

relvL

T =


vvL

Tc +

=1



Varianta 023




Varianta 024


IIa G mg=


0

0

cosl

l lα =

+ ∆

0

11

cos

l

l α∆ = minus

Rezultat final

0

1l

l

∆ =


eF k l= ∆


e

x

y

f e

e

f

F F

N mg F

F Nmicro

=

= minus

=

sin

cosx

y

e e

e e

F F

F F

αα

= sdot

= sdot

x

y

e

e

F

G Fmicro =

minus



Varianta 025


lF

k∆

=

Rezultat final

mN

k 540=



Varianta 026



mmgF

aminus=


c amgmT =minus



Varianta 027








d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 017



1 2G G Mg= =

3G mg=

Rezultat final

1 2

3

2

0 2

G G N

G N

= ==

c Ma Mg f T

Ma T Mg

ma mg f


2

mga

m M=

+

Rezultat final

2048

ma

s

d 2

2

mMf g

m M=

+


2

M M mT g

M m

+=

+



Varianta 018



21

12

mm

mmga

+minus

=


Tgm

gmT

m

m

minusminus

=2

1

2

1

( )Tmmgmm 21212 +=

gmm

mmT sdot

+=

21

212






Varianta 020



=minus+=minus

0sin

cos

mgFN

maFF f

αα



+= gamF

NF 556=


αsinmg

F ge



Rezultat final 2

317310coss

mtgg

mF

a cong===α

α


Varianta 021





amgmTAC 33 =minus

321

132

mmm

mmmga

++minusminus

=micro


d 0=a

1

32

m

mm minus=micro



Varianta 022


IIa

tva ∆

∆=


d vvv crel minus=

TL

vrel =

relvL

T =


vvL

Tc +

=1



Varianta 023




Varianta 024


IIa G mg=


0

0

cosl

l lα =

+ ∆

0

11

cos

l

l α∆ = minus

Rezultat final

0

1l

l

∆ =


eF k l= ∆


e

x

y

f e

e

f

F F

N mg F

F Nmicro

=

= minus

=

sin

cosx

y

e e

e e

F F

F F

αα

= sdot

= sdot

x

y

e

e

F

G Fmicro =

minus



Varianta 025


lF

k∆

=

Rezultat final

mN

k 540=



Varianta 026



mmgF

aminus=


c amgmT =minus



Varianta 027








d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 018



21

12

mm

mmga

+minus

=


Tgm

gmT

m

m

minusminus

=2

1

2

1

( )Tmmgmm 21212 +=

gmm

mmT sdot

+=

21

212






Varianta 020



=minus+=minus

0sin

cos

mgFN

maFF f

αα



+= gamF

NF 556=


αsinmg

F ge



Rezultat final 2

317310coss

mtgg

mF

a cong===α

α


Varianta 021





amgmTAC 33 =minus

321

132

mmm

mmmga

++minusminus

=micro


d 0=a

1

32

m

mm minus=micro



Varianta 022


IIa

tva ∆

∆=


d vvv crel minus=

TL

vrel =

relvL

T =


vvL

Tc +

=1



Varianta 023




Varianta 024


IIa G mg=


0

0

cosl

l lα =

+ ∆

0

11

cos

l

l α∆ = minus

Rezultat final

0

1l

l

∆ =


eF k l= ∆


e

x

y

f e

e

f

F F

N mg F

F Nmicro

=

= minus

=

sin

cosx

y

e e

e e

F F

F F

αα

= sdot

= sdot

x

y

e

e

F

G Fmicro =

minus



Varianta 025


lF

k∆

=

Rezultat final

mN

k 540=



Varianta 026



mmgF

aminus=


c amgmT =minus



Varianta 027








d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=










































































































Varianta 020



=minus+=minus

0sin

cos

mgFN

maFF f

αα



+= gamF

NF 556=


αsinmg

F ge



Rezultat final 2

317310coss

mtgg

mF

a cong===α

α


Varianta 021





amgmTAC 33 =minus

321

132

mmm

mmmga

++minusminus

=micro


d 0=a

1

32

m

mm minus=micro



Varianta 022


IIa

tva ∆

∆=


d vvv crel minus=

TL

vrel =

relvL

T =


vvL

Tc +

=1



Varianta 023




Varianta 024


IIa G mg=


0

0

cosl

l lα =

+ ∆

0

11

cos

l

l α∆ = minus

Rezultat final

0

1l

l

∆ =


eF k l= ∆


e

x

y

f e

e

f

F F

N mg F

F Nmicro

=

= minus

=

sin

cosx

y

e e

e e

F F

F F

αα

= sdot

= sdot

x

y

e

e

F

G Fmicro =

minus



Varianta 025


lF

k∆

=

Rezultat final

mN

k 540=



Varianta 026



mmgF

aminus=


c amgmT =minus



Varianta 027








d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 021





amgmTAC 33 =minus

321

132

mmm

mmmga

++minusminus

=micro


d 0=a

1

32

m

mm minus=micro



Varianta 022


IIa

tva ∆

∆=


d vvv crel minus=

TL

vrel =

relvL

T =


vvL

Tc +

=1



Varianta 023




Varianta 024


IIa G mg=


0

0

cosl

l lα =

+ ∆

0

11

cos

l

l α∆ = minus

Rezultat final

0

1l

l

∆ =


eF k l= ∆


e

x

y

f e

e

f

F F

N mg F

F Nmicro

=

= minus

=

sin

cosx

y

e e

e e

F F

F F

αα

= sdot

= sdot

x

y

e

e

F

G Fmicro =

minus



Varianta 025


lF

k∆

=

Rezultat final

mN

k 540=



Varianta 026



mmgF

aminus=


c amgmT =minus



Varianta 027








d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 022


IIa

tva ∆

∆=


d vvv crel minus=

TL

vrel =

relvL

T =


vvL

Tc +

=1



Varianta 023




Varianta 024


IIa G mg=


0

0

cosl

l lα =

+ ∆

0

11

cos

l

l α∆ = minus

Rezultat final

0

1l

l

∆ =


eF k l= ∆


e

x

y

f e

e

f

F F

N mg F

F Nmicro

=

= minus

=

sin

cosx

y

e e

e e

F F

F F

αα

= sdot

= sdot

x

y

e

e

F

G Fmicro =

minus



Varianta 025


lF

k∆

=

Rezultat final

mN

k 540=



Varianta 026



mmgF

aminus=


c amgmT =minus



Varianta 027








d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 023




Varianta 024


IIa G mg=


0

0

cosl

l lα =

+ ∆

0

11

cos

l

l α∆ = minus

Rezultat final

0

1l

l

∆ =


eF k l= ∆


e

x

y

f e

e

f

F F

N mg F

F Nmicro

=

= minus

=

sin

cosx

y

e e

e e

F F

F F

αα

= sdot

= sdot

x

y

e

e

F

G Fmicro =

minus



Varianta 025


lF

k∆

=

Rezultat final

mN

k 540=



Varianta 026



mmgF

aminus=


c amgmT =minus



Varianta 027








d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 024


IIa G mg=


0

0

cosl

l lα =

+ ∆

0

11

cos

l

l α∆ = minus

Rezultat final

0

1l

l

∆ =


eF k l= ∆


e

x

y

f e

e

f

F F

N mg F

F Nmicro

=

= minus

=

sin

cosx

y

e e

e e

F F

F F

αα

= sdot

= sdot

x

y

e

e

F

G Fmicro =

minus



Varianta 025


lF

k∆

=

Rezultat final

mN

k 540=



Varianta 026



mmgF

aminus=


c amgmT =minus



Varianta 027








d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 025


lF

k∆

=

Rezultat final

mN

k 540=



Varianta 026



mmgF

aminus=


c amgmT =minus



Varianta 027








d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 026



mmgF

aminus=


c amgmT =minus



Varianta 027








d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 027








d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=










































































































d fBBCtBAB FTGT ++=

ABA TG =




Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 029



tv

a∆∆=



Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 030





Rezultat final 5803

1 cong=micro


Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 031


IIa G mg=

Rezultat final

1

2

1

3

G N

G N

==



1 2

1 2

m mk g

l l

+=minus

Rezultat final 20

Nk

m=

c

2 2 1 10

1 2

m l m ll

m m

+=+



Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 032







d


sincossincos


FgmgmF

N

Ff

Rezultat final

73=micro


Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 033



makvmg =minus

c

0vkmg sdot=

0vmgk =


d gmkva +minus=







d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=











































































































d FN = FFf micro=



Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 035



b amFNG f =++

=minus=minus

0n

ft

GN

maFG





Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 036



21

2211 coscos

mm

FFa

+minus

=αα


111 =minus= αFgmN

1

11 sinα

gmF =


d 0cos 1

1 =minusTF α

0cos 2

2 =minus αFT

2

1

1

2

cos

cos

αα

=F

F


2 =FF


Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 037






d maFF f =minus


mmgt

amicrominus+= 1010

unde st 10=










Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=














































































































Mm

Mgmga


Rezultat final 2

1s

ma =

d mamgT minus=

MmmMg

T+




Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 040





1 24 sma =

b 22



2 4 sma minus=

c

11

0t

va

∆minus=

22

0t

va

∆minus=


gvdop micro42=






Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=










































































































Rezultat final 22

83065

s

m

s

ma cong=





Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 042



1 M Nv v v= minus

1

km45

hv = sau

m125

s

b

2 M Pv v v= +

2

km135

hv = sau

m375

s


12D

tv

∆ =


45 kmNd =

45 kmPd =



Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 043



Rezultat final 202

1 =m

m


Rezultat final 2

484s

ma =


tv

a∆∆=

tx

v m ∆∆=

20 v

v m+=



Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 044






Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 045





Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 046





c GFN y =+

yFGN minus=


N

Ff=micro

Rezultat final

3

1=micro


1



Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 047



forţa rarr

1F


ft FGF +=2

αmicro cosmgFf =

αmicro tgFF

FF

12

12

+minus

=


c maFG ft =minus








b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=










































































































b NFf micro=


g

a

mg

F minus=primemicro




Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 049


IIa mgG = NG 1=


yF

k∆∆=



kmg

y =



kagm

y)( +=



Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 050


IIa amTgm 22 =minus

amgmT 11 =minus

21

12

mm

mmga

+minus

=




Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 051



NFr micro=




c mamgT =microminus

gm

Ta microminus=

Rezultat final

21

s

ma =

d 22

rFNR +=

21 micro+= mgR



Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 052




021 llkT minus=






Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 053



)( alh

gmFf minus=



c





Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 054


)(

)(

33

2

11

agmT

mgT

agmT

+==

+=

Rezultat final

kNT

kNT

kNT

84

5

15

3

2

1

===


sm

v 2=

d

2

0 1atv m

+=

Rezultat final sm

v m 1=

e Graficul )(tv





2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=










































































































2

gmT A=









ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=












































































































ABs tvd sdot=





Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 057



1 2 sma =

b 22 maF = 111 tav ∆=∆

2

22 t

va

∆∆

=


c

21

1v

v m =


d 111 tvx m ∆=∆ 222 tvx m ∆=∆

21

1v

v m =

221

2vv

v m+

=

2121 xxx ∆+∆=∆



Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 058






Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 059



22 GN =



++++=

+=

ff 2121

21 )(

NNFFFR

ammR




Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 060





d

23

21T

TT ==



g

Tm 1

1 =

g

Tmm

sdot==

23

21



Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 061


gmM

Fa minus

+=


tv

a∆∆=

av

t∆=∆


SF=σ

4

2dS

π=

2

4

d

F

πσ =





22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=









































































































22

2

sin

cos

αmicro

Fmg

F

minus=


211

121 sincos

sincosFF

αmicroααmicroα

++

=


22

11

2

1

sinsin

αα

FmgFmg

NN

minusminus=

Rezultat final 1112

1 congNN

d [ ])sin(cos





Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 063




315 smsma cong

minus=

b fpc LEE =∆+∆

ααmicro

sincos

2

2 hmgmgh

mv minus=minus

minus=

αmicro

tgghv 12




3150min cong

minus=



3150min cong

+=


Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 064


IIa gmFf 11

micro=


=


12 m

mm minus=

micro


21

121 mm

mmga

+minus

=micro

( )21

212 mm

mmga

+minus

=micro




Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 065








t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=









































































































t

vv

tv

a if

∆minus

=∆∆=









Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 067









e 1NFap = gmN 00 =



Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 068






d

GF3βtg =


e

33 ∆kFe = 2

32

3 FGFe +=







1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=











































































































1 asymp=micro


Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 070





Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 071



amgmT

amTgm

11

22

=minus=minus

micro

Rezultat final

21

12

mmmm

ga+minus= micro

d

Rezultat final 21

21 )1(mm

gmmT

++= micro

e

Rezultat final 2

5s

ma =


Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 072



125

0

== dtgα

135

sin20

2=

+=

d

dα şi 1312

cos20

2

0 =+

=d

α

cmd 1020

2 =minusminus=∆


c

ααmicrocos

sinTmg

Tminus

=


43

0

=prime+=prime dd

tgα ( ) 5

3sin

20

2=

+prime+

prime+=primedd

ddα şi ( ) 5

4cos

20

2

0 =+prime+

=primedd

α

( ) cmdd 3020



mNT


= microαsin



Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 073



tv

a∆∆=


b maFG ft =minus





Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 074



gmMN )( +=


d ff FF = NFf 30 =

e 1 NN micromicro =

m

mM )( 1 +=

micromicro



Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 075



















1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=



















































































































1




Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 077



Rezultat final cmk

gm31

1 ==∆


Rezultat final 2

21

21 2 smgmm

mma =

+minus

=

c

gmm

mmT

21

212

+=


Rezultat final Ngmm

mmR 84

4

21

21 =+

=


Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 078




NFGFR

aamR

+++=

=cu=

f11

111 0

ft1x1

x1 0

FGFR

R

--=

= şi

n1y1

y1 0

GNR

R

-=

=


αcosmgN =





Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 079



1

11 t

va

∆∆

=

21 50 sma =

[ ]min453isint 2

22 t

va

∆∆

=


b 0=minus ft FF

GFf 10

1=


2

2mvEc =



Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 080



b

tx

v∆∆=



tv

a∆∆=


d

2

2mvEc =


e

2106 vv

v med+

=







Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=











































































































Varianta 082





cossinsm

MmMgmg

a =+

+minus= αmicroα

c ( )

NMm

mMgT 21

cossin1 =+

++= αmicroα



Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 083



α

αmicrocos1

2

mm

tg minus=



)(2 agmT += 2

370

sma minus=




2 =


Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 084






222

22




Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 085




Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 086




b

tv

a∆∆=1

tav ∆= 11


c tvs m∆=

210

1vv

v+

=


FF

a

a

1

2 =

Rezultat final 51

1

2 =a

a










Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=















































































































Rezultat final 252

)(sm

MmMm

ga =+






Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 088


IIa m=C 4x m=C 2-y

b 2

A2AA += yxr


d

t

=DA

m ∆∆

rarrr

v



e desen Cv

O

B

C

D

x

y

Ar

r∆

Cv


Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 089



nGN =

NFf micro=



b maFG ft =minus



c totc LE =∆

αmicro cos

2

2

mgLmghmv minus=



d θmicro tg=



Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 090



gmm

mmT sdot

+sdotsdot=

21

21 cosα


gmm

ma sdot

+sdot=

21

1 sinα




Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 091



( )21

21mm

mmga +minussdot=


)mm(gmm4T2F

21

21+==



Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 092




Rezultat final

minus=Gkv

ga 1


Rezultat final mNs

vmg

k 1200

==

d

m

kvga 1

1 minus=

minus=

0

11 1

v

vga



Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 093



0 872 sma =







Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 094







Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 095



gmmm

ma

++=

21




Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 096



tv

a∆∆=


b


1F rarr

2F rarrG

rarrN

rarr

rF )




c tvd m ∆sdot=

smvv

v infinm 60

2=

+=


d 2


1

11

1

11 t

vv

t

va if

∆minus

=∆∆

= 01 =fv

Rezultat final s

a

vt i 4

1

11 =

minus=∆


Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 097




NFf micro=

g

mF

a microminus=


c

tv

a∆∆=



FG=αsin

Rezultat final

6πα =


Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 098


IIa desen




06

12

5 10 15 20 25 30

18

24

30

36

42 (cm)∆

F (N)

O


Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 099



gmMMm

a+

+minus= micro


b ( )

gmM

MmT

+minus= micro1


gmMMm

a+

minus=prime micro




Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=







































































































Varianta 100



nGN =

NFf micro=



b

tv

a∆∆=

av

t =∆


2

2mvEc =


d αmicro tg=






































































































Rezolvari fizica mecanica subiectul II

Documents

Transcript of Rezolvari fizica mecanica subiectul II