2005 Electricity

2005 Electricity - AP® Physics C: Electricity and...

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Unformatted text preview: AP® Physics C: Electricity and Magnetism 2005 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 4,700 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three and a half 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. Copyright © 2005 by 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 Entrance Examination 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 Entrance Examination Board. PSAT/NMSQT is a registered trademark of the College Entrance Examination Board and National Merit Scholarship Corporation. Other products and services may be trademarks of their respective owners. Permission to use copyrighted College Board materials may be requested online at: http://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 and Pre-AP: apcentral.collegeboard.com. TABLE OF INFORMATION FOR 2005 CONSTANTS AND CONVERSION FACTORS 27 = 1.66 = 931 MeV/c ¥ 1 unified atomic mass unit, 10 - 1u UNITS Name Symbol 10 9 giga G kilogram kg 10 6 mega M 10 3 kilo k centi c milli m micro µ nano n pico p mn = 1.67 × 10 −27 kg second s Electron mass, me = 9.11 × 10 −31 kg ampere A e = 1.60 × 10 C kelvin N0 = 6.02 × 10 23 mol −1 R = Universal gas constant, K mole mol hertz 8.31 J / ( mol K ) ◊ Avogadro’s number, Hz Boltzmann’s constant, k B = 1.38 × 10 −23 J / K Speed of light, c = 3.00 × 10 8 m / s newton N Planck’s constant, h = 6.63 × 10 −34 J ⋅ s pascal Pa = 4.14 × 10 −15 eV ⋅ s hc = 1.99 × 10 −25 k = 1 / 4π θ sin θ cos θ tan θ C 0 0 1 0 V Ω 30 1/2 3 /2 3 /3 H 37 3/5 4/5 3/4 farad = G 6.67 g = 9.8 m / s 10 11 F tesla T 45 2 /2 2 /2 1 degree Celsius C 53 4/5 3/5 4/3 electronvolt eV 60 3 /2 1/2 3 90 3 m / kg s 2 1 atm = 1.0 × 10 5 N / m 2 = 1.0 × 10 5 Pa 1 electron volt, J W henry k = µ 0 / 4π = 10 −7 (T ⋅ m) / A ¥ 1 atmosphere pressure, VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES volt 2 = 9.0 × 10 9 N ⋅ m 2 / C 2 - Acceleration due to gravity at the Earth’s surface, 10 −12 1 0 ∞ ' Universal gravitational constant, 10 −9 ohm C / N⋅m 2 µ 0 = 4π × 10 −7 (T ⋅ m) / A Vacuum permeability, Magnetic constant, 0 = 8.85 × 10 10 −6 coulomb ◊ Coulomb’s law constant, 0 10 −3 watt J⋅m −12 10 −2 joule = 1.24 × 10 3 eV ⋅ nm Vacuum permittivity, Symbol m Neutron mass, Magnitude of the electron charge, Prefix meter 2 −19 Factor kg m p = 1.67 × 10 −27 kg Proton mass, PREFIXES 1 eV = 1.60 × 10 −19 J 2 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 2004 and 2005 t a= w Rs = t 12 t 2 a + + w -= FM = qv × B B•d = 1 f Bs = = ˆ r e -= p r2 Gm1m2 r 0 nI = B • dA dm dt dI = −L dt 1 U L = LI 2 2 e = = p m g Gm1m2 0I F= Id ×B m k f = w p = q FG 1 Ri z = 2 i 3 =− f q + w Tp 1 = Rp Ri P = IV 12 kx 2 2 i z = w kx 0 2 -= UG a = Ts A V = IR w= u Us R= I 0t dQ dt 1 1 Uc = QV = CV 2 2 2 I= m ¥= w= Â= Ú= 0 1 1 = Cs i Ci m t = t =t ¥ Fs T rp 12 I 2 Ci i ∑ = r m Cp = d ∑  Â= mr mr 2 a w u = w r 2 dm K q I net rcm L m D = F 0A r = I r Q V ∑ u r 2 0 q1 q 2 r Q q R r t U V = = = = = = = = = m= = k = r C= 4 1 f = u 2 C= ∑ Ú= ∑ ac UE = qV = r u £ m F dr 12 K m 2 dW P dt P Fv Ug mgh k N p p 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 p = Ú= W D= = F fric = dp dt F dt mv ma = = = = = = = = = L= m= N= P= p= r= r= T= t= U= = W= x= = = = = = ∑ = =u u J p Fnet a F f h I J K k e + F ( F - = 2 0 ) + u u 2 12 at 2 2 a x x0 0t + = u x0 at + x 0 ELECTRICITY AND MAGNETISM 1 q1 q 2 A = area F= 2 B = magnetic field 40r C = capacitance F d = distance E= q E = electric field = emf Q E • dA = F = force 0 I = current dV L = inductance E=− = length dr n = number of loops of wire qi 1 V= per unit length 4 0 i ri P = power p MECHANICS charge point charge resistance distance time potential or stored energy electric potential velocity or speed resistivity magnetic flux dielectric constant ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2004 and 2005 GEOMETRY AND TRIGONOMETRY area circumference volume surface area base height length width radius d f d f du dx du dx dn x nxn 1 dx dx e ex dx d 1 1n x dx x d sin x cos x dx d cos x sin x dx 1 n1 xn dx x ,n n1 ex dx ex dx ln x x cos xdx sin x ( ( ( =) ( -=) = Ú = Ú Ú Ú 4 sin xdx -= = p q a b = p p p Ú b + p p p q + a 90° cos x 1 -π ( =) c b c = =) q q tan = =) cos - A= C= V= S= b= h= = w= r= = Rectangle A = bh Triangle 1 A = bh 2 Circle A = r2 C=2r Parallelepiped V = wh Cylinder V = r2 S = 2 r + 2 r2 Sphere 43 V= r 3 S = 4 r2 Right Triangle a 2 + b2 = c2 a sin = c CALCULUS 2005 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS PHYSICS C Section II, ELECTRICITY AND MAGNETISM 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. Consider the electric field diagram above. = (a) Points A, B, and C are all located at y 0.06 m . i. At which of these three points is the magnitude of the electric field the greatest? Justify your answer. ii. At which of these three points is the electric potential the greatest? Justify your answer. (b) An electron is released from rest at point B. i. Qualitatively describe the electron’s motion in terms of direction, speed, and acceleration. ii. Calculate the electron’s speed after it has moved through a potential difference of 10 V. (c) Points B and C are separated by a potential difference of 20 V. Estimate the magnitude of the electric field midway between them and state any assumptions that you make. (d) On the diagram, draw an equipotential line that passes through point D and intersects at least three electric field lines. Copyright © 2005 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). GO ON TO THE NEXT PAGE. 5 2005 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS E&M. 2. In the circuit shown above, resistors 1 and 2 of resistance R1 and R2 , respectively, and an inductor of inductance L are connected to a battery of emf and a switch S. The switch is closed at time t = 0. Express all algebraic answers in terms of the given quantities and fundamental constants. e (a) Determine the current through resistor 1 immediately after the switch is closed. (b) Determine the magnitude of the initial rate of change of current, dI dt , in the inductor. (c) Determine the current through the battery a long time after the switch has been closed. (d) On the axes below, sketch a graph of the current through the battery as a function of time. Some time after steady state has been reached, the switch is opened. (e) Determine the voltage across resistor 2 just after the switch has been opened. Copyright © 2005 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). GO ON TO THE NEXT PAGE. 6 2005 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS E&M. 3. A student performs an experiment to measure the magnetic field along the axis of the long, 100-turn solenoid PQ shown above. She connects ends P and Q of the solenoid to a variable power supply and an ammeter as shown. End P of the solenoid is taped at the 0 cm mark of a meterstick. The solenoid can be stretched so that the position of end Q can be varied. The student then positions a Hall probe* in the center of the solenoid to measure the magnetic field along its axis. She measures the field for a fixed current of 3.0 A and various positions of the end Q. The data she obtains are shown below. Measured Magnetic Field (T) (directed from P to Q) 6.80 4 80 4.90 5 100 4.00 10 10 10 4 4 4 - 60 4 - 3 10 4 - 7.70 10 - 50 ¥ ¥ ¥ ¥ ¥ 2 9.70 n (turns/m) - 1 Position of End Q (cm) 40 Trial (a) Complete the last column of the table above by calculating the number of turns per meter. * A Hall Probe is a device used to measure the magnetic field at a point. Copyright © 2005 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). GO ON TO THE NEXT PAGE. 7 2005 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS (b) On the axes below, plot the measured magnetic field B versus n. Draw a best-fit straight line for the data points. 7 - 10 ( 4 T m A , determine the percent error in the experimental i m (d) Using the theoretical value of 0 value of 0 computed in part (c). the magnetic permeability of vacuum. ) 0, (c) From the graph, obtain the value of ¥p = m m END OF SECTION II, ELECTRICITY AND MAGNETISM Copyright © 2005 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). 8 ...
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This note was uploaded on 08/05/2009 for the course PHYS 101 taught by Professor Reich during the Spring '08 term at Johns Hopkins.

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