2006 C E_m Fr

2006 C E_m Fr - AP® Physics C: Electricity and Magnetism...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: AP® Physics C: Electricity and Magnetism 2006 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. © 2006 The College Board. All rights reserved. College Board, AP Central, APCD, Advanced Placement Program, AP, AP Vertical Teams, Pre-AP, SAT, and the acorn logo are registered trademarks of the College Board. Admitted Class Evaluation Service, CollegeEd, connect to college success, MyRoad, SAT Professional Development, SAT Readiness Program, and Setting the Cornerstones are trademarks owned by the College Board. PSAT/NMSQT is a registered trademark of the College Board and National Merit Scholarship Corporation. All other products and services may be trademarks of their respective owners. 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 1 unified atomic mass unit, 1 u = 1.66 × 10−27 kg Name = 931 MeV c 2 Proton mass, m p = 1.67 × 10 −27 kilogram kg Electron mass, me = 9.11 × 10−31 kg e = 1.60 × 10−19 C ampere Boltzmann’s constant, Speed of light, Planck’s constant, N 0 = 6.02 × 1023 mol−1 kelvin R = 8.31 J (moli K) k B = 1.38 × 10 −23 c = 3.00 × 10 m/s Vacuum permittivity, Coulomb’s law constant, k = 1 4π Vacuum permeability, 0 1 atmosphere pressure, m 1 atm = 1.0 × 10 N m 2 = 1.0 × 10 Pa 1 eV = 1.60 × 10−19 J 5 1 electron volt, Pa micro n pico -1 2 m nano -9 m p VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES kg is 2 J watt W θ sin θ cos θ coulomb C 0 0 1 0 V 30 1/2 3 /2 3 /3 W henry H 37 3/5 4/5 3/4 F 45 2 /2 2 /2 1 tesla 3 g = 9.8 m s 2 5 N 10 milli -6 c farad µ0 = 4π × 10−7 (T i m) A G = 6.67 × 10 Hz centi -3 k ohm = 9.0 × 109 Nim 2 C 2 Magnetic constant, k ′ = µ0 / 4π = 10−7 (T ⋅ m) A Universal gravitational constant, Acceleration due to gravity at Earth’s surface, 10 kilo -2 M volt eV i nm −11 10 mega 3 joule = 1.24 × 10 −12 2 C Nim2 0 = 8.85 × 10 3 10 mol pascal = 4.14 × 10−15 eVis hc = 1.99 × 10−25 J i m 10 K newton h = 6.63 × 10−34 J is 10 A hertz J/K 9 106 s mole 8 10 kg second Prefix Symbol giga G Factor m mn = 1.67 × 10−27 kg Avogadro’s number, Universal gas constant, Symbol meter Neutron mass, Electron charge magnitude, PREFIXES T 53 4/5 3/5 4/3 degree Celsius C 60 3 /2 1/2 3 90 1 0 • electronvolt eV tan θ 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 = u0 2 + 2a ( x - x0 )  F = Fnet = ma dp dt F= 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= 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 Ú r dm =  mr 2 2 rcm =  mr  m L = r ¥ p = Iw 12 Iw 2 T= 12 kx 2 E= F q ÚE Tp = 2p UG = 12 at 2 r2 Gm1m2 r q  rii 1 4p 0 V= i UE = qV = 1 q1q2 4p 0 r Q V C= k C= 0A 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 r3 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 = rJ m k Ts = 2 p F I J L 0 E=- A B C d E e Q dA= ∑ R= 2p 1 = w f FG = - w = w0 + at q = q0 + w0 t + 1 q1q2 4p 0 r 2 1 1 Uc = QV = CV 2 2 2 u = rw K= F= I= 2 t=r¥F I= ELECTRICITY AND MAGNETISM =- 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 area circumference volume surface area base height length width radius df d f du = dx du dx 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 Úx S = 2p r + 2p r 2 Úe Sphere V= 43 pr 3 S = 4p r 2 c Ú a 90° q a c b c tan q = x dx = e x dx = ln x x Ú sin x dx = - cos x a 2 + b2 = c2 cos q = dx = Ú cos x dx = sin x b Right Triangle sin q = 1 x n + 1 , n π -1 n +1 n a b 4 2006 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. The square of side a above contains a positive point charge +Q fixed at the lower left corner and negative point charges -Q fixed at the other three corners of the square. Point P is located at the center of the square. (a) On the diagram, indicate with an arrow the direction of the net electric field at point P. (b) Derive expressions for each of the following in terms of the given quantities and fundamental constants. i. The magnitude of the electric field at point P ii. The electric potential at point P (c) A positive charge is placed at point P. It is then moved from point P to point R, which is at the midpoint of the bottom side of the square. As the charge is moved, is the work done on it by the electric field positive, negative, or zero? ____ Positive ____ Negative ____ Zero Explain your reasoning. (d) i. Describe one way to replace a single charge in this configuration that would make the electric field at the center of the square equal to zero. Justify your answer. ii. Describe one way to replace a single charge in this configuration such that the electric potential at the center of the square is zero but the electric field is not zero. Justify your answer. © 2006 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 2006 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS E&M 2. The circuit above contains a capacitor of capacitance C, a power supply of emf e , two resistors of resistances R1 and R2 , and two switches, S1 and S2 . Initially, the capacitor is uncharged and both switches are open. Switch S1 then gets closed at time t = 0. (a) Write a differential equation that can be solved to obtain the charge on the capacitor as a function of time t. (b) Solve the differential equation in part (a) to determine the charge on the capacitor as a function of time t. Numerical values for the components are given as follows: e = 12 V C = 0.060 F R1 = R2 = 4700 W (c) Determine the time at which the capacitor has a voltage 4.0 V across it. After switch S1 has been closed for a long time, switch S2 gets closed at a new time t = 0. (d) On the axes below, sketch graphs of the current I1 in R1 versus time and of the current I 2 in R2 versus time, beginning when switch S2 is closed at new time t = 0. Clearly label which graph is I1 and which is I 2 . © 2006 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 2006 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS E&M 3. A loop of wire of width w and height h contains a switch and a battery and is connected to a spring of force constant k, as shown above. The loop carries a current I in a clockwise direction, and its bottom is in a constant, uniform magnetic field directed into the plane of the page. (a) On the diagram of the loop below, indicate the directions of the magnetic forces, if any, that act on each side of the loop. (b) The switch S is opened, and the loop eventually comes to rest at a new equilibrium position that is a distance x from its former position. Derive an expression for the magnitude B0 of the uniform magnetic field in terms of the given quantities and fundamental constants. © 2006 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 2006 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS The spring and loop are replaced with a loop of the same dimensions and resistance R but without the battery and switch. The new loop is pulled upward, out of the magnetic field, at constant speed u0 . Express algebraic answers to the following questions in terms of B0 , u0 , R, and the dimensions of the loop. (c) i. On the diagram of the new loop below, indicate the direction of the induced current in the loop as the loop moves upward. ii. Derive an expression for the magnitude of this current. (d) Derive an expression for the power dissipated in the loop as the loop is pulled at constant speed out of the field. (e) Suppose the magnitude of the magnetic field is increased. Does the external force required to pull the loop at speed u0 increase, decrease, or remain the same? _____ Increases _____ Decreases _____ Remains the same Justify your answer. END OF EXAM © 2006 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). 8 ...
View Full Document

This note was uploaded on 02/25/2010 for the course PHY 15166 taught by Professor Mr.donald during the Spring '10 term at 4.1.

Ask a homework question - tutors are online