AP Physics C: Electricity and Magnetism 2013 Free-Response Questions

Transcription

1 AP Physcs C: Electcty an Magnetsm 3 Fee-Response Questons About the College Boa The College Boa s a msson-ven not-fo-poft oganzaton that connects stuents to college success an oppotunty. Foune n 9, the College Boa was ceate to expan access to hghe eucaton. Toay, the membeshp assocaton s mae up of moe than 6, of the wol s leang eucatonal nsttutons an s ecate to pomotng excellence an equty n eucaton. Each yea, the College Boa helps moe than seven mllon stuents pepae fo a successful tanston to college though pogams an sevces n college eaness an college success nclung the SAT an the Avance Placement Pogam. The oganzaton also seves the eucaton communty though eseach an avocacy on behalf of stuents, eucatos, an schools. 3 The College Boa. College Boa, Avance Placement Pogam, AP, AP Cental, SAT, an the acon logo ae egstee taemaks of the College Boa. Amtte Class Evaluaton Sevce an nspng mns ae taemaks owne by the College Boa. All othe poucts an sevces may be taemaks of the espectve ownes. Vst the College Boa on the Web: Pemsson to use copyghte College Boa mateals may be equeste onlne at: Vst the College Boa on the Web: AP Cental s the offcal onlne home fo the AP Pogam: apcental.collegeboa.og.

2 Poton mass, Neuton mass, m p m n TABLE OF INFORMATION DEVELOPED FOR CONSTANTS AND CONVERSION FACTORS 7.67 kg Electon chage magntue, 7 9 e.6 C.67 kg 9 electon volt, ev.6 J 3 Electon mass, m e 9. kg Spee of lght, 8 c 3. m s 3 - Unvesal gavtatonal Avogao s numbe, N 6. mol constant, 3 G 6.67 m kg s Unvesal gas constant, R 8.3 J (mol K) Acceleaton ue to gavty at Eath s suface, g 9.8 m s 3 Boltzmann s constant,.38 J K k B 7 unfe atomc mass unt, u.66 kg 93 MeV c Planck s constant, 34 5 h 6.63 Js 4.4 ev s Vacuum pemttvty, Coulomb s law constant, Vacuum pemeablty, Magnetc constant, 5 3 hc.99 J m.4 ev nm 8.85 C Nm 9 k 4p 9. Nm C 7 m 4p (T m) A 7 k m 4 p (T m) A 5 5 atmosphee pessue, atm. N m. Pa UNIT SYMBOLS mete, m mole, mol watt, W faa, F klogam, kg hetz, Hz coulomb, C tesla, T secon, s newton, N volt, V egee Celsus, C ampee, A pascal, Pa ohm, W electon-volt, ev kelvn, K joule, J heny, H PREFIXES VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES Facto Pefx Symbol q gga G snq mega M cosq klo k tanq cent c 3 mll m 6 mco m 9 nano n pco p The followng conventons ae use n ths exam. I. Unless othewse state, the fame of efeence of any poblem s assume to be netal. II. The ecton of any electc cuent s the ecton of flow of postve chage (conventonal cuent). III. Fo any solate electc chage, the electc potental s efne as zeo at an nfnte stance fom the chage. --

3 ADVANCED PLACEMENT PHYSICS C EQUATIONS DEVELOPED FOR u u at x x ut at u u a x x F F ma F p t net J Ft Dp p mv Ffc mn W F K P P mu W t Fv DUg mgh ac u w t F I t tnet a I m m cm m m 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 = mpulse K = knetc enegy k = spng constant = length L = angula momentum m = mass N = nomal foce P = powe p = momentum = aus o stance = poston vecto T = peo t = tme U = potental enegy u = velocty o spee W = wok one on a system x = poston m = coeffcent of fcton q = angle t = toque w = angula spee a = angula acceleaton f = phase angle Fs Us k x kx x x max cos( wt f p T w f T s T p F U G G p p m k g Gm m Gm m ˆ qq F 4p E F q E A Q V E V U E 4p Q C V C C ELECTRICITY AND MAGNETISM q qq qv 4p k p A C C C I s Q t Uc QV CV R A E J I Neu A V R s IR R R R p P IV F qv B M A = aea B = magnetc fel C = capactance = stance E = electc fel e = emf F = foce I = cuent J = cuent ensty L = nuctance = length n = numbe of loops of we pe unt length N = numbe of chage caes pe unt volume P = powe Q = chage q = pont chage R = esstance = stance t = tme U = potental o stoe enegy V = electc potental u = velocty o spee = esstvty f m = magnetc flux k = electc constant m I B m B 4p F Bs I 3 I B m ni fm B A e E I e L t UL LI f t m -3-

4 ADVANCED PLACEMENT PHYSICS C EQUATIONS DEVELOPED FOR GEOMETRY AND TRIGONOMETRY CALCULUS Rectangle A bh Tangle A bh Ccle A p C p Rectangula Sol V wh Cylne V p S p p Sphee 4 3 V p 3 S 4p Rght Tangle a b c a snq c b cosq c a tanq b A = aea C = ccumfeence V = volume S = suface aea b = base h = heght = length w = wth = aus q c b 9 a f f u x u x n n x nx x x x e e x ln x x x sn x cos x x cos x sn x x n n x x x, n n x e x e x x ln x x cos x x sn x sn x x cos x -5-

5 3 AP PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS PHYSICS C: ELECTRICITY AND MAGNETISM SECTION II Tme 45 mnutes 3 Questons Dectons: Answe all thee questons. The suggeste tme s about 5 mnutes fo answeng each of the questons, whch ae woth 5 ponts each. The pats wthn a queston may not have equal weght. Show all you wok n ths booklet n the spaces pove afte each pat. E&M. A vey long, sol, nonconuctng cylne of aus R has a postve chage of unfom volume ensty. A secton of the cylne fa fom ts ens s shown n the agam above. Let epesent the aal stance fom the axs of the cylne. Expess all answes n tems of, R,, an funamental constants, as appopate. (a) Usng Gauss s law, eve an expesson fo the magntue of the electc fel at a aus < R. Daw an appopate Gaussan suface on the agam. (b) Usng Gauss s law, eve an expesson fo the magntue of the electc fel at a aus > R. (c) On the axes below, sketch the gaph of electc fel E as a functon of aal stance fo = to = R. Explctly label any ntecepts, asymptotes, maxma, o mnma wth numecal values o algebac expessons, as appopate. (). Deve an expesson fo the magntue of the potental ffeence between an R.. Is the potental hghe at = o = R? = = R 3 The College Boa. Vst the College Boa on the Web: GO ON TO THE NEXT PAGE.

6 3 AP PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS (e) The nonconuctng cylne s eplace wth a conuctng cylne of the same shape an same lnea chage ensty. On the axes below, sketch the electc fel E as a functon of fo = to = R. Explctly label any ntecepts, asymptotes, maxma, o mnma wth numecal values o algebac expessons, as appopate. 3 The College Boa. Vst the College Boa on the Web: GO ON TO THE NEXT PAGE.

7 3 AP PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS E&M. In a lab, you set up a ccut that contans a capacto C, a essto R, a swtch S, an a powe supply, as shown n the agam above. The capacto s ntally unchage. The swtch, whch s ntally open, can be move to postons A o B. (a). Incate the poston to whch the swtch shoul be move to chage the capacto. A B. On the agam, aw a voltmete that s popely connecte to the ccut n a manne that wll allow the voltage to be measue acoss the capacto. Afte a long tme you move the swtch to schage the capacto, an you lab patne stats a stopwatch. You collect the followng measuements of the voltage acoss the capacto at vaous tmes. t (s) VV ( ) You wsh to etemne the tme constant t of the ccut fom the slope of a lnea gaph. (b). Incate two quanttes you woul plot to obtan a lnea gaph.. Use the emanng ows n the table above, as neee, to eco any quanttes that you ncate that ae not gven. Label each ow you use an nclue unts. 3 The College Boa. Vst the College Boa on the Web: GO ON TO THE NEXT PAGE.

8 3 AP PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS (c) On the axes below, gaph the ata fom the table that wll pouce a lnea elatonshp. Clealy scale an label all axes nclung unts, f appopate. Daw a staght lne that best fts you ata ponts. () Fom you lne n pat (c), obtan the value of the tme constant t of the ccut. (e). In the expement, the capacto C ha a capactance of.5 m F. Calculate an expemental value fo the esstance R.. On the axes n pat (c), use a ashe lne to sketch a possble gaph f the capactance was geate than.5 m F but the esstance R was the same. Justfy you answe. 3 The College Boa. Vst the College Boa on the Web: GO ON TO THE NEXT PAGE.

9 3 AP PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS E&M 3. The fgue above shows a ccula loop of aea.5 m an esstance W that les n the plane of the page. A magnetc fel of magntue B ecte nto the page exsts n the aea of the loop. The fel vaes wth tme t, as shown n the gaph below. (a). Deve an expesson fo the magntue of the nuce emf n the loop as a functon of tme fo the nteval t = s to t = 8 s.. Calculate the magntue of the nuce cuent I n the loop at tme t = 4 s. 3 The College Boa. Vst the College Boa on the Web: -- GO ON TO THE NEXT PAGE.

10 3 AP PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS (b). Sketch a gaph of the nuce cuent I n the loop as a functon of tme t fom t = s to t = 8 s on the axes below, assumng that a counteclockwse (CCW) cuent s postve.. Fo the tme nteval s to 6 s, justfy the ecton of the cuent you have ncate n you gaph. (c) Calculate the total enegy sspate n the loop ung the fst 8 s shown. STOP END OF EXAM 3 The College Boa. Vst the College Boa on the Web: --