AP Physics C: Mechanics 2005 Free-Response Questions

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1 AP Phyic C: Mechanic 00 ee-repone Quetion he College Boa: Connecting Stuent to College Succe he College Boa i a not-fo-pofit membehip aociation whoe miion i to connect tuent to college ucce an oppotunity. oune in 900, the aociation i compoe of moe than 4,700 chool, college, univeitie, an othe eucational oganization. Each yea, the College Boa eve ove thee an a half million tuent an thei paent,,000 high chool, an,00 college though majo pogam an evice in college amiion, guiance, aement, financial ai, enollment, an teaching an leaning. Among it bet-known pogam ae the SA, the PSA/NMSQ, an the Avance Placement Pogam (AP ). he College Boa i committe to the pinciple of excellence an equity, an that commitment i emboie in all of it pogam, evice, activitie, an concen. Copyight 00 by College Boa. All ight eeve. College Boa, AP Cental, APCD, Avance Placement Pogam, AP, AP Vetical eam, Pe-AP, SA, an the acon logo ae egitee taemak of the College Entance Examination Boa. Amitte Cla Evaluation Sevice, CollegeE, Connect to college ucce, MyRoa, SA Pofeional Development, SA Reaine Pogam, an Setting the Conetone ae taemak owne by the College Entance Examination Boa. PSA/NMSQ i a egitee taemak of the College Entance Examination Boa an National Meit Scholahip Copoation. Othe pouct an evice may be taemak of thei epective owne. Pemiion to ue copyighte College Boa mateial may be equete online at: Viit the College Boa on the Web: AP Cental i the official online home fo the AP Pogam an Pe-AP: apcental.collegeboa.com.

Each yea, the College Boa eve ove thee an a half million tuent an thei paent,,000 high chool, an,00 college though majo pogam an evice in college amiion, guiance, aement, financial ai, enollment, an

2 ABLE O INORMAION OR 00 CONSANS AND CONVERSION ACORS - unifie atomic ma unit, u kg 9 MeV/ c Poton ma, m p kg Neuton ma, m n kg Electon ma, m e 9. 0 kg Magnitue of the electon chage, e C Avogao numbe, N mol Univeal ga contant, R. J/ ( mol K ) Boltzmann contant, k B. 0 J/K Spee of light, c m / Planck contant, h J ev hc J m 4. 0 ev nm Vacuum pemittivity, 0. 0 C / N m 9 Coulomb law contant, k / 4π Nm / C 7 Vacuum pemeability, µ 0 4π 0 ( m) / A Magnetic contant, k' µ / 4π 0 7 ( m) / A 0 Univeal gavitational contant, G m / kg Acceleation ue to gavity at the Eath uface, g 9. m/ atmophee peue, atm 0. 0 N / m 0. 0 Pa electon volt, ev J UNIS Name Symbol mete kilogam econ ampee kelvin mole hetz newton pacal joule watt coulomb volt ohm heny faa tela egee Celiu electonvolt m kg A K mol Hz N Pa J W C V Ω H C ev PREIXES acto Pefix Symbol 0 9 giga G 0 6 mega M 0 kilo k 0 centi c 0 milli m 0 6 mico µ 0 9 nano n 0 pico p VALUES O RIGONOMERIC UNCIONS OR COMMON ANGLES θ in θ co θ tan θ / / / 7 / 4/ /4 4 / / 4/ / 4/ 60 / / 90 0 he following convention ae ue in thi examination. I. Unle othewie tate, the fame of efeence of any poblem i aume to be inetial. II. he iection of any electic cuent i the iection of flow of poitive chage (conventional cuent). III. o any iolate electic chage, the electic potential i efine a zeo at an infinite itance fom the chage.

0 ev hc 99. 0 J m 4. 0 ev nm Vacuum pemittivity, 0. 0 C / N m 9 Coulomb law contant, k / 4π 0 90.

3 ADVANCED PLACEMEN PHYSICS C EQUAIONS OR 004 an 00 MECHANICS u u0 + at a acceleation foce x x0 + u0t + at f fequency h height u u0 + a( x - x0) I otational inetia Â net ma J impule K kinetic enegy p k ping contant l length J Ú Dp L angula momentum m ma p mv N nomal foce fic mn P powe p momentum W Ú aiu o itance K mu poition vecto peio W t time P U potential enegy u P v velocity o pee W wok one on a ytem DUg mgh x poition m u coefficient of fiction ac w q angle t t toque w angula pee Â t tnet Ia a angula acceleation I Ú m Â m cm Âm Âm u w L p Iw K Iw w w0 + a q q0 + w0t + at U U p G G t kx kx p w f m p k - p g Gm m Gm m - - l ˆ ELECRICIY AND MAGNEISM qq A aea 4p B magnetic fiel 0 E C capacitance itance q E electic fiel Q e emf E A foce 0 I cuent V E L inuctance l length q n numbe of loop of wie i V pe unit length 4p 0 i i P powe qq Q chage UE qv 4p 0 q point chage C Q R eitance itance V t time k 0 A U potential o toe enegy C V electic potential u velocity o pee Cp Ci eitivity i f m magnetic flux k ielectic contant C i Ci Q I Uc QV CV l R A V IR R R i i R R p i i P IV M qv B B m I 0 z I B B m0ni fm z B A fm e e L I UL LI

a ytem DUg mgh x poition m u coefficient of fiction ac w q angle t t toque w angula pee Â t tnet Ia a angula acceleation I Ú m Â m cm Âm Âm u w L p Iw K Iw w w0 + a q q0 + w0t + at U U p G G t kx kx

4 ADVANCED PLACEMEN PHYSICS C EQUAIONS OR 004 an 00 GEOMERY AND RIGONOMERY CALCULUS Rectangle A bh iangle A bh Cicle A p C p Paallelepipe V lwh Cyline V p l S pl + p Sphee V 4 p S 4p Right iangle a + b c in q a c b co q c tan q a b A aea C cicumfeence V volume S uface aea b bae h height l length w wih aiu q c b 90 a f f u x u x ( x n ) nx n- x ( e x x ) e x ( n x) x x ( in x) co x x ( co x) -in x x n n+ Ú xx x, nπ- n + x x Ú ex e x Ú ln x x Ú co xx in x Ú in xx -co x 4

aea C cicumfeence V volume S uface aea b bae h height l length w wih aiu q c b 90 a f f u x u x ( x n ) nx n- x ( e x

5 00 AP PHYSICS C: MECHANICS REE-RESPONSE QUESIONS PHYSICS C Section II, MECHANICS ime 4 minute Quetion Diection: Anwe all thee quetion. he uggete time i about minute fo anweing each of the quetion, which ae woth point each. he pat within a quetion may not have equal weight. Show all you wok in the pink booklet in the pace povie afte each pat, NO in thi geen inet. Mech.. A ball of ma M i thown vetically upwa with an initial pee of u 0. It expeience a foce of ai eitance given by -kv, whee k i a poitive contant. he poitive iection fo all vecto quantitie i upwa. Expe all algebaic anwe in tem of M, k, u 0, an funamental contant. (a) Doe the magnitue of the acceleation of the ball inceae, eceae, o emain the ame a the ball move upwa? inceae eceae emain the ame Jutify you anwe. (b) Wite, but o NO olve, a iffeential equation fo the intantaneou pee u of the ball in tem of time t a the ball move upwa. (c) Detemine the teminal pee of the ball a it move ownwa. () Doe it take longe fo the ball to ie to it maximum height o to fall fom it maximum height back to the height fom which it wa thown? longe to ie longe to fall Jutify you anwe. (e) On the axe below, ketch a gaph of velocity veu time fo the upwa an ownwa pat of the ball flight, whee t f i the time at which the ball etun to the height fom which it wa thown. Copyight 00 by College Entance Examination Boa. All ight eeve. Viit apcental.collegeboa.com (fo AP pofeional) an (fo AP tuent an paent). GO ON O HE NEX PAGE.

Show all you wok in the pink booklet in the pace povie afte each pat, NO in thi geen inet. Mech.. A ball of ma M i thown vetically upwa with an initial pee of u 0.

6 00 AP PHYSICS C: MECHANICS REE-RESPONSE QUESIONS Mech.. A tuent i given the et of obital ata fo ome of the moon of Satun hown below an i ake to ue the ata to etemine the ma M of Satun. Aume the obit of thee moon ae cicula. S Obital Peio, (econ) Obital Raiu, R (mete) (a) Wite an algebaic expeion fo the gavitational foce between Satun an one of it moon. (b) Ue you expeion fom pat (a) an the aumption of cicula obit to eive an equation fo the obital peio of a moon a a function of it obital aiu R. (c) Which quantitie houl be gaphe to yiel a taight line whoe lope coul be ue to etemine Satun ma? () Complete the ata table by calculating the two quantitie to be gaphe. Label the top of each column, incluing unit. (e) Plot the gaph on the axe below. Label the axe with the vaiable ue an appopiate numbe to inicate the cale. (f) Uing the gaph, calculate a value fo the ma of Satun. Copyight 00 by College Entance Examination Boa. All ight eeve. Viit apcental.collegeboa.com (fo AP pofeional) an (fo AP tuent an paent). 6 GO ON O HE NEX PAGE.

(b) Ue you expeion fom pat (a) an the aumption of cicula obit to eive an equation fo the obital peio of a moon a a function of it obital aiu R.

7 00 AP PHYSICS C: MECHANICS REE-RESPONSE QUESIONS OP VIEWS Mech.. A ytem conit of a ball of ma M an a unifom o of ma M an length. he o i attache to a hoizontal fictionle table by a pivot at point P an initially otate at an angula pee w, a hown above left. he otational inetia of the o about point P i M. he o tike the ball, which i initially at et. A a eult of thi colliion, the o i toppe an the ball move in the iection hown above ight. Expe all anwe in tem of M, M, w,, an funamental contant. (a) Deive an expeion fo the angula momentum of the o about point P befoe the colliion. (b) Deive an expeion fo the pee u of the ball afte the colliion. (c) Auming that thi colliion i elatic, calculate the numeical value of the atio M M. () A new ball with the ame ma M a the o i now place a itance x fom the pivot, a hown above. Again auming the colliion i elatic, fo what value of x will the o top moving afte hitting the ball? END O SECION II, MECHANICS Copyight 00 by College Entance Examination Boa. All ight eeve. Viit apcental.collegeboa.com (fo AP pofeional) an (fo AP tuent an paent). 7

he o tike the ball, which i initially at et. A a eult of thi colliion, the o i toppe an the ball move in the iection hown above ight. Expe all anwe in tem of M, M, w,, an funamental contant.

AP Physics B 2012 Free-Response Questions

AP Physics B 2012 Free-Response Questions AP Phyic B 01 Fee-Repone Quetion About the College Boad The College Boad i a miion-diven not-fo-pofit oganization that connect tudent to college ucce and oppotunity. Founded in 1900, the College Boad wa