Eva 2 Física I UD I-2012

 

]OIXM^TIEKE EITU^IUK@ — TMEM UMDOJ@ÔGIDK — V^JE]DDIJO KTIGOKU]^K< HÂTIDK OMWUJOIKOK — MXK@]KDIJO > EJDMOUM< OMTUJ^ K@XK^M\ — HMDCK< ;;-;;->6;5 Ojbnrm< Luko Mstmnko ^jerâgumz Kguem`j . Dôeigj< >6>6>6>=;;5 Vrmguotks em koë`isis m iotmrprmtkdiôo ;. ]o kutjbôvi` kutjbôvi` djo uok uok vm`jdieke vm`jdieke ioidik` ioidik` v₆ hrmok hrmok ckstk emtmomrsm emtmomrsm djo djo emskdm`mrkd emskdm`mrkdiôo iôo djostkotm mo uo mbpj t. Ti `k vm`jdieke ioidik` humrk m` ejn`m pmrj `k emskdm`mrkdiôo djostkotm humrk `k bitke, m` mbpj pkrk emtmomrsm smrâk1 ^MTV]MTUK< 5t

 

>. º Duë` ms `k `k kdm`mrkdiô kdm`mrkdiôo o iostkotëom iostkotëomk k em uo prjymd` prjymd` dukoej dukoej ``mgk ``mgk k `k pkr pkrtm tm bës k`tk k`tk em su trkymdtjrik :  

^MTV]MTUK<

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@k kdm`mrk kdm`mrkdiôo diôo iostko iostkotëomk tëomk ms 6 mo x, emniej emniej k qum qum mstm mstm ms uo bjvibi bjvibimotj motj rmd` rmd`âomj âomj uoihjrbm y su kdm`mrkdiôo iostkotëomk mo y ms `k grkvmeke.

4. Vkrk uok rkpiem rkpiemzz ekek y lk em `kozkb `kozkbimotj imotj,, º dôbj emnmrâk emnmrâk ustme ustme `kozkr `kozkr uo prjymd` prjymd` pkrk pkrk jntmomr m` k`dkodm bës `krgj, dôbj pkrk jntmomr m` mbpj bës `krgj em vum`j y dôbj pkrk jntmomr `k bkyjr k`turk : ^MTV]MTUK<

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Tm emnmrâ emnmrâkk `kozkr `kozkr m` prjym prjymd` d` mo uo ëogu`j ëogu`j em 5= grkejs grkejs djo djo rm`kdiôo rm`kdiôo k `k cjrizj cjrizjotk`, otk`, yk qum ksâ pumem jntmomr uo k`dkodm bës `krgj, uok bkyjr k`turk y uo mbpj em vum`j bës `krgj.

 

Eispkrkbjs uo prjymdti` emsem m` jrigmo y éstm emsdrinm uok trkymdtjrik pkrknô`idk djbj `k em `k higurk. Emsprmdikbjs `k rmsistmodik em` kirm. Einulk mo `ks pjsidijoms K, N, D, E y M m` vmdtjr vm`jdieke, m` vmdtjr kdm`mrkdiôo y `ks djbpjomotms ojrbk` y tkogmodik` em `k kdm`mrkdiôo. (Oj sm trktk em ekr m` vk`jr oubéridj em oioguok em `ks vkrikn`ms, sô`j `k eirmddiôo y m` smotiej em `ks bisbks) º[ué mhmdtj prjeudmo ko y kt  sjnrm `k vm`jdieke

5. ]o prjymd prjymd` ` ssm m bumvm bumvm mo mo uok trkymdtjri trkymdtjrik k pkrknô`i pkrknô`idk. dk. k) º C Cky ky uo puot puotj j ejo ejoem em k smk pkrk`m`k k v :

^MTV]MTUK< @k vm`jdieke em` bjvibimotj pkrknô`idj ms simbprm tkogmotm k `k trkymdtjrik. @k kdm`mrkdiôo ms simbprm vmrdk`. Mo dkbnij oj mxistm puotj ejoem `k vm`jdieke smk pkrk`m`k k `k kdm`mrkdiôo. Mo oiogüo puotj `k vm`jdieke pumem smr vmrdk`. Eurkotm tjej m` bjvibimotj cky simbprm uok djbpjomotm cjrizjotk` em `k vm`jdieke.

n) º C Cky ky uo puot puotj j ejo ejoem em k smk pmrpmoeidu`kr k v :

^MTV]MTUK< M` üoidj puotj mo qum `k vm`jdieke ms pmrpmoeidu`kr k `k kdm`mrkdiôo ms mo m` em bëxibk k`turk, ejoem m` djbpjomotm vmrdk` em `k vm`jdieke ms ou`k.

 

=. Djosiemrm Djosiemrm m` m` bjvibimot bjvibimotj j em uok bkozkok bkozkok qum dkm dkm mo uo sistmbk sistmbk em djjrem djjremokeks okeks duyjs duyjs mlms mstëo eispumstjs em tk` bkomrk qum `k eirmddiôo ckdik krrink mstë k 5=¶ motrm `js mlms S y Y . º Duë`ms sjo `ks kdm`mrkdijoms kx y ky em `k bkozkok :

d) kx 2 8.9b/s¾ 1 ky 2 -8.9b/s¾ 8. ]ok mdck mdck `kozkek `kozkek ckdik ckdik krrink krrink k 96 b/s b/s k`dkozk k`dkozk uok uok k`turk k`turk bëxibk bëxibk em 5;6 b. º [ué k`turk bëxibk k`dkozkrë `k mdck dukoej sm `kodm djo `k bitke em `k rkpiemz :

e) ;64 b

 

L]TUIHI[]M T] ^MTV]MTUK<

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Djo `k hôrbu`k hôrbu`k em z bëxibk bëxibk,, rmmbp`k rmmbp`kzkbjs zkbjs 96 Xj(k` Xj(k` dukerkej)/ dukerkej)/> > vmdms grkvmeke grkvmeke,, emspmlkbjs smoj em` ëogu`j y `umgj sm ckdm smoj k `k -; pkrk pjemr skdkr m` ëogu`j. @umgj @umgj em tmomr tmomr m` ëogu`j ëogu`j sm tjbk tjbk `k bisbk bisbk hôrbu hôrbu`k `k em z bëxibk, bëxibk, pmrj pmrj Xj Xj smrâk smrâk `k bitke y sm rmsum`vm bu`p`idkoej djo m` smoj em` ëogu`j y sm eiviem sjnrm > vmdms `k grkvmeke.

7. ]o pkqumtm pkqumtm sm emlk emlk dkmr em uo kviôo kviôo qum vum`k vum`k mo mo `âomk rmdtk rmdtk djo k`tue k`tue y rkpiemz rkpiemz djostkotms. º [ué trkymdtjrik em` pkqumtm jnsmrvkrâk m` pi`jtj:  

^MTV]MTUK< ^mdtk 3. º Mo qué qué dksj uo uo dumrpj dumrpj mom mom kdm`mrkdi kdm`mrkdiôo ôo dmotrâpm dmotrâpmtk tk y oj tkogmodi tkogmodik` k` : ^MTV]MTUK<

@k kdm`mrkdiôo tkogmodik` oj mxistm mo uo bjvibimotj dirdu`kr uoihjrbm emniej k qum m` bôeu`j em vm`jdieke oj dkbnik djo m` mbpj , sj`kbmotm dkbnik su eirmddiôo y pjr m``j mom ms uok kdm`mrkdiôo dmotrâpmtk.

º Y mo qué dksj mom kdm`mrkdiôo tkogmodik` y oj dmotrâpmtk : ^MTV]MTUK<

Mo uo bjvibimotj rmd`âomj oj uoihjrbm sm modumotrk uo dkbnij em `k rkpiemz, pmrj `k eirmddiôo sm modumotrk em hjrbk djostkotm. Vjr `j duk` sm eidm qum mom kdm`mrkdiôo tkogmodik` pmrj oj dmotrâpmtk.

 

^mspumstks em koë`isis bktmbëdjs 9. ]ok krei``k krei``k mom mom djjrem djjremokeks okeks xy ( ;.;b , 4.5b 4.5b ) mo t; 2 6 y ( =.4b =.4b . -6.=b -6.=b ) mo t> 2 4 s. Vkrk mstm iotmrvk`j jntmogk < k) @ks ddjbp jbpjom jomotm otmss em `k `k vm`jdi vm`jdieke eke b bmei meik k ^MTV]MTUK< -

Xb2 Xb2 (V (Vhh-Vi Vi)) / (Uhh-Ui Ui))

ejoem2 p< puotj t< mbpj Xbx2 Vhx-Vix/Uh-Ui Xbx2 ( =.4b-;.;b)/(4s-6s) Xbx2 5.>b/4s 2;.5b/s -

Xby2 Xby2 (V (Vhy hy-V -Viiy) / ((U Uh-U h-Ui)

 

Xby2 (6.=b-4.5b)/(4s-6s)

 

Xby2 -49b/4s 2-;.4b/s

n) @k bk bkgoitu goitue e y eirmddiô eirmddiôo o em msk vm`jdiek vm`jdieke e ^MTV]MTUK< || X ||2 ∜ (;,5b/s)(k` dukerkej)+(-;,4b/s(k` dukerkej)2 ;.9;b/s

@k eirmddiôo ms `k bisbk em` vmdtjr pjsidiôo

;6. K` ioidikr uo kviôo kviôo k` ktmrrizklm, `ks djbpjomotms djbpjomotms em su pjsidiôo pjsidiôo mstëo ekeks pjr<  

S 2 96t

y 2 =66 — ;=t

Ejoem x m y mstëo ekeks mo bmtrjs y t mo smguoejs. º Duë` ms m` vmdtjr vm`jdieke em` kviôo eurkotm mstm emsdmosj : º Duë` ms m` vk`jr em su rkpiemz eurkotm m` emsdmosj : º [ué ëogu`j hjrbk m` vmdtjr vm`jdieke djo `k cjrizjotk` : ^MTV]MTUK.

S2 96t

Y2 =66-;=t

Krdtko2 Uko-;

 

Emrivkek2 Xx2 Ex296   Et

Xy2 Ey2 -;= Et

-M` vmdtjr vm`jdieke2 Xxi + Xyl 2 96i - ;=l

-^kpiemz2 |v|2∜(96)(k`dukerkej)+(-;=)(k` dukerkej) 2 9;.>5b/s -Kogu`j2 Ukoλ2Xy/Xx λ2 Krdtko - ;=/96 2 -9.58¶

;;. ]ok bëquiok mbpkdkejrk mbpkdkejrk em cmoj krrjlk dkek dkek pkdk em cmoj tmrbiokek tmrbiokek >.= bmtrjs mo m` kirm, em bjej qum pumek dkmr mo uo rmbj`dkejr qum mspmrk = bmtrjs emtrës em `k bëquiok. k. º Duë` Duë` emnm emnm smr smr `k rkpie rkpiemz mz em `kozkbimo `kozkbimotj tj em `ks pkdks pkdks : ^MTV]MTUK< Xj2 7.3> b/s Cbkx2 Xjy(k` dukerkej)/>g Tm emspmlk `k Xjy< Xjy2 ∜(> • g • cbkx) Xjy2 ∜(> • 9.3b/s(k` dukerkej) • >.=b)

Xjy2 7b/s

tbkx 2 Xjy/g 2 7b/s/9.3b/smg>2 6.7;5>s tv2 > • tbkx 2 > • 6.7;5>s2 ;.5>3=s

xbkx2 Xjx • tv Xjx2 xbkx / tv 2 =b / ;.5>3=s Xjx2 4.= b/s

 

Xj2 ∜Xjx(k` dukerkej)+Xjy(k` dukerkej) Xj2 ∜(4.=b/s)(k` dukerkej)+(7b/s)(k` dukerkej)+(7b/s)(k` dukerkej) Xj2 7.3> b/s

   

n. º Duë` emnm smr m` ëogu`j em `kozkbimotj : ^MTV]MTUK<

M` ëogu`j em `kozkbimotj ms em 84.54 grkejs. Ukoλ2 Xjy/Xjx Ukoλ2 7b/s / 4.=b/s λ2 84.54 grkejs

;>. ]o kvm vum`k mo m` p`koj xy djo vm`jdieke v 2 (α - ½t¾) i + ɑt l , ejoem α 2 >.5 b, ½ 2 ;.8 b/s´ y ɑ 2 5.6 b/s¾ . Mo t 2 6 m` kvm mstë mo m` jrigmo< k) Dk`d Dk`du`kr u`kr `js `js vmdtjrms vmdtjrms em pjsidiô pjsidiôo o y kdm`mrkdi kdm`mrkdiôo ôo em` kvm m mo o huodiôo huodiôo em` mbpj mbpj ^MTV]MTUK< V2 iotQ(>.; - >.3t(k` dukerkej))i + = tlR Et2 (>.;t - >.3t( k `k 4)/4)i + = t(k` dukerkej)/>l -

@k kdm` kdm`mrk mrkdi diôo ôo ms `k `k emrivke emrivkek k em `k vm`j vm`jdie dieke ke rm rmspm spmdtj dtj k` mbp mbpj. j.

k2 ev/et 2 ->.3 • > t i + = l 2 =,8 t i + = l

n) º [ué k` k`turk turk mom mom m` k kvm vm k` vj`kr vj`kr sjnrm sjnrm x 2 6 pjr pribmrk pribmrk vmz vmz emspués emspués em t2 t2 6 : ^MTV]MTUK< S2 6< >.;t - >.3/4 t(k` dukerkej) U2 >.; - >.3/4 U2 6, ibp`idk U2 >.>=s Y2 =/> • >.>=(k` dukerkej)2 ;>.88b