2009BAP 2 - AP® Physics B 2009 Free-Response Questions...

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Unformatted text preview: AP® Physics B 2009 Free-Response Questions Form B The College Board 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 5,600 schools, colleges, universities and other educational organizations. Each year, the College Board serves seven million students and their parents, 23,000 high schools and 3,800 colleges through major programs and services in college readiness, 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. © 2009 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 = 1.67 ¥ 10 -27 kg Neutron mass, mn = 1.67 ¥ 10 -27 kg Electron mass, me = 9.11 ¥ 10 -31 kg Avogadro’s number, N 0 = 6.02 ¥ 1023 mol-1 Universal gas constant, Electron charge magnitude, e = 1.60 ¥ 10 -19 C 1 electron volt, 1 eV = 1.60 ¥ 10 -19 J Speed of light, Universal gravitational constant, Acceleration due to gravity at Earth’s surface, c = 3.00 ¥ 108 m s G = 6.67 ¥ 10 -11 m 3 kgis2 R = 8.31 J (mol iK) g = 9.8 m s2 Boltzmann’s constant, k B = 1.38 ¥ 10 -23 J K 1 unified atomic mass unit, Planck’s constant, Vacuum permittivity, Coulomb’s law constant, k = 1 4 p Vacuum permeability, 1 u = 1.66 ¥ 10 -27 kg = 931 MeV c 2 h = 6.63 ¥ 10 -34 J is = 4.14 ¥ 10 -15 eV is hc = 1.99 ¥ 10 -25 J im = 1.24 ¥ 103 eV i nm 0 0 = 8.85 ¥ 10 -12 C2 N im 2 = 9.0 ¥ 109 N im 2 C2 m0 = 4 p ¥ 10 -7 (T im) A Magnetic constant, k ¢ = m0 4 p = 10 -7 (T im) A 1 atmosphere pressure, meter, kilogram, second, ampere, kelvin, m kg s A K mole, hertz, newton, pascal, joule, mol Hz N Pa J 1 atm = 1.0 ¥ 105 N m 2 = 1.0 ¥ 105 Pa watt, coulomb, volt, ohm, henry, W C V W H farad, tesla, degree Celsius, electron-volt, F T ∞C eV UNIT SYMBOLS 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 u 2 = u0 2 + 2 a ( x - x0 )  F = Fnet = ma Ffric £ m N ac = a F f h J K k m N P p r T t U u W x m q t u2 r t = rF sin q p = mv J = FDt = Dp K= 12 mu 2 DUg = mgh W = F Dr cos q Pavg = W Dt = = = = = = = = = = = = = = = = = = = = = = 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 = qV = Eavg = V= C= C= Uc = V d 1 q1q2 4p 0 r e 1 4p 0 Q V 0A  i qi ri d 1 1 QV = CV 2 2 2 P Q q R r t U V = = = = = = = = = = = = = = = = = I avg = DQ Dt R= r A 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 V = IR P = IV Cp = P = F u cos q Fs = - k x  Ci i Us = 12 kx 2 1 1 = Cs Ci i Rs =  Ri i Ts = 2 p Tp = 2 p m k g 1 = Rp ÂR i 1 i FB = qu B sin q FB = BI sin q B= m0 I 2p r T= 1 f Gm1m2 r2 FG = - fm = BA cos q UG Gm1m2 =r eavg =- Dfm Dt e =Bu -3- ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2008 and 2009 FLUID MECHANICS AND THERMAL PHYSICS WAVES AND OPTICS P = P0 + rgh Fbuoy = rVg A1u1 = A2 u2 1 P + rgy + ru 2 = const. 2 D =a 0 DT H= P= kA DT L F A PV = nRT = Nk BT K avg 3 = k BT 2 urms = 3 RT = M 3k B T m W = - P DV DU = Q + W e= ec = W QH TH - TC TH 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 = fl n= c u n 1 sin q1 = n 2 sin q2 sin qc = n2 n1 1 1 1 + = si s0 f h s M= i =- i h0 s0 R 2 d sin q = m l f= 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 m lL d GEOMETRY AND TRIGONOMETRY Rectangle A = bh Triangle 1 A = bh 2 Circle A = pr 2 C = 2pr Parallelepiped V = wh Cylinder V = pr 2 A= C= V= S= b= h= = w= r= area circumference volume surface area base height length width radius ATOMIC AND NUCLEAR PHYSICS E = hf = pc K max = hf - f l= h p D E = ( Dm ) c 2 E = energy f = frequency K = kinetic energy m = mass p = momentum l = wavelength f = work function S = 2pr + 2pr 2 Sphere 4 V = pr 3 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- 2009 AP® PHYSICS B FREE-RESPONSE QUESTIONS (Form B) PHYSICS B SECTION II Time— 90 minutes 6 Questions Directions: Answer all six questions, which are weighted according to the points indicated. The suggested times are about 17 minutes for answering each of Questions 1-4 and about 11 minutes for answering each of Questions 5-6. The parts within a question may not have equal weight. Show all your work in this booklet in the spaces provided after each part, NOT in the lavender insert. 1. (15 points) An experiment is performed using the apparatus above. A small disk of mass m1 on a frictionless table is attached to one end of a string. The string passes through a hole in the table and an attached narrow, vertical plastic tube. An object of mass m2 is hung at the other end of the string. A student holding the tube makes the disk rotate in a circle of constant radius r, while another student measures the period P. (a) Derive the equation P = 2 p m1r that relates P and m2 . m2 g © 2009 The College Board. All rights reserved. Visit the College Board on the Web: www.collegeboard.com. GO ON TO THE NEXT PAGE. -5- 2009 AP® PHYSICS B FREE-RESPONSE QUESTIONS (Form B) The procedure is repeated, and the period P is determined for four different values of m2 , where m1 = 0.012 kg and r = 0.80 m. The data, which are presented below, can be used to compute an experimental value for g. m2 (kg) P (s) 0.020 1.40 0.040 1.05 0.060 0.80 0.080 0.75 (b) What quantities should be graphed to yield a straight line with a slope that could be used to determine g ? (c) On the grid below, plot the quantities determined in part (b), label the axes, and draw the best-fit line to the data. You may use the blank rows above to record any values you may need to calculate. (d) Use your graph to calculate the experimental value of g. © 2009 The College Board. All rights reserved. Visit the College Board on the Web: www.collegeboard.com. GO ON TO THE NEXT PAGE. -6- 2009 AP® PHYSICS B FREE-RESPONSE QUESTIONS (Form B) 2. (15 points) Three particles are arranged on coordinate axes as shown above. Particle A has charge q A = -0.20 nC , and is initially on the y-axis at y = 0.030 m . The other two particles each have charge qB = +0.30 nC and are held fixed on the x-axis at x = -0.040 m and x = +0.040 m , respectively. (a) Calculate the magnitude of the net electric force on particle A when it is at y = 0.030 m , and state its direction. (b) Particle A is then released from rest. Qualitatively describe its motion over a long time. In another experiment, particle A of charge q A = -0.20 nC is injected into a uniform magnetic field of strength 0.50 T directed into the page, as shown below, entering the field with speed 6000 m s . (c) On the diagram above, sketch a complete path of particle A as it moves in the magnetic field. (d) Calculate the magnitude of the force the magnetic field exerts on particle A as it enters the magnetic field. (e) An electric field can be applied to keep particle A moving in a straight line through the magnetic field. Calculate the magnitude of this electric field and state its direction. © 2009 The College Board. All rights reserved. Visit the College Board on the Web: www.collegeboard.com. GO ON TO THE NEXT PAGE. -7- 2009 AP® PHYSICS B FREE-RESPONSE QUESTIONS (Form B) 3. (15 points) An underground pipe carries water of density 1000 kg m 3 to a fountain at ground level, as shown above. At point A, 0.50 m below ground level, the pipe has a cross-sectional area of 1.0 ¥ 10 -4 m 2 . At ground level, the pipe has a cross-sectional area of 0.50 ¥ 10 -4 m 2 . The water leaves the pipe at point B at a speed of 8.2 m/s. (a) Calculate the speed of the water in the pipe at point A. (b) Calculate the absolute water pressure in the pipe at point A. (c) Calculate the maximum height above the ground that the water reaches upon leaving the pipe vertically at ground level, assuming air resistance is negligible. (d) Calculate the horizontal distance from the pipe that is reached by water exiting the pipe at 60∞ from the level ground, assuming air resistance is negligible. © 2009 The College Board. All rights reserved. Visit the College Board on the Web: www.collegeboard.com. GO ON TO THE NEXT PAGE. -8- 2009 AP® PHYSICS B FREE-RESPONSE QUESTIONS (Form B) 4. (15 points) The cylinder shown above has an open top, and gas is held inside it by a piston of mass m and area A. The gas is insulated from its surroundings and is initially in equilibrium at volume Vi . Express all algebraic answers in terms of the given quantities and fundamental constants. (a) Determine the absolute pressure Pi of the gas at equilibrium. The gas is heated by a circuit that contains three resistors, each of known resistance R0 , connected in parallel to a power source of emf e . The piston is held fixed so that the gas remains at constant volume while being heated for a period of time t. (b) Determine the resistance of the circuit. (c) Calculate the change in internal energy of the gas. After the time t, the circuit is disconnected. The piston is then released and the gas is allowed to expand adiabatically until it reaches volume V f . (d) Indicate below whether the temperature increases, decreases, or remains the same during this process. _____ Increases Justify your answer. (e) The gas is then compressed isothermally to its original pressure and volume. On the axes below, draw a PV diagram for the complete cycle described in this question, labeling Vi and V f on the volume axis. _____ Decreases _____ Remains the same © 2009 The College Board. All rights reserved. Visit the College Board on the Web: www.collegeboard.com. GO ON TO THE NEXT PAGE. -9- 2009 AP PHYSICS B FREE-RESPONSE QUESTIONS (Form B) 5. (10 points) A wide beam of white light is incident normal to the surface of a uniform oil film. An observer looking down at the film sees green light that has maximum intensity at a wavelength of 5.2 ¥ 10 -7 m . The index of refraction of the oil is 1.7. (a) Calculate the speed at which the light travels within the film. (b) Calculate the wavelength of the green light within the film. (c) Calculate the minimum possible thickness of the film. (d) The oil film now rests on a thick slab of glass with index of refraction 1.4, as shown in the figure below. A light ray is incident on the film at the angle shown. On the figure, sketch the path of the refracted light ray that passes through the film and the glass slab and exits into the air. Clearly show any bending of the ray at each interface. You are NOT expected to calculate the sizes of any angles. © 2009 The College Board. All rights reserved. Visit the College Board on the Web: www.collegeboard.com. GO ON TO THE NEXT PAGE. -10- 2009 AP® PHYSICS B FREE-RESPONSE QUESTIONS (Form B) 6. (10 points) The electron energy levels above are for an electron confined to a certain very small one-dimensional region of space. The energy En of the levels, where n = 1, 2, 3, . . ., is given by En = n2 E1 . Express all algebraic answers in terms of E1 and fundamental constants. (a) On the diagram above, label the three excited energy levels with the values for their energies in terms of E1 , the energy of the ground state. (b) Calculate the smallest frequency of light that can be absorbed by an electron in this system when it is in the ground state, n = 1. (c) If an electron is raised into the second excited state, draw on the diagram all the possible transitions that the electron can make in returning to the ground state. (d) Calculate the wavelength of the highest energy photon that can be emitted in the transitions in part (c). END OF EXAM © 2009 The College Board. All rights reserved. Visit the College Board on the Web: www.collegeboard.com. -11- ...
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