AP Physics C: Mechanics

08 AP Phyc C: Mechnc ee-repone Queton 08 The College Bod. College Bod, Advnced Plcement Pogm, AP, AP Centl, nd the con logo e egteed tdemk of the College Bod. Vt the College Bod on the Web: www.collegebod.og. AP Centl the offcl onlne home fo the AP Pogm: pcentl.collegebod.og.

Poton m, Neuton m, Electon m, Avogdo numbe, ADVANCED PLACEMENT PHYSICS C TABLE O INORMATION m p m n m e CONSTANTS AND CONVERSION ACTORS 7.67 0 kg 7.67 0 kg 3 9. 0 kg 3 N 0 6.0 0 mol Unvel g contnt, R 8.3 J (mol K) 3 Boltzmnn contnt,.38 0 J K k B Electon chge mgntude, 9 e.60 0 C 9 electon volt, ev.60 0 J Speed of lght, c 3.00 0 m Unvel gvttonl G 6.67 0 Nm kg Acceleton due to gvty t Eth ufce, contnt, g 9.8 m 7 unfed tomc m unt, u.66 0 kg 93 MeV c Plnck contnt, 34 5 h 6.63 0 J 4.4 0 ev 5 3 hc.99 0 J m.4 0 evnm Vcuum pemttvty, e 0 8.85 0 C Nm Coulomb lw contnt, k 4pe0 9.0 0 9 Nm C Vcuum pemeblty, 7 m0 4p 0 (Tm) A 7 Mgnetc contnt, k m0 4p 0 (Tm) A 5 5 tmophee peue, tm.0 0 N m.0 0 P 8 UNIT SYMBOLS mete, klogm, econd, mpee, kelvn, m kg A K mole, hetz, newton, pcl, joule, mol Hz N P J wtt, coulomb, volt, ohm, heny, W C V W H fd, tel, degee Celu, electon volt, T C ev PREIXES cto Pefx Symbol 9 0 gg G 6 0 meg M 3 0 klo k 0 cent c 3 0 mll m 6 0 mco m 9 0 nno n 0 pco p VALUES O TRIGONOMETRIC UNCTIONS OR COMMON ANGLES q 0 30 37 45 53 60 90 nq 0 35 45 3 coq 3 45 35 0 tnq 0 33 34 43 3 The followng umpton e ued n th exm. I. The fme of efeence of ny poblem netl unle othewe tted. II. The decton of cuent the decton n whch potve chge would dft. III. The electc potentl zeo t n nfnte dtnce fom n olted pont chge. IV. All bttee nd mete e del unle othewe tted. V. Edge effect fo the electc feld of pllel plte cpcto e neglgble unle othewe tted. --

ADVANCED PLACEMENT PHYSICS C EQUATIONS à x Ãx0 t x x x0 Ãx0t xt Ãx Ãx0 xx x0 net m m dp dt J dt Dp p mv f m N D E W d K mã P de dt P v DUg à c mgdh w t t t I I net I dm m x cm mx m à w L p Iw K Iw w w 0 t q q0 w0t t MECHANICS = cceleton E = enegy = foce f = fequency h = heght I = ottonl net J = mpule K = knetc enegy k = png contnt = length L = ngul momentum m = m P = powe p = momentum = du o dtnce T = peod t = tme U = potentl enegy v = velocty o peed W = wok done on ytem x = poton m = coeffcent of fcton q = ngle t = toque w = ngul peed = ngul cceleton f = phe ngle kdx U k x D x x mx co( wt f T T p w f T p U G G p p m k g Gm m Gm m ELECTRICITY AND MAGNETISM qq A = e E 4pe B = mgnetc feld 0 C = cpctnce d = dtnce E E q E = electc feld e = emf Q = foce E da e 0 I = cuent J = cuent denty dv Ex L = nductnce = length D n = numbe of loop of we V Ed pe unt length N = numbe of chge ce q V pe unt volume 4pe 0 P = powe Q = chge qq U q = pont chge E qv 4pe0 R = etnce = du o dtnce DV Q t = tme C U = potentl o toed enegy ke 0 A V = electc potentl C d v = velocty o peed = etvty Cp C = flux k = delectc contnt C C M qv B dq I B d m I 0 dt U m 0 Id C QDV C DV db 4p R A Id B B E J m0ni I Nevd A B B da D I V d e R B E d dt R R R R p P IDV di e L dt UL LI -3-

ADVANCED PLACEMENT PHYSICS C EQUATIONS GEOMETRY AND TRIGONOMETRY CALCULUS Rectngle A bh Tngle A Ccle bh A p C p q Rectngul Sold V wh Cylnde V p S p p Sphee 4 V p 3 S 4p 3 Rght Tngle A = e C = ccumfeence V = volume S = ufce e b = be h = heght = length w = wdth = du = c length q = ngle q d f d f du du d n x nx n d e x x e d ln x x d nx cox d cox nx n n x x, n n e x e x ln x x cox nx n x co x b c nq c b coq c tnq b q c b 90 VECTOR PRODUCTS AB ABcoq A B ABnq -4-

08 AP PHYSICS C: MECHANICS REE-RESPONSE QUESTIONS PHYSICS C: MECHANICS SECTION II Tme 45 mnute 3 Queton Decton: Anwe ll thee queton. The uggeted tme bout 5 mnute fo nweng ech of the queton, whch e woth 5 pont ech. The pt wthn queton my not hve equl weght. Show ll you wok n th booklet n the pce povded fte ech pt.. A tudent wnt to detemne the vlue of the cceleton due to gvty g fo pecfc locton nd et up the followng expement. A old phee held vetclly dtnce h bove pd by n electomgnet, hown n the fgue bove. The expementl equpment degned to elee the phee when the electomgnet tuned off. A tme lo tt when the electomgnet tuned off, nd the tme top when the phee lnd on the pd. () Whle tkng the ft dt pont, the tudent notce tht the electomgnet ctully elee the phee fte the tme begn. Would the vlue of g clculted fom th one meuement be gete thn, le thn, o equl to the ctul vlue of g t the tudent locton? Gete thn Le thn Equl to Jutfy you nwe. The electomgnet eplced o tht the tme begn when the phee eleed. The tudent ve the dtnce h. The tudent meue nd ecod the tme Δt of the fll fo ech ptcul heght, eultng n the followng dt tble. h (m) 0.0 0.0 0.60 0.80.00 Δt () 0.05 0.3 0.34 0.40 0.45 (b) Indcte below whch quntte hould be gphed to yeld tght lne whoe lope could be ued to clculte numecl vlue fo g. Vetcl x: Hozontl x: Ue the emnng ow n the tble bove, needed, to ecod ny quntte tht you ndcted tht e not gven n the tble. Lbel ech ow you ue nd nclude unt. 08 The College Bod. Vt the College Bod on the Web: www.collegebod.og. -5- GO ON TO THE NEXT PAGE.

08 AP PHYSICS C: MECHANICS REE-RESPONSE QUESTIONS (c) Plot the dt pont fo the quntte ndcted n pt (b) on the gph below. Clely cle nd lbel ll xe, ncludng unt f ppopte. Dw tght lne tht bet epeent the dt. (d) Ung the tght lne, clculte n expementl vlue fo g. Anothe tudent ft the dt n the tble to qudtc equton. The tudent equton fo the dtnce fllen y functon of tme t y = At + Bt + C, whee A = 5.75 m, B = 0.54 m, nd C = +0.080 m. Vetclly down the potve decton. (e) Ung the tudent equton bove, do the followng.. Deve n expeon fo the velocty of the phee functon of tme.. Clculte the new expementl vlue fo g.. Ung 9.8 m the ccepted vlue fo g t th locton, clculte the pecent eo fo the vlue found n pt (e). v. Aumng the phee t heght of.40 m t t= 0, clculte the velocty of the phee jut befoe t tke the pd. 08 The College Bod. Vt the College Bod on the Web: www.collegebod.og. -6- GO ON TO THE NEXT PAGE.

08 AP PHYSICS C: MECHANICS REE-RESPONSE QUESTIONS. Two ct e on hozontl, level tck of neglgble fcton. Ct h eno tht meue the foce exeted on t dung collon wth ct, whch h png ttched. Ct movng wth peed of v = 3.00 m 0 towd ct, whch t et, hown n the fgue bove. The totl m of ct nd the foce eno 0.500 kg, the m of ct.05 kg, nd the png h neglgble m. The png h png contnt of k = 30 N m. The dt fo the foce the png exet on ct e hown n the gph below. A tudent model the dt the qudtc ft = (300 N )t - (500 N )t. () Ung ntegl clculu, clculte the totl mpule delveed to ct dung the collon. (b). Clculte the peed of ct fte the collon.. In whch decton doe ct move fte the collon? Left Rght The decton undefned, becue the peed of ct zeo fte the collon. (c). Clculte the peed of ct fte the collon.. Show tht the collon between the two ct eltc. (d). Clculte the peed of the cente of m of the two-ct png ytem.. Clculte the mxmum eltc potentl enegy toed n the png. 08 The College Bod. Vt the College Bod on the Web: www.collegebod.og. -7- GO ON TO THE NEXT PAGE.

08 AP PHYSICS C: MECHANICS REE-RESPONSE QUESTIONS 3. A tngul od, hown bove, h length L, m M, nd nonunfom lne m denty gven by the M equton λ = x, whee x the dtnce fom one end of the od. L () Ung ntegl clculu, how tht the ottonl net of the od bout t left end ML. The thn hoop hown bove n gue h m M, du L, nd ottonl net ound t cente of ML. Thee od dentcl to the od fom pt () e now ftened to the thn hoop, hown n gue bove. (b) Deve n expeon fo the ottonl net I tot of the hoop-od ytem bout the cente of the hoop. Expe you nwe n tem of M, L, nd phycl contnt, ppopte. The hoop-od ytem ntlly t et nd held n plce but fee to otte ound t cente. A contnt foce exeted tngent to the hoop fo tme Δt. (c) Deve n expeon fo the fnl ngul peed ω of the hoop-od ytem. Expe you nwe n tem of M, L,, Δt, nd phycl contnt, ppopte. 08 The College Bod. Vt the College Bod on the Web: www.collegebod.og. -8- GO ON TO THE NEXT PAGE.

08 AP PHYSICS C: MECHANICS REE-RESPONSE QUESTIONS The hoop-od ytem ollng wthout lppng long level hozontl ufce wth the ngul peed ω found n pt (c). At tme t = 0, the ytem begn ollng wthout lppng up mp, hown n the fgue bove. (d). On the fgue of the hoop-od ytem below, dw nd lbel the foce (not component) tht ct on the ytem. Ech foce mut be epeented by dtnct ow ttng t, nd pontng wy fom, the pont t whch the foce exeted on the ytem.. Jutfy you choce fo the decton of ech of the foce dwn n pt (d). (e) Deve n expeon fo the chnge n heght of the cente of the hoop fom the moment t eche the bottom of the mp untl the moment t eche t m xmum heght. Expe you nwe n tem of M, L, I, ω, nd phycl contnt, ppopte. tot STOP END O EXAM 08 The College Bod. Vt the College Bod on the Web: www.collegebod.og. -9-