2009BAP 1 - AP® Physics B 2009 Free-Response Questions The...

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Unformatted text preview: AP® Physics B 2009 Free-Response Questions 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 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 17 minutes for answering each of Questions 1 and 3 and about 11 minutes for answering each of Questions 2 and 4-7. 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 green insert. 1. (15 points) In an experiment, students are to calculate the spring constant k of a vertical spring in a small jumping toy that initially rests on a table. When the spring in the toy is compressed a distance x from its uncompressed length L0 and the toy is released, the top of the toy rises to a maximum height h above the point of maximum compression. The students repeat the experiment several times, measuring h with objects of various masses taped to the top of the toy so that the combined mass of the toy and added objects is m. The bottom of the toy and the spring each have negligible mass compared to the top of the toy and the objects taped to it. (a) Derive an expression for the height h in terms of m, x, k, and fundamental constants. With the spring compressed a distance x = 0.020 m in each trial, the students obtained the following data for different values of m. m (kg) 0.020 0.030 0.040 0.050 0.060 (b) h (m) 0.49 0.34 0.28 0.19 0.18 i. What quantities should be graphed so that the slope of a best-fit straight line through the data points can be used to calculate the spring constant k ? ii. Fill in one or both of the blank columns in the table with calculated values of your quantities, including units. © 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 (c) On the axes below, plot your data and draw a best-fit straight line. Label the axes and indicate the scale. (d) Using your best-fit line, calculate the numerical value of the spring constant. (e) Describe a procedure for measuring the height h in the experiment, given that the toy is only momentarily at that maximum height. © 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 2. (10 points) Two small objects, labeled 1 and 2 in the diagram above, are suspended in equilibrium from strings of length L. Each object has mass m and charge +Q. Assume that the strings have negligible mass and are insulating and electrically neutral. Express all algebraic answers in terms of m, L, Q, q , and fundamental constants. (a) On the following diagram, sketch lines to illustrate a 2-dimensional view of the net electric field due to the two objects in the region enclosed by the dashed lines. (b) Derive an expression for the electric potential at point A, shown in the diagram at the top of the page, which is midway between the charged objects. (c) On the following diagram of object 1, draw and label vectors to represent the forces on the object. (d) Using the conditions of equilibrium, write— but do not solve—two equations that could, together, be solved for q and the tension T in the left-hand string. © 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 3. (15 points) A metal rod of mass 0.22 kg lies across two parallel conducting rails that are a distance of 0.52 m apart on a tabletop, as shown in the top view above. A 3.0 W resistor is connected across the left ends of the rails. The rod and rails have negligible resistance but significant friction with a coefficient of kinetic friction of 0.20. There is a magnetic field of 0.80 T perpendicular to the plane of the tabletop. A string pulls the metal rod to the right with a constant speed of 1.8 m/s. (a) Calculate the magnitude of the current induced in the loop formed by the rod, the rails, and the resistor. (b) Calculate the magnitude of the force required to pull the rod to the right with constant speed. (c) Calculate the energy dissipated in the resistor in 2.0 s. (d) Calculate the work done by the string pulling the rod in 2.0 s. (e) Compare your answers to parts (c) and (d). Provide a physical explanation for why they are equal or unequal. © 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 4. (10 points) The cylinder represented above contains 2.2 kg of water vapor initially at a volume of 2.0 m3 and an absolute pressure of 3.0 ¥ 105 Pa. This state is represented by point A in the PV diagram below. The molar mass of water is 18 g, and the water vapor can be treated as an ideal gas. (a) Calculate the temperature of the water vapor at point A. The absolute pressure of the water vapor is increased at constant volume to 4.0 ¥ 105 Pa at point B, and then the volume of the water vapor is increased at constant pressure to 2.5 m3 at point C, as shown in the PV diagram. (b) Calculate the temperature of the water vapor at point C. (c) Does the internal energy of the water vapor for the process A→B→C increase, decrease, or remain the same? ____Increase Justify your answer. (d) Calculate the work done on the water vapor for the process A→B→C. ____Decrease ____Remain 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 5. (10 points) Three objects of identical mass attached to strings are suspended in a large tank of liquid, as shown above. (a) Must all three strings have the same tension? ____ Yes ____ No Justify your answer. Object A has a volume of 1.0 10 -5 m 3 and a density of 1300 kg m 3 . The tension in the string to which object A is attached is 0.0098 N. (b) Calculate the buoyant force on object A. (c) Calculate the density of the liquid. (d) Some of the liquid is now drained from the tank until only half of the volume of object A is submerged. Would the tension in the string to which object A is attached increase, decrease, or remain the same? ____ Increase Justify your answer. ____ Decrease ____ Remain 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. -10- 2009 AP® PHYSICS B FREE-RESPONSE QUESTIONS 6. (10 points) In a classroom demonstration, a beam of coherent light of wavelength 550 nm is incident perpendicularly onto a pair of slits. Each slit has a width w of 1.2 ¥ 10 -6 m, and the distance d between the centers of the slits is 1.8 ¥ 10 -5 m. The class observes light and dark fringes on a screen that is a distance L of 2.2 m from the slits. Your notebook shows the following setup for the demonstration. (a) Calculate the frequency of the light. (b) Calculate the distance between two adjacent dark fringes on the screen. The entire apparatus is now immersed in a transparent fluid having index of refraction 1.4. (c) What is the frequency of the light in the transparent fluid? (d) Does the distance between the dark fringes increase, decrease, or remain the same? _____ Increase _____ Decrease _____ Remain the same Explain your reasoning. © 2009 The College Board. All rights reserved. Visit the College Board on the Web: www.collegeboard.com. GO ON TO THE NEXT PAGE. -11- 2009 AP® PHYSICS B FREE-RESPONSE QUESTIONS 7. (10 points) A photon of wavelength 250 nm ejects an electron from a metal. The ejected electron has a de Broglie wavelength of 0.85 nm. (a) Calculate the kinetic energy of the electron. (b) Assuming that the kinetic energy found in (a) is the maximum kinetic energy that it could have, calculate the work function of the metal. (c) The incident photon was created when an atom underwent an electronic transition. On the energy level diagram of the atom below, the transition labeled X corresponds to a photon wavelength of 400 nm. Indicate which transition could be the source of the original 250 nm photon by circling the correct letter. Justify your answer. END OF EXAM © 2009 The College Board. All rights reserved. Visit the College Board on the Web: www.collegeboard.com. -12- ...
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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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