2007 C E_m Fr

2007 C E_m Fr - AP® Physics C: Electricity and Magnetism...

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Unformatted text preview: AP® Physics C: Electricity and Magnetism 2007 Free-Response Questions The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the association is composed of more than 5,000 schools, colleges, universities, and other educational organizations. Each year, the College Board serves seven million students and their parents, 23,000 high schools, and 3,500 colleges through major programs and services in college admissions, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT®, the PSAT/NMSQT®, and the Advanced Placement Program® (AP®). The College Board is committed to the principles of excellence and equity, and that commitment is embodied in all of its programs, services, activities, and concerns. © 2007 The College Board. All rights reserved. College Board, Advanced Placement Program, AP, AP Central, SAT, and the acorn logo are registered trademarks of the College Board. PSAT/NMSQT is a registered trademark of the College Board and National Merit Scholarship Corporation. Permission to use copyrighted College Board materials may be requested online at: www.collegeboard.com/inquiry/cbpermit.html. Visit the College Board on the Web: www.collegeboard.com. AP Central is the official online home for the AP Program: apcentral.collegeboard.com. TABLE OF INFORMATION FOR 2006 and 2007 UNITS CONSTANTS AND CONVERSION FACTORS PREFIXES 1 u = 1.66 ¥ 10 -27 kg Name = 931 MeV c 2 1 unified atomic mass unit, meter m kilogram kg Proton mass, m p = 1.67 ¥ 10 -27 kg Neutron mass, mn = 1.67 ¥ 10 -27 kg Electron mass, me = 9.11 ¥ 10 -31 kg Boltzmann’s constant, second kelvin K 10 R = 8.31 J (mol iK) mole mol k B = 1.38 ¥ 10 -23 J /K hertz Hz h = 6.63 ¥ 10 -34 J is newton N pascal Pa joule J = 1.24 ¥ 103 eV i nm watt W 8.85 ¥ 10 -12 C2 N im 2 coulomb = 9.0 ¥ 109 N im 2 C2 hc = 1.99 ¥ 10 -25 J im Magnetic constant, Universal gravitational constant, Acceleration due to gravity at Earth’s surface, 1 atmosphere pressure, mega 10 -12 m nano 10 -9 m micro -6 c milli -3 k centi -2 M kilo 3 n pico p VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES k = 1 4p 0 m0 = 4 p ¥ 10 -7 (T im) A k ¢ = m0 /4 p = 10 -7 (T ◊ m) A G = 6.67 ¥ 10 -11 m 3 kgis2 g = 9.8 m s 2 1 atm = 1.0 ¥ 105 N m 2 1 eV = 1.60 ¥ 10 -19 J q sin q C 0 0 1 0 volt V 30 1/2 3 /2 3 /3 ohm W henry H 37 3/5 4/5 3/4 farad F 45 2 /2 2 /2 1 tesla 0= = 1.0 ¥ 105 Pa 1 electron volt, 10 N 0 = 6.02 ¥ 1023 mol -1 = 4.14 ¥ 10 -15 eVis Vacuum permeability, 10 s 10 c = 3.00 ¥ 108 m s Prefix Symbol giga G 9 106 A Planck’s constant, Coulomb’s law constant, 10 ampere Speed of light, Vacuum permittivity, Factor e = 1.60 ¥ 10 -19 C Electron charge magnitude, Avogadro’s number, Universal gas constant, Symbol cos q tan q T 53 4/5 3/5 4/3 degree Celsius ∞C 60 3 /2 1/2 3 electronvolt eV 90 1 0 • The following conventions are used in this examination. I. Unless otherwise stated, the frame of reference of any problem is assumed to be inertial. II. The direction of any electric current is the direction of flow of positive charge (conventional current). III. For any isolated electric charge, the electric potential is defined as zero at an infinite distance from the charge. -2- ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2006 and 2007 MECHANICS u = u0 + at x = x0 + u0 t + 12 at 2 u 2 = u02 + 2 a ( x - x0 )  F = Fnet = ma F= dp dt J = Ú F dt = Dp p = mv F fric £ m N W= ÚF K= 12 mu 2 P= dW dt ∑ dr P=Fv DUg = mgh ac = a F f h I J K k = = = = = = = = = L= m= N= P= p= r= r= T= t= U= u= W= x= m= q= t= w= a= ELECTRICITY AND MAGNETISM acceleration force frequency height rotational inertia impulse kinetic energy spring constant length angular momentum mass normal force power momentum radius or distance position vector period time potential energy velocity or speed work done on a system position coefficient of friction angle torque angular speed angular acceleration u = w2 r r Fs = - k x Us =  t = t net = I a I = Ú r dm =  mr 2 2 rcm =  mr  m E= F q ÚE T= 12 kx 2 L = r ¥ p = Iw 12 Iw 2 FG = - w = w0 + at UG = 12 at 2 r2 Gm1m2 r q  rii 1 4p 0 V= i UE = qV = 1 q1q2 4p 0 r Q V C= 0A k C= d  Ci Cp = i 1 1 = Cs Ci i dQ dt r A V = IR Rs = ˆ r  Ri 1 = Rp 1 ÂR i P = IV FM = qv ¥ B -3- area magnetic field capacitance distance electric field emf force current current density inductance length number of loops of wire per unit length number of charge carriers per unit volume power charge point charge resistance distance time potential or stored energy electric potential velocity or speed resistivity magnetic flux dielectric constant N= P Q q R r t U = = = = = = = V= u= r= fm = k= ÚB ∑ d = m0 I dB = m0 I d ¥ r 4p r 3 ÚI d ¥B Bs = m0 nI fm = Ú B ∑ d A d fm dt e i i n = = = = = = = = = = = = F= I = Neud A g Gm1m2 dV dr E=- E = rJ m k Tp = 2 p F I J L 0 R= 2p 1 = f w Ts = 2 p dA= ∑ A B C d E e Q 1 1 Uc = QV = CV 2 2 2 u = rw q = q0 + w0t + 1 q1q2 4p 0 r 2 I= 2 t=r¥F K= F= =- e = -L UL = dI dt 12 LI 2 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2006 and 2007 GEOMETRY AND TRIGONOMETRY Rectangle A = bh Triangle A= 1 bh 2 Circle A = pr2 C = 2p r Parallelepiped V = wh Cylinder A= C= V= S= b= h= = w= r= CALCULUS df d f du = dx du dx area circumference volume surface area base height length width radius dn ( x ) = nxn - 1 dx dx (e ) = e x dx d (1n x ) = 1 dx x d (sin x ) = cos x dx d (cos x ) = - sin x dx V = pr2 Sphere 43 pr 3 a c tan q = dx = e x dx = ln x x Ú sin x dx = - cos x a 2 + b2 = c 2 b c x Ú cos x dx = sin x Right Triangle cos q = dx = Ú S = 4p r 2 sin q = n Úe S = 2p r + 2p r 2 V= 1 x n + 1 , n π -1 n +1 Úx c a 90° q a b b -4- 2007 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS PHYSICS C: ELECTRICITY AND MAGNETISM SECTION II Time—45 minutes 3 Questions Directions: Answer all three questions. The suggested time is about 15 minutes for answering each of the questions, which are worth 15 points each. The parts within a question may not have equal weight. Show all your work in the pink booklet in the spaces provided after each part, NOT in this green insert. E&M 1. A student sets up the circuit above in the lab. The values of the resistance and capacitance are as shown, but the constant voltage e delivered by the ideal battery is unknown. At time t = 0, the capacitor is uncharged and the student closes the switch. The current as a function of time is measured using a computer system, and the following graph is obtained. (a) Using the data above, calculate the battery voltage e. (b) Calculate the voltage across the capacitor at time t = 4.0 s. (c) Calculate the charge on the capacitor at t = 4.0 s. © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). GO ON TO THE NEXT PAGE. -5- 2007 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS (d) On the axes below, sketch a graph of the charge on the capacitor as a function of time. (e) Calculate the power being dissipated as heat in the resistor at t = 4.0 s. (f) The capacitor is now discharged, its dielectric of constant k = 1 is replaced by a dielectric of constant k = 3 , and the procedure is repeated. Is the amount of charge on one plate of the capacitor at t = 4.0 s now greater than, less than, or the same as before? Justify your answer. _____Greater than _____Less than _____The same © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). GO ON TO THE NEXT PAGE. -6- 2007 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS E&M 2. In the figure above, a nonconducting solid sphere of radius a with charge +Q uniformly distributed throughout its volume is concentric with a nonconducting spherical shell of inner radius 2a and outer radius 3a that has a charge -Q uniformly distributed throughout its volume. Express all answers in terms of the given quantities and fundamental constants. (a) Using Gauss’s law, derive expressions for the magnitude of the electric field as a function of radius r in the following regions. i. Within the solid sphere ( r < a ) ii. Between the solid sphere and the spherical shell ( a < r < 2 a ) iii. Within the spherical shell ( 2 a < r < 3a ) iv. Outside the spherical shell ( r > 3a ) (b) What is the electric potential at the outer surface of the spherical shell ( r = 3a )? Explain your reasoning. (c) Derive an expression for the electric potential difference VX - VY between points X and Y shown in the figure. © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). GO ON TO THE NEXT PAGE. -7- 2007 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS E&M 3. In the diagram above, a nichrome wire of resistance per unit length l is bent at points P and Q to form horizontal conducting rails that are a distance L apart. The wire is placed within a uniform magnetic field of magnitude B pointing into the page. A conducting rod of negligible resistance, which was aligned with end PQ at time t = 0, slides to the right with constant speed u and negligible friction. Express all algebraic answers in terms of the given quantities and fundamental constants. (a) Indicate the direction of the current induced in the circuit. ______Clockwise ______Counterclockwise Justify your answer. (b) Derive an expression for the magnitude of the induced current as a function of time t. (c) Derive an expression for the magnitude of the magnetic force on the rod as a function of time. (d) On the axes below, sketch a graph of the external force Fext as a function of time that must be applied to the rod to keep it moving at constant speed while in the field. Label the values of any intercepts. (e) The force pulling the rod is now removed. Indicate whether the speed of the rod increases, decreases, or remains the same. ______Increases _____Decreases ______Remains the same Justify your answer. END OF EXAM © 2007 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). -8- ...
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