Energie Cinetique

 

DLDVIOD EOLD^ORTD  ― DLDVIOD PC^DL^ODHHD  

DZDVEOED O ; DLDVIOD EOLD^ORTD  EOLD^ORTD  Tl nosqud jcmciêld nd edltrd C dt nd rbycl r = 20em, b uld mbssd M = 2,5ai. Nbls uld prdmoêrd dxpïrodled, hd nosqud rcuhd sbls ihossdr sur ul phbl oleholï qu quoo gbot ul blihd = 50° bvde h‟jc h‟jc ro roz z c ltbhd. ltbhd. Hb vo v otdssd olotobhd lotobhd d dst st luhhd. 2° - Dxpromdr h‟ïldriod eolïtoqud tctbhd nu nosqud dl gcletocl nd hb votdssd nu edltrd nd irbvotï. irbvotï. 6° - Ubejblt qud hd trbvboh nds gcreds dxtïrodurds bpphoquïds bu nosqud sd rïnuot bu trbvboh nds gcreds gc reds nd pdsbltdur, pdsbltdur, ebheuhdr ebheuhdr h‟beeïhïrbtocl ‟beeïhïrbtocl nu edltrd nd irbv irbvootï. Cl prdlnrb i = 20m/s6 

UCHT^OCL  2° - Dldriod eolïtoqud tctbhd nu nosqud  nosqud   Vbppdh. Vbppdh.   Uo ul nosqud jcmciêld nd rbycl r rcuhd sbls ihossdr, hb votdssd v nu edltrd nd irbvotï irbvotï C dst hoïd à hb v otdssd bliuhb bliuhb ord Ѣ nu nosqud pbr hb rd rdhhbtocl v=VѢ  Pcur nïmcltrdr, cfsdrvcls qud bvde hds crodltbtocls olnoquïds sur hb goiurd, cl b ; 

h‟bfseossd  

dst ncle hoïd à h‟blihd κ nclt hd nosqud b tcurlï pbr ; pbr  ; x = r κ 

N‟cÿ dl nïrovblt pbr rbppcrt rbppcrt bu b u tdmps ; tdmps  ; v= r.

 

Ѣ

 

  Dldriod eolïtoqud nd trblsh Dldriod trblshbt btooc l ;

Dldriod eolïtoqud nd rctbtocl rctbtocl ;  ; 

dl nïsoilblt pbr K 0  hd mcmdlt m cmdlt n‟oldrtod n‟oldrtod nu nosqud pbr rbppcrt à C. c l sbot qud qud  ;  

n‟cÿ h‟ïldriod eolïtoqud nd rctbtocl ; rctbtocl  ; 

cu ecmmd  .  H‟ïldriod eolïtoqud tc H‟ïldrio tctbhd tbhd De   nu nosqud dst hb scmmd nd h‟ïldriod eolïtoqud dt nd h‟ïldriod eolïtoqud nd rctbtocl n‟cÿ ; n‟cÿ  ; 

6° - Beeïhïrbtocl nu edltrd nd irbvotï  irbvotï   Uduh hd pcons trbvbohhd 1 hd trbvboh nd hb pdsbltdur qubln hd edltrd sd nïphbed nd (pdlnblt hd tdmps t) dst ;

 

  Cl cftodlnrbot hd mëmd rïsuhtbt dl cfsdrvblt qud hd edltrd C ndsedln n‟uld nostbled nostbled ; 

n‟cÿ H‟ïldriod eolïtoqud à h‟olstblt t   dst ; eolïtoqud à h‟olstblt

, s o lc us lctc ls ^0   h‟ïldriod

t = 0, 0, cl sbo s bott qud hb vbro vbr obtocl n‟ïldriod e eoolïto lït oqud ; qud ;  

dst ïibhd bu trbvboh nds gc gcreds reds dxtïrodurds dxtïrodurds n‟cÿ n‟c ÿ ;

Dl nïrovblt pbr rbppcrt à t , cl cftodlt ;  

Cu ecmmd ;

Bpphoebt Bppho ebtooc l lumïroqud lumïroqud

; 

DZDVEOED OO O ―  Cl prdln i = 20 m.s-6 . H‟betocl nd h‟bor bolso qud tcus hds grcttdmdlts sclt lïihoidbfhds. Cl suppcsd qud hds gohs sclt oldxtdlsofhds dt nd mbssds lïihoidbfhds. lïiho idbfhds. Hds pbrt pbrtoods O, OO, OOO sclt olnïpdlnbltds.   Tl vchblt jcmciêld, nd rbycl V = 20 em, dst mcfohd butcur nd scl bxd mboltdlu goxd dt jcro jc rozc zcltbh ltbh..  Ucl mcmdlt n‟oldrtod pbr rbppcrt à edt bxd dst K = 7,:.20 ->  Ai.m6 . Uur hd vchblt s‟dlrcuhd ul goh nclt h‟uld nds dxtrïmotïs dst goxïd bu vchblt, h‟butrd scutodlt ul ecrps B nd mbssd mB = 200i. Hd systêmd ïtblt bfblncllï sbls votdssd olotobhd,

 

ïtunodr hb lbturd nu mcuvdmdlt nd B dt ebheuhdr h‟beeïhïrbtocl bliuhbord nu vchblt.  OO ― Cl goxd sur ed vc vc hblt uld pcuhod pcuhod ecbxo ec bxobhd, bhd, nd mbssd mbs sd lïiho lïihoidbf idbfhd, hd, nd rbyc rbycl l r = > em. Nbls hb icrid nd n d edttd pcuhod s‟dlrcuhd ul goh nclt h‟uld nds dxtrïmotïs dst goxïd à hb pcuhod, h‟butrd scutodlt ul ecrps F nd mbssd mF  = 600i. Hds gohs sc sclt lt dlrc dlrc uhïs uhïs dl d l sdls olvdrsd  sur hd vch vc hblt dt sur s ur hb hb pcuho pc uhod d.  Hd systêmd, systê md, olotobhdmdlt olotobhdmdlt bu rdpcs, rdpc s, dst bfblncllï à hu huo-mëmd o-mëmd..  2°- Ebheuhdr h‟beeïhïrbtocl bliuhbord nu systêmd vchbltvchblt pcuhod  

6°- Dtunodr hb lbturd nu mcuvdmdlt nd B. Ebheuhdr h‟dspbed pbrecuru pbr B bu fcut nd 2 sdeclnd nd mcuvdmdlt. 

5°- Dtunodr hb lbturd nu mcuvdmdlt nd F. Ebheuhdr h‟dspbed pbrecuru pbr F bu fcut nd 2sdeclnd nd mcuvdmdlt.  Hd ecrps B ihossd hd hcli nd hb hoild nd phus irblnd pdltd n‟ul phbl oleholï gbosblt bvde hd phbl jcrozcltbhd h‟blihd

. Hd goh bttbejï bu ecrps B

rdstd pbrbhh pbrbhhê hd à hb hb hoild nd nd phus phus irblnd pdltd. Hd systêmd, systê md, olo olott ob hdmdlt bu rdpcs, dst bfblncllï à huo-mëmd. 

 

2° - Ebheuhdr h‟beeïhïrbtocl bliuhbord nu systêm bliuhbord s ystêmd d vc vc hblt pc pcuho uhod. d.   6° - Dtunodr hb lbturd nu mcuvdmdlt nd B. Ebheuhdr h‟dspbed

pbrecuru pbrecuru

pbr

B

bu

fcut

nd

2s

nd

mcuvdmdlt. 

5° - B edt olstblt prïeos, hd goh hoblt hd ecrps B bu vchblt ebssd frusqudmdlt. Dtunodr hds mcuvdmdlts uhtïrodurs nds ecrps B dt F, dl suppcsblt qu‟ohs ld rdlecltrdlt pbs n‟cfstbehds dt qud hd ecrps ec rps B rdstd bu ec ltbet nu phbl.  

OOO - Hd ecrps B ihossd hd hcli nd hb hoild nd phus irblnd pdltd n‟ul phbl oleholï gbosblt bvde hd phbl jcrozcltbh h‟blihd

. Hd goh,

bttbejï bu ecrps B rdstd pbrbhhêhd à hb hoild nd phus irblnd pdltd. Cl nïtbejd hd ecrps F, h‟dxtrïmotï hofrd nu goh dst bttbejïd à ul rdsscrt dl jïhoed 1 à spords lcl  kcolto  kcol tovds vds nd mbssd lïih lïihooidbfhd. idbfhd. Ed rdsscrt rdsscrt dst goxï goxï dl U bu sch, rdstd vdr vdrto toebh ebh 1 sb hcliudur à vond dst h0   = 20 em dt oh s‟bhhclid nd 2em scus h‟betocl n‟uld gcred nd 2L. 

 

  2° - Ebheuhdr à h‟ïquohofrd hb hcliudur nu rdsscrt  6° - Hd ecrps B nïphbeï, à pbrtor nd sb pcsotocl n‟ïquohofrd nd 6em vdrs hd fbs, hd hc li nd hb hb hoild nd ph phus us irblnd irblnd pdltd, dst bfblncllï sbls votdssd votdssd olot olot ob hd. Cl suppcsd qud hds hds gohs rdstdlt tdlnus 1 ïtunodr hd mc uvdmdlt uvdmdlt nd B, prïeosdr prïeosdr h‟dxprdssocl nd h‟ïhclibtocl dl gcletocl nu tdmps. 

UCHT^OCL O -2°) H‟beeïh H‟beeïhïrbt ïrbtoc ocl l bliuhbo bliuhb ord nu n u vchblt ; vchblt  ;  . B dggdetud ul mcuvdmdlt rdetohoild ulogcrmïmdlt beeïhïrï  beeïhïrï   suovblt hb vdrtoebhd ndsedlnbltd nd ;

6°- B dggdetud ul mcuvdmdlt rdetohoild ulogcrmïmdlt beeïhïrï   suovblt hb vdrtoebhd vdrtoebh d ndsedlnbltd ndsed lnbltd nd ;  

H‟dspbed dst xB  = 0,4 m  5° - F dggdetud ul mcuvdmdlt rdetohoild ulogcrmïmdlt beeïhïrï suovblt hb vdrtoebhd vdrtoebh d bsedlnbltd bs edlnbltd nd

OO- 2°- Beeïhïrbto Beeïhïrbtocl cl bliuhbord bliuhbord ;  ; 

6° 5° - B dggdetud n‟bfcrn ul mcuvdmdlt rdetohoild ulogcrmïmdlt rdtbrnï ndpuos h‟olstblt nd rupturd suovblt hb hoild nd phus irblnd pdltd kusqu'à ed qud hb votdssd

s‟blluhd.

ndsedlnblt 2drd pjbsd ; 

Puos

ul

mcuvdmdlt

rdetohoild

ulogcrmïmdlt

beeïhïrï

 

  quo nurd nurd t td t d hhd hhd qud ;   -4 t6 +2,4 = 0 t = 0,5s 6êmd  pjbsd ; 

F dggdetud ul mcuv mc uvdmdlt dmdlt rdetoho rdetohoild ild ulogcrmïmdlt beeïhïrï beeïhïrï ndsedlnblt suovblt suovblt hb vdrtoebhd nd ;  

OOO- 2° -

6°- 

B dggdetud ul mcuvdmdlt rdetohoild ulogcrmïmdlt soluscãnbh. Uuovblt hb hoild nd phus irblnd pdltd ;  

DZDVEOED OOO Nbls tcut hd hd prcfhêmd prcfhêmd,, dl prdln i = 20 m.s m .s-6  dt cl lïihoid tcus hds grcttdmdlts. grc ttdmdlts. 

B ― 2° - Ndux pdtotds pdtotds fohhds, bssomohbfhds bssomohbfhds à nds pcolts mbtïro mbtï rod d hs, h‟uld B nd mbssd mbss d m2   = >m, h‟butrd  h‟butrd  F nd mbssd m6   = 5m, sclt phbeïds bux dxtrïmotïs n‟uld toid roiond ^ nd mbssd lïihoidbfhd mcfohd butcur n‟ul bxd jcrozcltbhd pdrpdlnoeuhbord à ^ dl C (goi .2)  

 

 

Goi2   CB = 6H, CF = H. Hd systêmd ïtblt dl ïquohofrd, cl h‟ïebrtd nbls ul sdls ejcoso ejc oso ecmmd ecmm d pcsotog, n‟ul n‟u l pdtot blihd bli hd olotobhd à

dt c l h‟bfblnclld h‟bfblnclld   sbls votdssd votdss d

t = 0.  

b) Dtbfhor h‟ïqubtocl noggïrdltodhhd rïiossblt hd mcuvdmdlt nu systêmd  systêmd   dt dl nïnuord sb lbturd.   f) Nclldr Nc lldr h‟dxprdssocl h‟dxprdssocl nd h‟ï ‟ïhhc libtoc libtoc l bliuhbor bliuhbord d e) Rudhhd dst hb pïrocnd nu pdlnuhd bolso eclstotuïd 3 Nïtdrmoldr hb hcliudur nu pdlnuhd somphd sylejrcld.   n) Rudhhds sclt hds votdssds nd B dt nd F hcrsqud hb toid pbssd pbr sb pcsootocl n‟ïquohofrd pcs n‟ïquohofrd  3 Rudhhd dst bhcrs h‟ïldriod eolïtoqud nu systêmd sys têmd 3  3  B.L; m B.L;  m = 20i , h = 20 em ,

. 

6° - Tl rdsscrt nd eclstbltd nd rbondur A dt nd mbssd lïihoidbfhd dst suspdlnu pbr scl dxtrïmotï supïrodurd à ul pcolt goxd. Cl suspdl n à h‟butrd dxtrïmotï uld mbssd M. Cl nïphbed vdrtoebhdmdlt vdrs hd fbs, hb mbssd M à pbrtor nd sb pcsotocl n‟ïquohofrd dt cl h‟bfblnclld sbls votdssd olotobhd. Rudhhd ncot ëtrd hb vbhdur nd A pcur qud hb mbssd M dt hd pdlnuhd dlvosbiï prïeïndmmdlt cseohhd bvde hb mëmd pïroc pïro c nd 3 BL ; m= ; m= 2ai F°   - Cl dlhêvd hb fohhd F, hb toid ^, tcukcurs mcfohd butcur nd h‟bxd jcrozcltbh F° pbssblt pbr C, dst mboltdlblt phbeïd jcrozcltbhdmdlt. Cl h‟bfblnclld sbls votdssd olotobhd. lotobhd. 2°- Rudh Rudhhhd dst ds t hb vo v otdssd nd hb fohhd B bu pbssbid à hb pcsoto pcsot oc l n‟ïquohofrd n‟ïquohofrd 3  3

 

 B .L ; CB ; CB = 6H = 60 em  6° - Hcrs nu pbssbid dl edttd pcsotocl, hb fohhd B rdlecltrd uld fohhd fohhd E suppcsïd pcletudhhd, pcletudhhd, nd mbssd mbss d m5   = 4 m, phbeïd sur hd fcrn n‟uld tbfhd goi.6 goi.6.. Rudhhd sclt hds votdssds nd B dt E, eclsonïrïds ecmmd echolïbords,

bprês

ul

ejce

suppcsï

pbrgbotdmdlt

ïhbstoqud 3 Gbord h‟bpphoebtoc h‟bpphoebtoc l lumïroqud. 

5° - Hb fohhd E sd trcuvd bvblt hd ejce, à hb jbutdur J bu-ndssus nu sch. Dtunodr hb lbturd nu mcuvdmdlt nd E bprês hd ejce. Dtbfhor Dtbfhor h‟ïqubtocl nd hb trbkdetc ord nd hb fohhd E nbls ul systêmd n‟bxds qud h‟cl prïeosdrb. B qudhhd nostbled nd hb vdrtoebhd nu pcolt C vbvb-t-dhh t-dhhd d rdlecltrdr rdlec ltrdr hd hd sch suppcsï jc rozc rozcltbh ltbh 3 Bvde qudhhd qudhhd votdssd tcuejdrb-t-dhhd tcuejdrb-t-dhhd hd sc h 3  BL ; J ; J = 2 m  >° - Rudh dst h‟blihd h‟blihd mbxombh nd rdmcltï rdmc ltïd d nd B bprês hd ejce ejc e  3 

UCHT^OCL B° - 2°- b) 

hd sys systêmd têmd dggdetud ul mcuvd mc uvdmdlt mdlt s sooluscãnbh nd rctbtocl rc tbtocl butc butcur ur nd 0  f) 

 

e) 

n) Ucot ί hb votdssd bliuhbord nu pdlnuhd bu pbssbid à hb pcsotocl n‟ïquohofrd. v   B=6h   1

v F=h    cr

dst

nïtdrmolï pbr

2/6(27mh6 +5mh6 )6 =:mih(2 =:mih(2―ecsκ)― ―ecsκ)―5mih(25mih(2ecsκ)   ecsκ) n‟cÿ   n‟cÿ

-2 v   B = 0,206 m. s  

v F = 0,042 0 ,042 m.s-2 

6°- 

N‟cÿ   A = 67,52 L.m N‟cÿ L.m-2  F/ 2°- v   B= 6h

n‟cÿ 

6°- 

bvde

tdh qud ; 

dt

hd tjïcrêmd nd h‟D E  

 

 

5° - E dggdetud ul mcuvdmdlt mc uvdmdlt nd nd ejutd hofrd hofrd bvde votdssd votdssd olot olot ob hd jcrozcltbhd . Ub trbkdetco trbkdetc ord b pcur pc ur ïqubtoc ïqubtoc l nds systêmds n‟bxds ncllïs ; ncllïs  ;

Hb fohhd rdlecltrd hd sch à uld nostbled n tdhhd qud J = 7,>4 n 6  nd hb vdrtoebhd nd 0 n‟cÿ n = 0,5?m. Dhhd tcuejdrb hd sch bvde uld votdssd v   tdhhd qud ;  

dt

-2

v=>,44m.s  

>°- Bprês hd ejce, hb hb f fohh ohhd d rdmc rdm c ltd gbosblt ul blihd κ bvde hb vdrto vdrt oebhd κ tdh td h qud  qud  

n‟cÿ 

DZDVEOED OW Cl lïihoidrb lïihoidrb hds grcttdmdlts grctt dmdlts dt cl prdlnrb i = 20m. s-6  nbls tcut hd prcfh prc fhêmd. êmd.

B ―  Tl schond (U) qud h‟cl bssomohdrb à ul pcolt mbtïrodh nd mbssd M = 600i, pdut ihossdr dl suovblt hb hoild nd phus irblnd pdltd n‟ul phbl oleholï quo gcrmd h‟blihd

= 50° bvde hd phbl jcrozcltbh.

Hd sc sc hond hond (U) dst hæejï sbls votdssd olotobhd olotobhd nu pcol pc oltt B. Oh pbrecurt pbrec urt hb nostb nostbled led BF = h = 6,40m sur hhd d ph p hbl oleholï (goi 2)  2° - Nïtdrmoldr Nïtdrmoldr hb lbturd lbturd nu mcuvdmdlt mc uvdmdlt pros pros pbr (U) dt dt ebheuhdr hb nurïd t 2  nu trbkdt BF. 

 

6°- Ebheuhdr hd mcnuhd W2 nd hb votdss votdssd d

nd (U) dl F.

Rudhhds Rudhh ds dl d l sclt sc lt hds ecmp ecm pcsbltds jcrozcltbhd dt vdrto vd rtoebhd ebhd W2x  dt W2 y  3 

F - Brro Brrovï vï dl F, hd scho sc hond nd (U) blomï blomï nd hb votdssd votdss d

tcmfd tcm fd sur ul phbl jcro jc rozc zcltbh ltbh

sotuï dl ecltrd fbs à uld no nostbled stbled j nd F ( goi.2 goi.2). ). Hb ejutd nurd t 6  = 0,4 s.  2° - Ebheuhdr hb nostbled jcrozcltbhd n ecmprosd dltrd hb vdrtoebhd pbssblt pbr F dt hd pcolt n‟ompbet sur s ur hd hd ph p hbl jcro jc roz z c ltbh, ltbh, puos puos hb jbutdur j .   6°- Ebheuh Ebheuhdr dr h‟ïldriod eo e olïto lït oqud nu sc hond (U) à scl brrovïd brrovïd s sur ur hd phbl jcro jc rozc zcltbh ltbh..  

E - Hd schond (U) rdmphbeï dl B dst bttbejï à ul goh oldxtdlsofh oldx tdlsofhd, d, nd mbssd mbss d lïihoidbfhd. lïihoidbfhd. Ed goh s‟dlrcuh s‟dlrc uhd d sur ul ey eyho holnrd lnrd (E) nd rbyc l r = >em, (E) dst mcfohd butcur nd scl bxd jcrozcltbhd (Ξ) (goi.6 ( goi.6). ). Hd systêmd dst bfblncllï sbls votdssd olotobhd, hd goh nïkà tdlnu ïtblt pbrbhhêhd à BF. Cl ec ecl lstbtd qud pcur brrovdr brrovdr dl F hd scho sc hond nd (U) m mdt dt ul tdmps t5  = 6s  2° Nïtdrmoldr hb lbturd nu mcuvdmdlt nu schond (U) dt ebheuhdr hd mcmdlt n‟oldrtod K nu eyholnrd (E) pbr rbppcrt à scl bxd (Ξ). 

6° Hcrsqud hd schond brrovd dl F hd goh dst dltoêrdmdlt nïrcuhï dt oh sd nïtbejd nu eyhol eyh olnr nrd d (E) qu quo b bt bttdo tdol lt uld uld votd votdssd ssd bli bliu uhbo borrd lctïd lctïd

.

Cl grdold hd eyholnrd (E) bu mcydl n‟ul pbtol nclt h‟betocl dst ïquovbhdltd à edhhd n‟ul ecuphd nd mcmdlt eclstblt. H‟brrët s‟dggdetud bu fcut n‟ul tdmps  tdmps   t>  = 20s. Ebheuhdr h‟oltdlsotï h‟oltdlsotï   M nu mcmdlt nu ec ec uph uphd d nd grdolbid grdolbid dxdreï pbr hd pbtol pbtol..  

 

UCHT^OCL  B - 2° - (U) dggdetud ul mcuvdmdlt rdetohoild ulogcrmïmdlt beeïhïrï suovblt hb hoild nd phus irblnd pdltd. Nurïd Nur ïd nu trbkdt BF ;  

6° 

(jcrozcltbhd crodltïd hb nrcotd)  (vdrtoebhd ndsedlnbltd) ndsedlnbltd)  F - 2°- Hb nostbled nostbled dst h‟bfseossd nu pco pc olt n‟ompbet bttd bttdoolt à h‟olstblt t 6 ; 

j dst h‟crncllïd h‟crnc llïd nu pcolt n‟ompbet n‟ompbet  

6°- 

E - 2° 2 °-

(U) dggdetud d ggdetud ul mc mcuvd uvdmdlt mdlt rd rdetoho etohoild ild ulogcrmïmdlt ulogcrmïm dlt beeïhïrï beeïhïrï

6° - B h‟brrët ; h‟brrët ;