phy2 - AP® Physics C: Mechanics 2009 Free-Response...

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Unformatted text preview: AP® Physics C: Mechanics 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: Visit the College Board on the Web: AP Central is the official online home for the AP Program: 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. -2- ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2008 and 2009 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 F= dp dt a F f h I J K k J = Ú F dt = Dp p = mv Ffric £ m N W= K= P= ÚF ∑ dr 1 mu 2 2 dW dt P=Fv DUg = mgh = = = = = = = = = L= m= N= P= p= r= r= T= t= U= u= W= x= m= q= t= w= a= 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 F= E= 1 q1q2 4p 0 r 2 F q ∑ A B C d E ÚE dA = dV dr Q 0 E=V= 1 4p 0  rii i q = = = = = e= F= I= J= L= = n= N= UE = qV = C= C= Q V k 0A 1 4p 0 q1q2 r d Cp =  Ci i 1 1 = Cs i Ci I= dQ dt 1 1 QV = CV 2 2 2 P= Q= q= R= r= t= U= V= u= r= area magnetic field capacitance distance electric field emf force current current density inductance length number of loops of wire per unit length number of charge carriers per unit volume power charge point charge resistance distance time potential or stored energy electric potential velocity or speed resistivity fm = magnetic flux k = dielectric constant ac = u2 = w2r r Fs = - kx t=r¥F  t = t net = I a I = Ú r 2 dm =  mr 2 Uc = ÚB ∑ d = m0 I Us = T= 12 kx 2 2p 1 = w f r R= A E = rJ I = Neud A dB = F= m0 I d ¥ r 4p r3 ¥B ÚI d rcm =  mr  m u = rw Ts = 2 p Tp = 2 p FG = - m k g ˆ r Bs = m0 nI fm = Ú B ∑ dA V = IR Rs = L = r ¥ p = Iw K= 12 Iw 2  Ri i e i =- Gm1m2 r2 1 = Rp ÂR i 1 d fm dt dI dt e = -L w = w0 + at q = q0 + w0 t + 12 at 2 UG = - Gm1m2 r P = IV FM = qv ¥ B UL = 12 LI 2 -3- ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2008 and 2009 GEOMETRY AND TRIGONOMETRY Rectangle A = bh Triangle CALCULUS A= Circle 1 bh 2 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 df d f du = dx du dx dn ( x ) = nx n -1 dx dx (e ) = e x dx d (1n x ) = 1 dx x d (sin x ) = cos x dx d (cos x ) = - sin x dx S = 2pr + 2pr 2 Sphere Úx Úe n dx = 1 x n + 1 , n π -1 n +1 x dx = e x V= 43 pr 3 Ú dx = ln x x S = 4pr 2 Right Triangle Ú cos x dx = sin x Ú sin x dx = - cos x c q b 90° a a 2 + b2 = c2 sin q = cos q = tan q = a c b c a b -4- 2009 AP® PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS PHYSICS C: MECHANICS SECTION II 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 this booklet in the spaces provided after each part, NOT in the green insert. Mech. 1. A 3.0 kg object is moving along the x-axis in a region where its potential energy as a function of x is given as U ( x ) = 4.0 x 2 , where U is in joules and x is in meters. When the object passes the point x = -0.50 m, its velocity is +2.0 m/s. All forces acting on the object are conservative. (a) Calculate the total mechanical energy of the object. (b) Calculate the x-coordinate of any points at which the object has zero kinetic energy. (c) Calculate the magnitude of the momentum of the object at x = 0.60 m. (d) Calculate the magnitude of the acceleration of the object as it passes x = 0.60 m. © 2009 The College Board. All rights reserved. Visit the College Board on the Web: GO ON TO THE NEXT PAGE. -5- 2009 AP® PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS (e) On the axes below, sketch graphs of the object’s position x versus time t and kinetic energy K versus time t. Assume that x = 0 at time t = 0 . The two graphs should cover the same time interval and use the same scale on the horizontal axes. © 2009 The College Board. All rights reserved. Visit the College Board on the Web: GO ON TO THE NEXT PAGE. -6- 2009 AP® PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS Mech. 2. You are given a long, thin, rectangular bar of known mass M and length with a pivot attached to one end. The bar has a nonuniform mass density, and the center of mass is located a known distance x from the end with the pivot. You are to determine the rotational inertia I b of the bar about the pivot by suspending the bar from the pivot, as shown above, and allowing it to swing. Express all algebraic answers in terms of I b , the given quantities, and fundamental constants. (a) i. ii. By applying the appropriate equation of motion to the bar, write the differential equation for the angle q the bar makes with the vertical. By applying the small-angle approximation to your differential equation, calculate the period of the bar’s motion. (b) Describe the experimental procedure you would use to make the additional measurements needed to determine I b . Include how you would use your measurements to obtain I b and how you would minimize experimental error. (c) Now suppose that you were not given the location of the center of mass of the bar. Describe an experimental procedure that you could use to determine it, including the equipment that you would need. © 2009 The College Board. All rights reserved. Visit the College Board on the Web: GO ON TO THE NEXT PAGE. -7- 2009 AP® PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS Mech. 3. A block of mass M 2 rests on a frictionless horizontal table, as shown above. It is connected to one end of a string that passes over a massless pulley and has another block of mass M 2 hanging from its other end. The apparatus is released from rest. (a) Derive an expression for the speed uh of the hanging block as a function of the distance d it descends. Now the block and pulley system is replaced by a uniform rope of length L and mass M, with one end of the rope hanging slightly over the edge of the frictionless table. The rope is released from rest, and at some time later there is a length y of rope hanging over the edge, as shown below. Express your answers to parts (b), (c), and (d) in terms of y, L, M, and fundamental constants. (b) Determine an expression for the force of gravity on the hanging part of the rope as a function of y. (c) Derive an expression for the work done by gravity on the rope as a function of y, assuming y is initially zero. (d) Derive an expression for the speed ur of the rope as a function of y. (e) The hanging block and the right end of the rope are each allowed to fall a distance L (the length of the rope). The string is long enough that the sliding block does not hit the pulley. Indicate whether uh from part (a) or ur from part (d) is greater after the block and the end of the rope have traveled this distance. ____ uh is greater. Justify your answer. ____ ur is greater. ____ The speeds are equal. END OF EXAM © 2009 The College Board. All rights reserved. Visit the College Board on the Web: -8- ...
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This note was uploaded on 01/10/2011 for the course PHYS 100 taught by Professor Razasuleman during the Spring '10 term at University of Engineering & Technology.

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