AP Physics C: Mechanics 2011 Free-Response Questions

Transcription

1 AP Phyc C: Mechanc Fee-Repone Queton About the College Boa The College Boa a mon-ven not-fo-poft oganzaton that connect tuent to college ucce an oppotunty. Foune n 9, the College Boa wa ceate to epan acce to hghe eucaton. Toay, the membehp aocaton mae up of moe than 5,9 of the wol leang eucatonal nttuton an ecate to pomotng ecellence an equty n eucaton. Each yea, the College Boa help moe than even mllon tuent pepae fo a ucceful tanton to college though pogam an evce n college eane an college ucce nclung the SAT an the Avance Placement Pogam. The oganzaton alo eve the eucaton communty though eeach an avocacy on behalf of tuent, eucato an chool. The College Boa. College Boa, Avance Placement Pogam, AP, AP Cental, SAT an the acon logo ae egtee taemak of the College Boa. Amtte Cla Evaluaton Sevce an npng mn ae taemak owne by the College Boa. All othe pouct an evce may be taemak of the epectve owne. Vt the College Boa on the Web: Pemon to ue copyghte College Boa mateal may be equete onlne at: Vt the College Boa on the Web: AP Cental the offcal onlne home fo the AP Pogam: apcental.collegeboa.com.

2 Poton ma, Neuton ma, m p m n TABLE OF INFORMATION FOR an CONSTANTS AND CONVERSION FACTORS kg Electon chage magntue, -7-9 e.6 C.67 kg -9 electon volt, ev.6 J -3 8 Electon ma, m e 9. kg Spee of lght, c 3. m 3 - Unveal gavtatonal - 3 Avogao numbe, N 6. mol contant, G 6.67 m kg Unveal ga contant, R 8.3 J (mol K) Acceleaton ue to gavty at Eath uface, g 9.8 m -3 Boltzmann contant,.38 J K k B -7 unfe atomc ma unt, u.66 kg 93 MeV c Planck contant, h 6.63 J 4.4 ev Vacuum pemttvty, Coulomb law contant, Vacuum pemeablty, Magnetc contant, -5 3 hc.99 J m.4 ev nm C Nm 9 k 4p 9. Nm C -7 m 4p (T m) A 7 k m 4 p - (T m) A 5 5 atmophee peue, atm. N m. Pa UNIT SYMBOLS mete, m mole, mol watt, W faa, F klogam, kg hetz, Hz coulomb, C tela, T econ, newton, N volt, V egee Celu, C ampee, A pacal, Pa ohm, W electon-volt, ev kelvn, K joule, J heny, H PREFIXES VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES Facto Pef Symbol q gga G nq mega M coq klo k tanq cent c 3 - mll m 6 - mco m 9 - nano n - pco p The followng conventon ae ue n th eam. I. Unle othewe tate, the fame of efeence of any poblem aume to be netal. II. The ecton of any electc cuent the ecton of flow of potve chage (conventonal cuent). III. Fo any olate electc chage, the electc potental efne a zeo at an nfnte tance fom the chage. --

3 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR an u u + at + ut + at u ( ) u + a -  F F ma F p t net J Ft Dp p mv Ffc W K P mn F mu W t P F v D Ug mgh ac t u w F  I t tnet a I m  m cm Âm Âm u w L p Iw K Iw w w + at q q + wt + at MECHANICS a acceleaton F foce f fequency h heght I otatonal neta J mpule K knetc enegy k png contant length L angula momentum m ma N nomal foce P powe p momentum au o tance poton vecto T peo t tme U potental enegy u velocty o pee W wok one on a ytem poton m coeffcent of fcton q angle t toque w angula pee a angula acceleaton F U -k k p T w f T T p F U G G p p m k g Gm m - Gm m - ˆ F ELECTRICITY AND MAGNETISM qq 4p E F q Q E A V E - q V 4p  U C C C E qv Q V k p A  C  C C I Q t qq 4p Uc QV CV R A E J I Neu A V R IR  R  R R P p IV F qv B M A aea B magnetc fel C capactance tance E electc fel e emf F foce I cuent J cuent enty L nuctance length n numbe of loop of we pe unt length N numbe of chage cae pe unt volume P powe Q chage q pont chage R etance tance t tme U potental o toe enegy V electc potental u velocty o pee etvty f m magnetc flu k electc contant B m B I m I 4p 3 F I B B m m ni f B A e E - I e - L t UL LI f t m -3-

4 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR an GEOMETRY AND TRIGONOMETRY CALCULUS Rectangle A bh Tangle A bh Ccle A p C p Paalleleppe V wh Cylne V p S p + p Sphee 4 3 V p 3 S 4p Rght Tangle A aea C ccumfeence V volume S uface aea b bae h heght length w wth au f f u u n n- ( ) n ( ) e e ( ln ) ( n ) ( co ) co - n n n+, n π - n + e e ln co n n -co a + b c nq coq a c b c q c b 9 a tanq a b -4-

5 AP PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS PHYSICS C: MECHANICS SECTION II Tme 45 mnute 3 Queton Decton: Anwe all thee queton. The uggete tme about 5 mnute fo anweng each of the queton, whch ae woth 5 pont each. The pat wthn a queton may not have equal weght. Show all you wok n the pnk booklet n the pace pove afte each pat, NOT n th geen net. Mech.. A pojectle fe hozontally fom a launchng evce, etng wth a pee u. Whle the pojectle n the launchng evce, the mpule mpate to t J p, an the aveage foce on t F avg. Aume the foce become zeo jut a the pojectle eache the en of the launchng evce. Epe you anwe to pat (a) an (b) n tem of u, J p, F avg, an funamental contant, a appopate. (a) Detemne an epeon fo the tme eque fo the pojectle to tavel the length of the launchng evce. (b) Detemne an epeon fo the ma of the pojectle. The pojectle fe hozontally nto a block of woo that clampe to a tabletop o that t cannot move. The pojectle tavel a tance nto the block befoe t top. Epe all algebac anwe to the followng n tem of an the gven quantte pevouly ncate, a appopate. (c) Deve an epeon fo the wok one n toppng the pojectle. () Deve an epeon fo the aveage foce F b eete on the pojectle a t come to et n the block. Now a new pojectle an block ae ue, entcal to the ft one, but the block not clampe to the table. The pojectle agan fe nto the block of woo an tavel a new tance n nto the block whle the block le aco the table a hot tance D. Aume the followng: the pojectle ente the block wth pee u, the aveage foce F b between the pojectle an the block ha the ame value a etemne n pat (), the aveage foce of fcton between the table an the block f T, an the collon ntantaneou o the fctonal foce neglgble ung the collon. (e) Deve an epeon fo n n tem of, D, f T, an F b, a appopate. (f) Deve an epeon fo n n tem of, the ma m of the pojectle, an the ma M of the block. The College Boa. Vt the College Boa on the Web: GO ON TO THE NEXT PAGE. -5-

6 AP PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS Mech.. An amuement pak e featue a paenge compatment of ma M that eleae fom et at pont A, a hown n the fgue above, an move along a tack to pont E. The compatment n fee fall between pont A an B, whch ae a tance of 3R 4 apat, then move along the ccula ac of au R between pont B an D. Aume the tack fctonle fom pont A to pont D an the menon of the paenge compatment ae neglgble compae to R. (a) On the ot below that epeent the paenge compatment, aw an label the foce (not component) that act on the paenge compatment when t at pont C, whch at an angle q fom pont B. (b) In tem of q an the magntue of the foce awn n pat (a), etemne an epeon fo the magntue of the centpetal foce actng on the compatment at pont C. If you nee to aw anythng bee what you have hown n pat (a) to at n you oluton, ue the pace below. Do NOT a anythng to the fgue n pat (a). (c) Deve an epeon fo the pee u D of the paenge compatment a t eache pont D n tem of M, R, an funamental contant, a appopate. A foce act on the compatment between pont D an E an bng t to et at pont E. () If the compatment bought to et by fcton, calculate the numecal value of the coeffcent of fcton m between the compatment an the tack. The College Boa. Vt the College Boa on the Web: GO ON TO THE NEXT PAGE. -6-

7 AP PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS (e) Now cone the cae n whch thee no fcton between the compatment an the tack, but ntea the compatment bought to et by a bakng foce -kv, whee k a contant an v the velocty of the compatment. Epe all algebac anwe to the followng n tem of M, R, k, u D, an funamental contant, a appopate.. Wte, but o NOT olve, the ffeental equaton fo u ( t).. Solve the ffeental equaton you wote n pat.. On the ae below, ketch a gaph of the magntue of the acceleaton of the compatment a a functon of tme. On the ae, eplctly label any ntecept, aymptote, mama, o mnma wth numecal value o algebac epeon, a appopate. The College Boa. Vt the College Boa on the Web: GO ON TO THE NEXT PAGE. -7-

8 AP PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS Mech. 3. The toon penulum hown above cont of a k of otatonal neta I upene by a fleble o attache to a g uppot. When the k twte though a mall angle q, the twte o eet a etong toque t that popotonal to the angula placement: t - bq, whee b a contant. The moton of a toon penulum analogou to the moton of a ma ocllatng on a png. (a) In tem of the quantte gven above, wte but o NOT olve the ffeental equaton that coul be ue to etemne the angula placement q of the toon penulum a a functon of tme t. (b) Ung the analogy to a ma ocllatng on a png, etemne the peo of the toon penulum n tem of the gven quantte an funamental contant, a appopate. To etemne the toon contant b of the o, k of ffeent, known value of otatonal neta ae attache to the o, an the ata below ae obtane fom the eultng ocllaton. Rotatonal Ineta I of Dk ( kg m ) Aveage Tme fo Ten Ocllaton () Peo T () T ( ) The College Boa. Vt the College Boa on the Web: GO ON TO THE NEXT PAGE. -8-

9 AP PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS (c) On the gaph below, plot the ata pont. Daw a taght lne that bet epeent the ata. () Detemne the equaton fo you lne. (e) Calculate the toon contant b of the o fom you lne. (f) What the phycal gnfcance of the ntecept of you lne wth the vetcal a? END OF EXAM The College Boa. Vt the College Boa on the Web: -9-