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Chapter 17Practice Test 1

Section IPHYSICS CPhysics C has two exams: Physics C (Mechanics) and Physics C (Electricity & Magnetism):Physics C (Mechanics)Physics C (Electricity & Magnetism)First 45 min.Sec. I, Multiple Choice35 questionsSec. I, Multiple Choice35 questionsSecond 45 min.Sec. II, Free-Response3 questionsSec. II, Free-Response3 questionsYou may take just Mechanics or just Electricity and Magnetism, or both. If you take both, you will receive a separate grade foreach. Each section of each examination is 50 percent of the total grade; each question in a section has equal weight. Calculators areNOT permitted on the multiple-choice section of the exam but are allowed on the free-response section. However, calculators cannotbe shared with other students and calculators with typewriter-style (QWERTY) keyboards will not be permitted. On the followingpages you will find the Table of Information that is provided to you during the exam.If you are taking— Mechanics only, please be careful to answer numbers 1–35;— Electricity and Magnetism only, please be careful to answer numbers 36–70;— the entire examination (Mechanics and Electricity and Magnetism), answer numbers 1 –70 on your answer sheet.GO ON TO THE NEXT PAGE.510 Cracking the AP Physics C Exam

Section IAdvanced Placement ExaminationPHYSICS CSECTION ITABLE OF INFORMATION FOR 2010TABLE OF INFORMATIONFORFOR20062009and 2007–272eGO ON TO THE NEXT PAGE.Practice Test 1 5 11

Section IPHYSICS CSECTION I, MECHANICSTime—45 minutes35 QuestionsDirections: Each of the questions or incomplete statements below is followed by five suggested answers or completions. Select theone that is best in each case and then mark it on your answer sheet.1. A rock is dropped off a cliff and falls the first half of thedistance to the ground in t1 seconds. If it falls the secondhalf of the distance in t2 seconds, what is the value of t2/t1? (Ignore air resistance.)((A) 1 2 2(B) 1I. Conservation of linear momentumII. Zero net external forceIII. Zero net external torque)2(C) 1/2((D) 1 1(E)4. Which of the following conditions will ensure that angular momentum is conserved?2)(A)(B)(C)(D)(E)I and II onlyI and III onlyII and III onlyII onlyIII only2 1FT2. A box of mass m slides on a horizontal surface with initial speed v0. It feels no forces other than gravity and theforce from the surface. If the coefficient of kinetic frictionbetween the box and the surface is µ, how far does thebox slide before coming to rest?θmR 2(A) v0 (2 g )(B)v02 ( g )(C) 2 v ( g )20(D)mv02 ( g )(E)2 mv02 ( g )3. An object initially at rest experiences a time-varyingacceleration given by a (2 m/s3)t for t 0. How fardoes the object travel in the first 3 seconds?(A)(B)(C)(D)(E)9m12 m18 m24 m27 m5. In the figure shown, a tension force FT causes a particleof mass m to move with constant angular speed ω in a circular path (perpendicular to the page) of radius R. Whichof the following expressions gives the magnitude of FT?(A) mω 2 R(B)m ω 4 R 2 g2(C)m ω 4 R 2 g2(((D) m ω 2 R g(E)m ω2R g))GO ON TO THE NEXT PAGE.512 Cracking the AP Physics C Exam

Section I6. An object (mass m) above the surface of the Moon(mass M) is dropped from an altitude h equal to theMoon’s radius (R). With what speed will the object strikethe lunar surface?(A)GM / R(B)GM / (2 R )(C)2GM / R(D)2GMm / R(E)GMm / (2 R )F 9. A uniform cylinder, initially at rest on a frictionless,horizontal surface, is pulled by a constant force F fromtime t 0 to time t T. From time t T on, this force isremoved. Which of the following graphs best illustratesthe speed, v, of the cylinder’s center of mass from t 0 tot 2T?(A)vtimem7. The figure above shows a linear spring anchored to theceiling. If the mass of the block hanging from its lowerend is doubled, what effect will this change have on theblock’s equilibrium position and oscillation period?(A) Equilibrium position: Lowered by a factor of 2Oscillation period: Decreased by a factor of 2(B) Equilibrium position: Lowered by a factor of 2Oscillation period: Increased by a factor of 2(C) Equilibrium position: Lowered by a factor of 2Oscillation period: Increased by a factor of 2(D) Equilibrium position: Lowered by a factor of 2Oscillation period: Decreased by a factor of 2(E) Equilibrium position: Lowered by a factor of 2Oscillation period: Increased by a factor of 2(B)vtime(C)vtime(D)vtimemass m(E)8. A uniform cylinder of mass m and radius r unrolls withoutslipping from two strings tied to a vertical support. If therotational inertia of the cylinder is 12 mr2, find the acceleration of its center of mass.(A)(B)14g12g(C)13(D)23(E)34vtimegggGO ON TO THE NEXT PAGE.Practice Test 1 513

Section I10. An engine provides 10 kW of power to lift a heavy loadat constant velocity a distance of 20 m in 5 s. What is themass of the object being lifted?(A)(B)(C)(D)(E)100 kg150 kg200 kg250 kg500 kg14. A disk of radius 0.1 m initially at rest undergoes an angular acceleration of 2.0 rad/s2. If the disk only rotates, findthe total distance traveled by a point on the rim of thedisk in 4.0 s.(A)(B)(C)(D)(E)0.4 m0.8 m1.2 m1.6 m2.0 m11. A satellite is in circular orbit around Earth. If the workrequired to lift the satellite to its orbit height is equal tothe satellite’s kinetic energy while in this orbit, how highabove the surface of Earth (radius R) is the satellite?(A)(B)1223R2RRR(C) R(D)32xsurfaceR(E) 2R1215. In the figure above, a small ball slides down a frictionlessquarter-circular slide of radius R. If the ball starts fromrest at a height equal to 2R above a horizontal surface,find its horizontal displacement, x, at the moment itstrikes the surface.MM(A) 2RSupport 1Support 2(B)52R(C) 3R12. The figure above shows a uniform bar of mass M restingon two supports. A block of mass 12 M is placed on thebar twice as far from Support 2 as from Support 1. If F1and F2 denote the downward forces on Support 1 andSupport 2, respectively, what is the value of F2/F1?(A)(B)(C)(D)(E)(D)72R(E) 4R1/22/33/44/55/613. A rubber ball (mass 0.08 kg) is dropped from a heightof 3.2 m, and after bouncing off the floor, rises almostto its original height. If the impact time with the floor ismeasured to be 0.04 s, what average force did the floorexert on the ball?(A)(B)(C)(D)(E)0.16 N0.16 N0.32 N0.36 N0.64 NGO ON TO THE NEXT PAGE.514 Cracking the AP Physics C Exam

Section IparticleScreen 2yI. The car will experience a greater impulse thanthe truck.R0II. The car will experience a greater change in momentum than the truck.0Screen 1x16. The figure above shows a particle executing uniformcircular motion in a circle of radius R. Light sources (notshown) cause shadows of the particle to be projectedonto two mutually perpendicular screens. The positivedirections for x and y along the screens are denoted bythe arrows. When the shadow on Screen 1 is at positionx –(0.5)R and moving in the x direction, what is trueabout the position and velocity of the shadow on Screen 2at that same instant?(A)(B)(C)(D)(E)18. A lightweight toy car crashes head-on into a heaviertoy truck. Which of the following statements is true as aresult of the collision?y –(0.866)R; velocity in –y directiony –(0.866)R; velocity in y directiony –(0.5)R; velocity in –y directiony (0.866)R; velocity in –y directiony (0.866)R; velocity in y directionm14LIII. The magnitude of the acceleration experiencedby the car will be greater than that experiencedby the truck.(A)(B)(C)(D)(E)I and II onlyII onlyIII onlyII and III onlyI, II, and III19. A homogeneous bar is lying on a flat table. Besides thegravitational and normal forces (which cancel), the bar isacted upon by exactly two other external forces, F1 andF2, which are parallel to the surface of the table. If thenet force on the rod is zero, which one of the following isalso true?(A) The net torque on the bar must also be zero.(B) The bar cannot accelerate translationally orrotationally.(C) The bar can accelerate translationally if F1 and F2are not applied at the same point.(D) The net torque will be zero if F1 and F2 are appliedat the same point.(E) None of the aboveFL2m17. The figure shows a view from above of two objectsattached to the end of a rigid massless rod at rest on africtionless table. When a force F is applied as shown, theresulting rotational acceleration of the rod about its centerof mass is kF/(mL). What is k?(A)38(B)12(C)58(D)34(E)5620. An astronaut lands on a planet whose mass and radius areeach twice that of Earth. If the astronaut weighs 800 Non Earth, how much will he weigh on this planet?(A) 200 N(B) 400 N(C) 800 N(D) 1600 N(E) 3200 NGO ON TO THE NEXT PAGE.Practice Test 1 515

Section IF (N)24. If L, M, and T denote the dimensions of length, mass, andtime, respectively, what are the dimensions of impulse?20(A)(B)(C)(D)(E)10123x (in m)4y21. A particle of mass m 1.0 kg is acted upon by a variableforce, F(x), whose strength is given by the graph givenabove. If the particle’s speed was zero at x 0, what isits speed at x 4 m?(A)(B)(C)(D)(E)45 v2 v'25. The figure shown is a view from above of two clay ballsmoving toward each other on a frictionless surface. Theycollide perfectly inelastically at the indicated point andare observed to then move in the direction indicated bythe post-collision velocity vector, v’. If m1 2m2 what isv2?(A)(B)(C)(D)(E)v0m260 v14161621631641m xm15.0 m/s8.7 m/s10 m/s14 m/s20 m/s22. The radius of a collapsing spinning star (assumed to be a1uniform sphere) decreases to 16 its initial value. What isthe ratio of the final rotational kinetic energy to the initialrotational kinetic energy?(A)(B)(C)(D)(E)LM/T 3LM/T 2LM/TL2M/T 2M 2L/Tv1(sin 45 )/(2 sin 60 )v1(cos 45 )/(2 cos 60 )v1(2 cos 45 )/(cos 60 )v1(2 sin 45 )/(sin 60 )v1(cos 45 )/(2 sin 60 )60 20 m0m23. A ball is projected with an initial velocity of magnitudev0 40 m/s toward a vertical wall as shown in the figureabove. How long does the ball take to reach the wall?(A)(B)(C)(D)(E)0.25 s0.6 s1.0 s2.0 s3.0 sGO ON TO THE NEXT PAGE.516 Cracking the AP Physics C Exam

Section I s 0.80zmM(1 m, 1 m)26. In the figure above, the coefficient of static friction between the two blocks is 0.80. If the blocks oscillate witha frequency of 2.0 Hz, what is the maximum amplitudeof the oscillations if the small block is not to slip on thelarge block?(A)(B)(C)(D)(E)(3 m, 3 m)3.1 cm5.0 cm6.2 cm7.5 cm9.4 cm27. When two objects collide, the ratio of the relative speedafter the collision to the relative speed before the collision is called the coefficient of restitution, e. If a ballis dropped from height H1 onto a stationary floor, andthe ball rebounds to height H2, what is the coefficient ofrestitution of the collision?(0, 0)Path 1(A) 60 J(B) 80 J(C) 90 J(D) 100 J(E) 120 Jspring constant kmH2 H1(C)H1 H2(D)H2 H1(E)( H1 H2 )2x 040 cm40 cmF28. The figure above shows a square metal plate of sidelength 40 cm and uniform density, lying flat on a table.A force F of magnitude 10 N is applied at one of thecorners, as shown. Determine the torque produced by Frelative to the center of rotation.(A)(B)(C)(D)(E)x29. A small block of mass m 2.0 kg is pushed from theinitial point (xi , zi) (0 m, 0 m) upward to the final point(xf , zf) (3 m, 3 m) along the path indicated. Path 1 is aportion of the parabola z x2, and Path 2 is a quarter circlewhose equation is (x – 2)2 (z – 2)2 2. How much work isdone by gravity during this displacement?(A) H2 H1(B)Path 2x A30. In the figure shown, the block (mass m) is at rest atx A. As it moves back toward the wall due to the forceexerted by the stretched spring, it is also acted upon by africtional force whose strength is given by the expressionbx, where b is a positive constant. What is the block’sspeed when it first passes through the equilibrium position (x 0)?(A)A ( k b) m(B)A ( k b) m(C)A(D) A(E) A( 12 k b ) m( 21 k b) m1k b) m2(0 N m1.0 N m1.4 N m2.0 N m4.0 N mGO ON TO THE NEXT PAGE.Practice Test 1 5 17

Section I33. At what angle to the horizontal should an ideal projectile be launched so that its horizontal displacement (therange) is equal to its maximum vertical displacement?xx Lx 031. The rod shown above can pivot about the point x 0 androtates in a plane perpendicular to the page. Its lineardensity, λ, increases with x such that λ(x) kx, wherek is a positive constant. Determine the rod’s moment ofinertia in terms of its length, L, and its total mass, (D)(E)34. A particle’s kinetic energy is changing at a rate of –6.0 J/swhen its speed is 3.0 m/s. What is the magnitude of theforce on the particle at this moment?(A)(B)(C)(D)(E)32. A particle is subjected to a conservative force whosepotential energy function isU(x) (x – 2)3 – 12xwhere U is given in joules when x is measured in meters.Which of the following represents a position of stableequilibrium?(A) x –4(B) x –2(C) x 0(D) x 2(E) x 4sin–1 (1/g)cos–1 (1/g)45 tan–1 2tan–1 40.5 N2.0 N4.5 N9.0 N18 N35. An object of mass 2 kg is acted upon by three externalforces, each of magnitude 4 N. Which of the followingcould NOT be the resulting acceleration of the object?(A)(B)(C)(D)(E)0 m/s22 m/s24 m/s26 m/s28 m/s2END OF SECTION I518 Cracking the AP Physics C Exam

Section IIPHYSICS CSECTION IIFree-Response QuestionsMechanics45 minutes3 required questions of equal weightTABLE OF INFORMATIONTABLE OF INFORMATIONFORFOR20062009and 2007–272eGO ON TO THE NEXT PAGE.Practice Test 1 519

Section IIADVANCED PLACEMENT PHYSICS C EQUATIONSGO ON TO THE NEXT PAGE.520 Cracking the AP Physics C Exam

Section IIADVANCED PLACEMENT PHYSICS C EQUATIONSGO ON TO THE NEXT PAGE.Practice Test 1 521

Section IIPHYSICS CSECTION II, MECHANICSTime—45 minutes3 QuestionsDirections: Answer all three questions. The suggested time is about 15 minutes per question for answering each of the questions,which are worth 15 points each. The parts within a question may not have equal weight.Mech 1.A massless, frictionless pulley is suspended from a rigid rod attached to the roof of an elevator car. Two masses, m andM (with M m), are suspended on either side of the pulley by a light, inextendable cord. The distance from the top ofthe elevator car to the center of mass of the pulley, yp , is fixed.top ofelevator sha cableypm(a)(b)MelevatorcarAssume that the elevator car is descending at constant velocity. For each of the following, write your answerin terms of m, M, and g.(i)Determine the accelerations of the masses.(ii)Find the tension in the cord.Now assume that the elevator car is descending with a nonzero (but constant) acceleration, b.(i)State why the coordinate system that uses the center of the pulley as its origin is not an inertial reference system.For parts (ii) and (iii), use the top of the elevator shaft as a reference. Write your answers in terms of m, M, g, and b.(ii)Find the acceleration of the masses.(iii)Determine the tension in the cord.(iv)For what value of b would the answer to part (iii) be zero?GO ON TO THE NEXT PAGE.522 Cracking the AP Physics C Exam

Section IIMech 2.A narrow tunnel is drilled through Earth (mass M, radius R), connecting points P and Q, as shown in the diagramon the left below. The perpendicular distance from Earth’s center, C, to the tunnel is x. A package (mass m) isdropped from Point P into the tunnel; its distance from P is denoted y and its distance from C is denoted r. See thediagram on the right.PPRRyCxxCrpackageQ(a)QAssuming that Earth is a homogeneous sphere, use the fact that the gravitational force F on the package is dueto m and the mass contained within the sphere of radius r R to show thatF GMmrR3(b)Use the equation F(r) –dU/dr to find an expression for the change in gravitational potential energy of thepackage as it moves from Point P to a point where its distance from Earth’s center is r. Write your answer interms of G, M, m, R, and r.(c)Apply Conservation of Energy to determine the speed of the package in terms of G, M, R, x, and y. (Ignorefriction.)(d)(i)At what point in the tunnel—that is, for what value of y—will the speed of the package be maximized?(ii)What is this maximum speed? (Write your answer in terms of G, M, R, and x.)GO ON TO THE NEXT PAGE.Practice Test 1 523

Section IIMech 3.The diagram below is a view from above of three sticky hockey pucks on a frictionless horizontal surface. The puckswith masses m and 2m are connected by a massless rigid rod of length L and are initially at rest. The puck of mass 3mis moving with velocity v directly toward puck m. When puck 3m strikes puck m, the collision is perfectly inelastic.2mL3m(a)(b)vmImmediately after the collision,(i)where is the center of mass of the system?(ii)what is the speed of the center of mass? (Write your answer in terms of v.)(iii)what is the angular speed of the system? (Write your answer in terms of v and L.)What fraction of the system’s initial kinetic energy is lost as a result of the collision?STOPEND OF SECTION II, MECHANICS524 Cracking the AP Physics C Exam

Section ITABLE OF INFORMATIONTABLE OF INFORMATIONFORFOR20062009and 2007–272eGO ON TO THE NEXT PAGE.Practice Test 1 525

Section IPHYSICS CSECTION I, ELECTRICITY AND MAGNETISMTime—45 minutes35 QuestionsDirections: Each of the questions or incomplete statements below is followed by five suggested answers or completions. Select theone that is best in each case and mark it on your answer sheet.36. A nonconducting sphere is given a nonzero net electriccharge, Q, and then brought close to a neutral conducting sphere of the same radius. Which of the followingwill be true?(A) An electric field will be induced within theconducting sphere.(B) The conducting sphere will develop a net electriccharge of –Q.(C) The spheres will experience an electrostaticattraction.(D) The spheres will experience an electrostaticrepulsion.(E) The spheres will experience no electrostaticinteraction.38. Each of the following ionized isotopes is projected withthe same speed into a uniform magnetic field B such thatthe isotope’s initial velocity is perpendicular to B. Whichcombination of mass and charge would result in a circularpath with the largest radius?(A)(B)(C)(D)(E)m 16 u, q –5 em 17 u, q –4 em 18 u, q –3 em 19 u, q –2 em 20 u, q –1 e37. Which of the following would increase the capacitance ofa parallel-plate capacitor?(A) Using smaller plates(B) Replacing the dielectric material between the plateswith one that has a smaller dielectric constant(C) Decreasing the voltage between the plates(D) Increasing the voltage between the plates(E) Moving the plates closer togetherGO ON TO THE NEXT PAGE.526 Cracking the AP World History Exam

Section I39. An ellipsoid-shaped conductor is negatively charged.Which one of the following diagrams best illustrates thecharge distribution and electric field lines?AB(A)CD(B)(C)40. The four wires shown above are each made ofaluminum. Which wire will have the greatestresistance?(A)(B)(C)(D)(E)Wire AWire BWire CWire DAll the wires have the same resistance, becausethey’re all composed of the same material.41. Which of the following is NOT equal to one tesla?(A)(B)(C)(D)(E)1 J/(A m2)1 kg/(C s)1 N/(A m)1 V·s/m21 A·N/V(D)(E)GO ON TO THE NEXT PAGE.Practice Test 1 527

Section IIISectionneutralinsulating supportdddd–q42. The figure above shows two Gaussian surfaces: a cubewith side length d and a sphere with diameter d. The netelectric charge enclosed within each surface is the same, Q. If ΦC denotes the total electric flux through the cubical surface, and ΦS denotes the total electric flux throughthe spherical surface, then which of the following is true?(A)(B)(C)(D)(E)ΦC (π/6)ΦSΦC (π/3)ΦSΦC ΦSΦC (3/π)ΦSΦC (6/π)ΦSx43. The figure above shows two large vertical conductingplates that carry equal but opposite charges. A ball ofmass m and charge –q is suspended from a light string inthe region between the plates. If the voltage between theplates is V, which of the following gives the angle θ?(A)(B)(C)(D)(E)cos–1 (qV/mgx)sin–1 (qV/mgx)tan–1 (qV/mgx)cos–1 (qV/x)sin–1 (qV/x)44. An object carries a charge of –1 C. How many excesselectrons does it contain?(A)(B)(C)(D)(E)6.25 10188.00 10181.60 10193.20 10196.25 1019GO ON TO THE NEXT PAGE.528 Cracking the AP Physics C Exam

Section IIISection47. What is the value of the following product?Questions 45–46Each of the resistors shown in the circuit below has a resistanceof 200 Ω. The emf of the ideal battery is 24 V.R1εR2R3R445. How much current is provided by the source?(A)(B)(C)(D)(E)30 mA48 mA64 mA72 mA90 mA46. What is the ratio of the power dissipated by R1 to thepower dissipated by R4?(A)(B)(C)(D)(E)1/91/4149(A)(B)(C)(D)(E)20 µF 500 Ω0.01 henry0.01 ampere per coulomb0.01 weber0.01 second0.01 volt per ampere B 48. A copper wire in the shape of a circle of radius 1 m,lying in the plane of the page, is immersed in a magnetic field, B, that points into the plane of the page. Thestrength of B varies with time, t, according to the equationB(t) 2t(1 – t)where B is given in teslas when t is measured in seconds.What is the magnitude of the induced electric field in thewire at time t 1 s?(A) (1/π) N/C(B) 1 N/C(C) 2 N/C(D) π N/C(E) 2π N/CGO ON TO THE NEXT PAGE.Practice Test 1 529

Section IIISectionaaayaB1aI23axam2Iaa49. In the figure above, the top half of a rectangular loop ofwire, x meters by y meters, hangs vertically in a uniformmagnetic field, B. Describe the magnitude and directionof the current in the loop necessary for the magnetic forceto balance the weight of the mass m supported by theloop.(C)51. The figure above shows a pair of long, straight currentcarrying wires and four marked points. At which of thesepoints is the net magnetic field zero?(A)(B)(C)(D)(E)(A) I mg/xB, clockwise(B) I mg/xB, counterclockwise1 I mg / x y B , clockwise2 4Point 1 onlyPoints 1 and 2 onlyPoint 2 onlyPoints 3 and 4 onlyPoint 3 only(D) I mg / x 1 y B , counterclockwise2 (E) I mg/(x y)B, clockwiseRaxisL50. A solid nonconducting cylinder of radius R and lengthL contains a volume charge density given by the equation ρ(r) ( 3 C/m4)r, where r is the radial distancefrom the cylinder’s central axis. This means that thetotal charge contained within a concentric cylinder ofradius r R and length L is equal to 2π r3. Find anexpression for the strength of the electric field insidethis cylinder.(A) 1/e0r2(B) r/2e0(C) 2r/e0(D) r2/e0(E) r2/2e0530 Cracking the AP Physics C ExamGO ON TO THE NEXT PAGE.

Section IIISection QQ1 24 µC qC1 3 µFfixed inposition52. The figure above shows two positively charged particles.The Q charge is fixed in position, and the q charge isbrought close to Q and released from rest. Which of thefollowing graphs best depicts the acceleration of the qcharge as a function of its distance r from Q? S(A)Q2 12 µCaC2 6 µFr(B)ar53. Once the switch S in the figure above is closed and electrostatic equilibrium is regained, how much charge willbe stored on the positive plate of the6 µF capacitor?(A)(B)(C)(D)(E)9 µC18 µC24 µC27 µC36 µC(C)ar(D)ar(E)arGO ON TO THE NEXT PAGE.Practice Test 1 531

Section IIISectionX2RB vLY54. A metal bar of length L is pulled with velocity v througha uniform magnetic field, B, as shown above. What is thevoltage produced between the ends of the bar?(A)(B)(C)(D)(E)vB, with Point X at a higher potential than Point YvB, with Point Y at a higher potential than Point XvBL, with Point X at a higher potential than Point YvBL, with Point Y at a higher potential than Point XNone of the above55. An electric dipole consists of a pair of equal but oppositepoint charges of magnitude 4.0 nC separated by a distance of 2.0 cm. What is the electric field strength at thepoint midway between the charges?(A)(B)(C)(D)(E)09.0 104 V/m1.8 105 V/m3.6 105 V/m7.2 105 V/mRinsulatingsupport56. The figure above shows a cross section of two concentricspherical metal shells of radii R and 2R, respectively.Find the πε0R4πε0R8πε0R57. Traveling at an initial speed of 1.5 106 m/s, a protonenters a region of constant magnetic field, B, of magnitude 1.0 T. If the proton’s initial velocity vector makes anangle of 30 with the direction of B, compute the proton’sspeed 4 s after entering the magnetic field.(A)(B)(C)(D)(E)5.0 105 m/s7.5 105 m/s1.5 106 m/s3.0 106 m/s6.0 106 m/sGO ON TO THE NEXT PAGE.532 Cracking the AP Physics C Exam

Section IIISectionQuestions 58–60There is initially no current through any circuit element in thefollowing diagram.60. After having been closed for a long time, the switch issuddenly opened. What is the current through r immediately after S is opened?(A) 0(B)S (C)Rr(D)RεL(E)εr Rεr 2Rε(r R)rRε(2 R)r (2 R ) 2 R58. What is the current through r immediately after theswitch S is closed?(C)(D)ε(B)(C)(D)(E) 6a2aY r 2R qε(r R)rRε(2 R)2 Rr 2 R59. After the switch has been kept closed for a long time,how much energy is stored in the inductor?(A)2aXLε 22(r R )2Lε 22(r 2 R )2Lε 24 (2r R ) 2L (εR)28(2r R)2(E)εr R(B)(A) 02a 2a 2a61. A solid, neutral metal sphere of radius 6a contains asmall cavity, a spherical hole of radius a as shown above.Within this cavity is a charge, q. If EX and EY denote thestrength of the electric field at points X and Y respectively, which of the following is true?(A)(B)(C)(D)(E)EY 4EXEY 16EXEY EXEY (11/5)EXEY (11/5)2EXLε 28(2r R )2GO ON TO THE NEXT PAGE.Practice Test 1 533

Section IIISection64. What is the maximum number of 40 W light bulbs thatcould be connected in parallel with a 120 V source? Thetotal current cannot exceed 5 A or the circuit will blow afuse.y(m)4P2 Q–4 Q–22x(m)(A) 3(B) 6(C) 9(D) 12(E) 15462. Two particles of charge Q are located on the x-axis, asshown above. Determine the work done by the electricfield to move a particle of charge –Q from very far awayto point P.(A)2 kQ5(B)2 kQ 252 kQ52kQ(D)5(C) (E) B 65. The metal loop of wire shown above is situated in amagnetic field B pointing out of the plane of the page. IfB decreases uniformly in strength, the induced electriccurrent within the loop is(A)(B)(C)(D)(E)2clockwise and decreasingclockwise and increasingcounterclockwise and decreasingcounterclockwise and constantcounterclockwise and increasing3kQ 2563. A battery is connected in series with a switch, a resistorof resistance R, and an inductor of inductance L. Initially,there is no current in the circuit. Once the switch is closedand the circuit is completed, how long will it take for thecurrent to reach 99% of its maximum value?(A) (ln99) RL100Lε 28(2r1 R )2)L / R(C) (ln100(D) L / R(ln 100 )99(B)(E)(ln 100)LRGO ON TO THE NEXT PAGE.534 Cracking the AP Physics C Exam

Section Iarea AWvacuumddielectric slab4Id66. A dielectric of thickness 3 is placed between the plates2IU3Idielectric constant of the slab, what is the capacitance?(B)dε 0 A(2 3K )(C)3ε 0 Ad (2 K 1)(D)3 Kε 0 Ad ( 2 K 1)(E)3 Kε 0 Ad QY68. The figure above shows four current-carrying wirespassing perpendicularly through the interior of a squarewhose vertices are W, X, Y, and Z. The points where thewires pierce the plane of the square (namely, R, S, T, andU) themselves form the vertices of a square each side ofwhich has half the length of each side of WXYZ. If thecurrents are as labeled in the figure, what is the absolutevalue ofwhere the integral is taken around WXYZ?1µI2 0(B) µ0I(A)–Q67. Consider the two source charges shown above. At howmany points in the plane of the page, in a region aroundthese charges are both the electric field and the electricpotential equal to zero?(A)(B)(C)(D)(E)TZof a parallel-plate capacitor, as shown above. If K is theε 0 A(2 3K )dSIvacuum(A)XRd3(C)2 µ0I(D) 2µ0I(E) 5µ0I01234GO ON TO THE NEXT PAGE.Practice Test 1 535

Section I Q qL Qxx–Q–q45 Q70. Two point charges, each Q, are fixed a distance L apart.A particle of charge –q and mass m is placed as shown inthe figure above. What is this particle’s initial acceleration when released from rest?69. The positions of two isolated point charges, Q and –Q,are fixed as shown in the figure above. Which of the following statements is/are true?(B)I. A charge q moving along line wouldexperience no change in electrical potentialenergy.(C)II. There is exactly one point on line where thetotal electrostatic force on q is equal to zero.III. At any point P on line , the intersection of theequipotential surface containing P with the planeof the figure is an ellipse with the charges Qand –Q at the foci.(A)(B)(C)(D)(E)(A)(D)(E)I onlyI and II onlyII onlyI and III onlyII and III onlySTOPEND OF SECTION I, ELECTRICITY AND MAGNETISM536 Cracking the AP Physics C Exam

Section IIPHYSICS CSECTION IIFree-Response QuestionsElectricity and Magnetism45 minutes3 required questions of equal weightTABLE OF INFORMATIONTABLE OF INFORMATIONFORFOR20062009and 2007–272eGO ON TO THE NEXT PAGE.Practice Test 1 537

Section IIADVANCED PLACEMENT PHYSICS C EQUATIONSGO ON TO THE NEXT PAGE.538 Cracking the AP Physics C Exam

Section IIADVANCED PLACEMENT PHYSICS C EQUATIONSGO ON TO THE NEXT PAGE.Practice Test 1 539

Section IIPHYSICS CSECTION II, ELECTRICITY AND MAGNETISMTime—45 minutes3 QuestionsDirections: Answer all three questions. The suggested time is about 15 minutes per question for answering each of the questions,which are worth 15 points each. The parts within a question may not have equal weight.E & M 1.A uniformly charged, nonconducting, circular ring of radius R carries a charge Q. Its central axis is labeled the z-axis,and the center of the ring is z 0. Points above the ring on the z-axis have positive zcoordinates; those below have negative z coordinates.z-axis Q,uniformly distributedaround the ringRz 0(a)Calculate the electric potential at an arbitrary point on the z-axis. W

510 racking the AP Physics C ExamC PHYSICS C Physics C has two exams: Physics C (Mechanics) and Physics C (Electricity & Magnetism): Physics C (Mechanics) Physics C (Electricity & Magnetism) First 45 min. Sec. I, Multiple Choice Sec. I, Multiple Choice 35 questions 35 questions Second 45 min. Sec. II, Free-Response

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