2008BAP 1 - AP® Physics B 2008 Free-Response Questions The...

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Unformatted text preview: AP® Physics B 2008 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. © 2008 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 2008 and 2009 CONSTANTS AND CONVERSION FACTORS Proton mass, m p Neutron mass, mn Electron mass, me Avogadro’s number, N 0 Universal gas constant, 1.67 1.67 10 10 27 27 31 kg kg kg Electron charge magnitude, e 1.60 10 19 C 1 electron volt, 1 eV Speed of light, Universal gravitational constant, Acceleration due to gravity at Earth’s surface, 1.60 10 19 J 9.11 10 6.02 c G 3.00 6.67 108 m s 10 11 1023 mol -1 m 3 kg s2 R 8.31 J (mol K) 1.38 10 23 g 9.8 m s2 Boltzmann’s constant, k B JK 1u h hc 1 unified atomic mass unit, Planck’s constant, Vacuum permittivity, Coulomb’s law constant, k Vacuum permeability, Magnetic constant, k 1 atmosphere pressure, meter, kilogram, second, ampere, kelvin, m kg s A K mole, hertz, newton, pascal, joule, mol Hz N Pa J 1.66 6.63 1.99 8.85 9.0 4p 10 7 10 10 10 10 27 34 25 12 kg Js Jm 2 931 MeV c 2 4.14 1.24 2 10 15 3 eV s 10 eV nm 0 C Nm 1 4p 0 109 N m 2 C2 10 7 m0 m0 4 p (T m) A (T m) A 1 atm 1.0 105 N m 2 W C V W H 1.0 105 Pa F T C eV UNIT SYMBOLS watt, coulomb, volt, ohm, henry, farad, tesla, degree Celsius, electron-volt, PREFIXES Factor Prefix Symbol 10 9 106 103 10 2 VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES q 30 0 37 45 53 60 90 giga mega kilo centi milli micro nano pico G M k c m sin q cos q tan q 0 1 0 12 32 33 35 45 34 22 22 1 45 35 43 32 1 0 12 3 10 3 10 6 10 9 m n p 10 12 The following conventions are used in this exam. 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. IV. For mechanics and thermodynamics equations, W represents the work done on a system. -2- ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2008 and 2009 NEWTONIAN MECHANICS ELECTRICITY AND MAGNETISM u u0 at x x0 u0 t 12 at 2 x0 u2 u0 2 2a x F Ffric ac Fnet mN u2 r rF sin q ma a F f h J K k m N P p r T t U u W x m q t t p J K mv FDt 12 mu 2 mgh F Dr cos q W Dt Dp DUg W Pavg = = = = = = = = = = = = = = = = = = = = = = acceleration force frequency height impulse kinetic energy spring constant length mass normal force power momentum radius or distance period time potential energy velocity or speed work done on a system position coefficient of friction angle torque F E 1 q1q2 4p 0 r 2 F q A B C d E F I UE Eavg V C C Uc I avg qV V d 1 4p 0 Q V 0A 1 q1q2 4p 0 r e i qi ri d 1 QV 2 1 CV 2 2 P Q q R r t U V = = = = = = = = = = = = = = = = = DQ Dt R V P Cp 1 Cs Rs r A IR IV i u= r= q= fm = area magnetic field capacitance distance electric field emf force current length power charge point charge resistance distance time potential (stored) energy electric potential or potential difference velocity or speed resistivity angle magnetic flux P Fs F u cos q kx 12 kx 2 Ci Us 1 i Ci i Ri Ts Tp 2p 2p m k g 1 Rp FB FB B i 1 Ri qu B sin q BI sin q m0 I 2p r BA cos q T 1 f Gm1m2 r2 FG fm UG Gm1m2 r eavg Dfm Dt Bu e -3- ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2008 and 2009 FLUID MECHANICS AND THERMAL PHYSICS WAVES AND OPTICS P Fbuoy P0 rgh rVg A1u1 P D A2 u2 rgy a 12 ru 2 0 DT const. H P kA DT L F A PV K avg nRT 3 kT 2B Nk BT urms 3 RT M 3k B T m W DU P DV Q W e W QH TH TH TC A = area e = efficiency F = force h = depth H = rate of heat transfer k = thermal conductivity K avg =average molecular kinetic energy = length L = thickness M = molar mass n = number of moles N = number of molecules P = pressure Q = heat transferred to a system T = temperature U = internal energy V = volume u = velocity or speed urms =root-mean-square velocity W = work done on a system y = height a = coefficient of linear expansion m = mass of molecule r = density u n fl c u n 1 sin q1 sin qc 1 si 1 s0 n 2 sin q2 n2 n1 1 f M f hi h0 si s0 R 2 d sin q ml m lL d d = separation f = frequency or focal length h = height L = distance M = magnification m = an integer n = index of refraction R = radius of curvature s = distance u = speed x = position l = wavelength q = angle xm GEOMETRY AND TRIGONOMETRY Rectangle A bh Triangle 1 A bh 2 Circle A pr 2 C 2pr Parallelepiped V wh Cylinder V pr 2 ec A= C= V= S= b= h= = w= r= area circumference volume surface area base height length width radius ATOMIC AND NUCLEAR PHYSICS E hf hf pc K max f l h p DE ( Dm ) c 2 E = energy f = frequency K = kinetic energy m = mass p = momentum l = wavelength f = work function S 2pr 2pr 2 Sphere 43 V pr 3 S 4pr 2 Right Triangle a 2 b2 c2 a sin q c b cos q c a tan q b c q b 90 a -4- 2008 AP® PHYSICS B FREE-RESPONSE QUESTIONS PHYSICS B SECTION II Time— 90 minutes 7 Questions Directions: Answer all seven questions, which are weighted according to the points indicated. The suggested times are about 11 minutes for answering Questions 1 and 4-7 and about 17 minutes for answering each of Questions 2 and 3. 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. 1. (10 points) Several students are riding in bumper cars at an amusement park. The combined mass of car A and its occupants is 250 kg. The combined mass of car B and its occupants is 200 kg. Car A is 15 m away from car B and moving to the right at 2.0 m/s, as shown, when the driver decides to bump into car B, which is at rest. (a) Car A accelerates at 1.5 m s2 to a speed of 5.0 m s and then continues at constant velocity until it strikes car B. Calculate the total time for car A to travel the 15 m. (b) After the collision, car B moves to the right at a speed of 4.8 m s . i. Calculate the speed of car A after the collision. ii. Indicate the direction of motion of car A after the collision. ____ To the left ____ Yes ____ To the right ____ None; car A is at rest. (c) Is this an elastic collision? ____ No Justify your answer. © 2008 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- 2008 AP® PHYSICS B FREE-RESPONSE QUESTIONS 2. (15 points) Block A of mass 2.0 kg and block B of mass 8.0 kg are connected as shown above by a spring of spring constant 80 N/m and negligible mass. The system is being pulled to the right across a horizontal frictionless surface by a horizontal force of 4.0 N, as shown, with both blocks experiencing equal constant acceleration. (a) Calculate the force that the spring exerts on the 2.0 kg block. (b) Calculate the extension of the spring. The system is now pulled to the left, as shown below, with both blocks again experiencing equal constant acceleration. (c) Is the magnitude of the acceleration greater than, less than, or the same as before? ____ Greater Justify your answer. (d) Is the amount the spring has stretched greater than, less than, or the same as before? ____ Greater Justify your answer. (e) In a new situation, the blocks and spring are moving together at a constant speed of 0.50 m s to the left. Block A then hits and sticks to a wall. Calculate the maximum compression of the spring. ____ Less ____ The same ____ Less ____ The same © 2008 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- 2008 AP® PHYSICS B FREE-RESPONSE QUESTIONS 3. (15 points) A rectangular wire loop is connected across a power supply with an internal resistance of 0.50 W and an emf of 16 V. The wire has resistivity 1.7 10 8 W m and cross-sectional area 3.5 supply is turned on, the current in the wire is 4.0 A. (a) Calculate the length of wire used to make the loop. The wire loop is then used in an experiment to measure the strength of the magnetic field between the poles of a magnet. The magnet is placed on a digital balance, and the wire loop is held fixed between the poles of the magnet, as shown below. The 0.020 m long horizontal segment of the loop is midway between the poles and perpendicular to the direction of the magnetic field. The power supply in the loop is turned on, so that the 4.0 A current is in the direction shown. 10 9 m 2 . When the power Note: Figure not drawn to scale. (b) In which direction is the force on the magnet due to the current in the wire segment? ____Upward Justify your answer. (c) The reading on the balance changed by 0.060 N when the power supply was turned on. Calculate the strength of the magnetic field. ____Downward © 2008 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- 2008 AP® PHYSICS B FREE-RESPONSE QUESTIONS Suppose that various rectangular loops with the same total length of wire as found in part (a) were constructed such that the lengths of the horizontal segments of the wire loops varied between 0.02 m and 0.10 m. The horizontal segment of each loop was always centered between the poles, and the current in each loop was always 4.0 A. The following graph represents the theoretical relationship between the magnitude of the force on the magnet and the length of the wire. (d) On the graph above, sketch a possible relationship between the magnitude of the force on the magnet and the length of the wire segment if the wire segments were misaligned and placed at a constant nonperpendicular angle to the magnetic field, as shown below. (e) Suppose the loops are correctly placed perpendicular to the field and the following data are obtained. Describe a likely cause of the discrepancy between the data and the theoretical relationship. © 2008 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. -8- 2008 AP® PHYSICS B FREE-RESPONSE QUESTIONS 4. (10 points) A drinking fountain projects water at an initial angle of 50° above the horizontal, and the water reaches a maximum height of 0.150 m above the point of exit. Assume air resistance is negligible. (a) Calculate the speed at which the water leaves the fountain. (b) The radius of the fountain’s exit hole is 4.00 10 3 m . Calculate the volume rate of flow of the water. 10 3 (c) The fountain is fed by a pipe that at one point has a radius of 7.00 fountain’s opening. The density of water is 1.0 pipe at this point. 3 3 m and is 3.00 m below the 10 kg m . Calculate the gauge pressure in the feeder 5. (10 points) A 0.03 mol sample of helium is taken through the cycle shown in the diagram above. The temperature of state A is 400 K. (a) For each process in this cycle, indicate in the table below whether the quantities W, Q, and DU are positive (+), negative ( ), or zero (0). W is the work done on the helium sample. Process AB BC CA W Q DU (b) Explain your response for the signs of the quantities for process A B. (c) Calculate VC . © 2008 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. -9- 2008 AP® PHYSICS B FREE-RESPONSE QUESTIONS 6. (10 points) The figure above shows a converging mirror, its focal point F, its center of curvature C, and an object represented by the solid arrow. (a) On the figure above, draw a ray diagram showing at least two incident rays and the image formed by them. (b) Is the image real or virtual? ____ Real ____ Virtual Justify your answer. (c) The focal length of this mirror is 6.0 cm, and the object is located 8.0 cm away from the mirror. Calculate the position of the image formed by the mirror. (Do NOT simply measure your ray diagram.) (d) Suppose that the converging mirror is replaced by a diverging mirror with the same radius of curvature that is the same distance from the object, as shown below. For this mirror, how does the size of the image compare with that of the object? ____ Larger than the object Justify your answer. ____ Smaller than the object ____ The same size as the object © 2008 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. -10- 2008 AP® PHYSICS B FREE-RESPONSE QUESTIONS 7. (10 points) In an electron microscope, a tungsten cathode with work function 4.5 eV is heated to release electrons that are then initially at rest just outside the cathode. The electrons are accelerated by a potential difference to create a beam of electrons with a de Broglie wavelength of 0.038 nm. Assume nonrelativistic equations apply to the motion of the electrons. (a) Calculate the momentum of an electron in the beam, in kg m s . (b) Calculate the kinetic energy of an electron in the beam, in joules. (c) Calculate the accelerating voltage. (d) Suppose that light, instead of heat, is used to release the electrons from the cathode. What minimum frequency of light is needed to accomplish this? END OF EXAM © 2008 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). -11- ...
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This note was uploaded on 02/09/2011 for the course PHYS 10 taught by Professor Davidnewton during the Spring '11 term at DeAnza College.

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