2008APTestMech - AP Physics C: Mechanics 2008 Free-Response...

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Unformatted text preview: AP Physics C: Mechanics 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 J K 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 3 2 3 3 35 45 34 2 2 2 2 1 45 35 43 3 2 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 1 2 at 2 u2 u0 2 2a x ma x0 F F J Fnet dp dt F dt a F f h I J K k Dp p Ffric W K P P DUg mv mN F dr 1 mu 2 2 dW dt F v 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 E dA Q 0 A B C d E E V dV dr 1 4p 0 qi ri = = = = = e= F = I = J = L = = n = i N = UE C C Cp 1 Cs I qV Q V k 0A 1 4p 0 q1q2 r d i Ci 1 i Ci dQ dt 1 QV 2 1 CV 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 r w2r Fs kx 1 2 kx 2 t t Uc B d m0 I r F t net Ia mr 2 Us T R 1 f E I I r 2 dm 2p w r A rJ Neud A dB F Bs fm m0 I d r 4p r3 Id m0 nI B rcm u rw mr m Ts Tp FG 2p 2p m k g ^ r V Rs IR i B dA L K w q r p Iw Ri e e UL 1 2 Iw 2 Gm1m2 r2 1 Rp P IV i 1 Ri d fm dt L dI dt w0 q0 at UG w0 t 1 2 at 2 Gm1m2 r FM qv B 1 2 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 pr 2 A 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 dx d n x dx d x e dx d f du du dx nx n ex 1 x cos x sin x 1 n ex 1 d 1n x dx d sin x dx d cos x dx x n dx S Sphere 2pr 4 3 pr 3 4pr 2 2pr 2 1 x n 1, n 1 e x dx dx x V S a2 sin q cos q tan q ln x sin x cos x cos x dx Right Triangle b2 a c b c a b c2 c q b 90 a sin x dx -4- 2008 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 the pink booklet in the spaces provided after each part, NOT in this green insert. Mech. 1. A skier of mass M is skiing down a frictionless hill that makes an angle with the horizontal, as shown in the diagram. The skier starts from rest at time t = 0 and is subject to a velocity-dependent drag force due to air resistance of the form F b, where is the velocity of the skier and b is a positive constant. Express all algebraic answers in terms of M , b, , and fundamental constants. (a) On the dot below that represents the skier, draw a free-body diagram indicating and labeling all of the forces that act on the skier while the skier descends the hill. (b) Write a differential equation that can be used to solve for the velocity of the skier as a function of time. (c) Determine an expression for the terminal velocity uT of the skier. (d) Solve the differential equation in part (b) to determine the velocity of the skier as a function of time, showing all your steps. 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 C: MECHANICS FREE-RESPONSE QUESTIONS (e) On the axes below, sketch a graph of the acceleration a of the skier as a function of time t, and indicate the initial value of a. Take downhill as positive. 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 C: MECHANICS FREE-RESPONSE QUESTIONS Mech. 2. The horizontal uniform rod shown above has length 0.60 m and mass 2.0 kg. The left end of the rod is attached to a vertical support by a frictionless hinge that allows the rod to swing up or down. The right end of the rod is supported by a cord that makes an angle of 30 with the rod. A spring scale of negligible mass measures the tension in the cord. A 0.50 kg block is also attached to the right end of the rod. (a) On the diagram below, draw and label vectors to represent all the forces acting on the rod. Show each force vector originating at its point of application. (b) Calculate the reading on the spring scale. (c) The rotational inertia of a rod about its center is 1 ML2 , where M is the mass of the rod and L is its length. 12 Calculate the rotational inertia of the rod-block system about the hinge. (d) If the cord that supports the rod is cut near the end of the rod, calculate the initial angular acceleration of the rod-block system about the hinge. 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 C: MECHANICS FREE-RESPONSE QUESTIONS Mech. 3. In an experiment to determine the spring constant of an elastic cord of length 0.60 m, a student hangs the cord from a rod as represented above and then attaches a variety of weights to the cord. For each weight, the student allows the weight to hang in equilibrium and then measures the entire length of the cord. The data are recorded in the table below: Weight (N) Length (m) 0 10 15 20 25 0.60 0.97 1.24 1.37 1.64 (a) Use the data to plot a graph of weight versus length on the axes below. Sketch a best-fit straight line through the data. (b) Use the best-fit line you sketched in part (a) to determine an experimental value for the spring constant k of the cord. 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 C: MECHANICS FREE-RESPONSE QUESTIONS The student now attaches an object of unknown mass m to the cord and holds the object adjacent to the point at which the top of the cord is tied to the rod, as represented above. When the object is released from rest, it falls 1.5 m before stopping and turning around. Assume that air resistance is negligible. (c) Calculate the value of the unknown mass m of the object. (d) i. Calculate how far down the object has fallen at the moment it attains its maximum speed. ii. Explain why this is the point at which the object has its maximum speed. iii. Calculate the maximum speed of the object. 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). -9- ...
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This note was uploaded on 08/29/2010 for the course PHYS 45925 taught by Professor Ramesh during the Spring '10 term at University of California, Berkeley.

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