AP Physics C: Mechanics

1 2021. AP Physics C: . Mechanics Free-Response Questions Set 2. 2021 College Board. College Board, Advanced Placement, AP, AP Central, and the acorn logo are registered trademarks of College Board. Visit College Board on the web: AP Central is the official online home for the AP Program: ADVANCED PLACEMENT Physics C TABLE OF INFORMATION. CONSTANTS AND CONVERSION FACTORS. Proton mass, m p 10 27 kg Electron charge magnitude, e 10 19 C. Neutron mass, mn 10 27 kg 1 electron volt, 1 eV 10 19 J. Electron mass, me 10 31 kg Speed of light, c 108 m s Universal gravitational 10 11 N<m 2 kg 2. Avogadro's number, N 0 10 23 mol 1 G. constant, Acceleration due to gravity Universal gas constant, R J (mol <K). at Earth's surface, g m s2. Boltzmann's constant, k B 10 23 J K. 1 unified atomic mass unit, 1u 10 27 kg 931 MeV c 2. Planck's constant, h 10 34 J <s 10 15 eV <s hc 10 25 J <m 103 eV < nm Vacuum permittivity, e0 10 12 C2 N < m 2.

2 Coulomb's law constant, k 1 4 pe0 109 N< m 2 C2. Vacuum permeability, m0 4 p 10 7 (T <m) A. Magnetic constant, k m0 4 p 1 10 7 (T< m) A. 1 atmosphere pressure, 1 atm 105 N m 2 105 Pa meter, m mole, mol watt, W farad, F. kilogram, kg hertz, Hz coulomb, C tesla, T. UNIT second, s newton, N volt, V degree Celsius, C. SYMBOLS. ampere, A pascal, Pa ohm, W electron volt, eV. kelvin, K joule, J henry, H. PREFIXES VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES. D. Factor Prefix Symbol q 0 30D 37D 45D 53D 60D 90D. 109 giga G sin q 0 12 35 2 2 45 3 2 1. 106 mega M cos q 1 3 2 45 2 2 35 12 0. 103 kilo k tan q 0 3 3 34 1 43 3 . 10 2 centi c 10 3 milli m The following assumptions are used in this exam. 10 6 micro m I. The frame of reference of any problem is inertial unless otherwise stated. 10 9 nano n II. The direction of current is the direction in which positive charges 10 12 pico p would drift.

3 III. The electric potential is zero at an infinite distance from an isolated point charge. IV. All batteries and meters are ideal unless otherwise stated. V. Edge effects for the electric field of a parallel plate capacitor are negligible unless otherwise stated. ADVANCED PLACEMENT Physics C EQUATIONS. Mechanics ELECTRICITY AND MAGNETISM. x x 0 a x t a = acceleration G 1 q1q2 A = area E= energy FE B = magnetic field 1 2 4pe0 r 2. x x0 x 0 t at F = force C = capacitance 2 x G. f = frequency G FE d = distance x2 2. x 0 2 a x x x0 E. h = height q E = electric field G G I = rotational inertia e emf =. G. a F Fnet J = impulse G G Q F = force m m K = kinetic energy v E < dA e0 I = current G G k = spring constant J = current density dp dV. F A = length Ex L = inductance dt dx L = angular momentum A = length G G G G G. J m= mass n F dt Dp P = power DV E <dr = number of loops of wire per unit length G G p = momentum N = number of charge carriers p mv 1 q G G.

4 R = radius or distance V. 4pe0 rii P = power per unit volume T = i Ff m FN period t = time Q = charge G G 1 q1q2. U= potential energy UE qV q = point charge DE W F <dr 4pe0 r R = resistance v = velocity or speed 1 2 r = radius or distance K m W= work done on a system Q. 2 x = DV t = time position C. m = coefficient of friction U = potential or stored energy dE k e0 A V = electric potential P q = angle C. dt d t = torque v = velocity or speed G G r = resistivity P F <v w = angular speed Cp a = angular acceleration Ci F = flux i DUg mg Dh f = phase angle k = dielectric constant G G 1 1 G G G. Fs k D x Cs C FM qv B. 2 i i ac w2r G G. r G G G. Us 1. k Dx 2. I. dQ v < d A m0 I. B. 2 dt t r F G. x xmax cos( wt f G m0 I d A r . G G 1. QDV. 1. C DV 2 dB. G t t net UC 4p r 2. a 2 2. I I 2p 1 G G G. T rA. w f R F A B. I d 2 2 A. I r dm mr m G G Bs m0 nI. Ts 2p E rJ. k mi xi G G. x cm I Nevd A FB B < dA.)

5 Mi Tp 2p A. g G G. rw DV d FB. G I e v < d A. E . G Gm1m2 R dt G G G FG. L r p Iw r2 Rs Ri dI. e L. 1 2 Gm1m2 i dt K Iw UG . 2 r 1 1 1 2. R UL LI. Rp i i 2. w w0 at 1 2 P I DV. q q0 w0 t at 2. ADVANCED PLACEMENT Physics C EQUATIONS. GEOMETRY AND TRIGONOMETRY CALCULUS. Rectangle A = area df d f du A bh C = circumference dx du dx V = volume Triangle d n S = surface area x nx n 1. 1 dx A bh b = base 2 d ax h = height e aeax Circle = length dx A pr2 w = width d 1. ln ax r = radius dx x C 2p r s = arc length d s rq q = angle dx >sin ax @ a cos ax Rectangular Solid d V wh dx >cos ax @ a sin ax Cylinder s r n 1 n 1. V pr . 2. q x dx n 1. x , n 1. ax 1 ax S 2p r 2p r 2. e dx e a Sphere dx 4 3 x a ln x a V pr 3. 1. S 4p r 2 cos ax dx a sin ax 1. Right Triangle sin ax dx cos ax a a 2 b2 c2. VECTOR PRODUCTS. a . sin q c A B AB cos q c . b a A B AB sin q cos q c q 90 . b a tan q b AP Physics C: Mechanics 2021 Free-Response Questions Begin your response to QUESTION 1 on this page.

6 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. 1. Students design an experiment using blocks of adjustable mass to investigate friction using the setup shown. Block 1 of initial mass kg is placed on a rough horizontal surface and connected by a string to block 2 of initial mass kg. The string extends over a pulley that has negligible mass and friction. (a) Calculate the minimum value of the coefficient of static friction ms that would keep the two-block system at rest. GO ON TO THE NEXT PAGE. Use a pencil or pen with black or dark blue ink only. Do NOT write your name. Do NOT write outside the box.

7 2021 College Board. Visit College Board on the web: 2. 166 V OFFSET Rear Bklt AP Physics C: Mechanics 2021 Free-Response Questions Continue your response to QUESTION 1 on this page. The coefficient of friction is such that when block 2 is released from rest, block 1 travels across the surface. The acceleration a of each block is recorded with motion detectors 1 and 2, as shown in the figure. The data for the motion detectors as functions of time t are shown on the graphs. For each motion detector, the positive direction is away from the detector. (b) On the dots below, which represent the blocks, draw and label the forces (not components) that act on each block. Each force must be represented by a distinct arrow starting on, and pointing away from, the dot. (c) Calculate the coefficient of kinetic friction mk between block 1 and the table. GO ON TO THE NEXT PAGE. Use a pencil or pen with black or dark blue ink only.

8 Do NOT write your name. Do NOT write outside the box. 2021 College Board. Visit College Board on the web: 3. 166 V Front Bklt mk AP Physics C: Mechanics 2021 Free-Response Questions Continue your response to QUESTION 1 on this page. (d) Careful measurements determine that the coefficient of kinetic friction is larger than the value calculated in part (c). Does the following explanation sufficiently account for the observed discrepancy? The horizontal table was not perfectly level before the experiment was conducted. The observed difference in the angle accounts for the difference in the expected and calculated values of mk .. _____Yes _____ No Justify your answer. The experiment is moved to a surface with negligible friction and run for eight trials. In each trial, the students vary the masses m1 and m 2 of blocks 1 and 2, respectively, while keeping the total mass (m1 + m 2) = kg constant.

9 The data for the acceleration a of block 1 as a function of m 2 are shown on the graph below. (e). i. Draw a best-fit line for the data points. ii. Using the straight line, calculate an experimental value for the acceleration due to gravity g . GO ON TO THE NEXT PAGE. Use a pencil or pen with black or dark blue ink only. Do NOT write your name. Do NOT write outside the box. 2021 College Board. Visit College Board on the web: 4. 166 V OFFSET Rear Bklt (. AP Physics C: Mechanics 2021 Free-Response Questions Continue your response to QUESTION 1 on this page. (f) The students lift the left end of the surface so that the surface is inclined at an angle to the horizontal, and the experiment for m 2 = kg is repeated. Would the acceleration of the system be greater than, less than, or equal to the acceleration of the system in the original experiment? _____ Greater than _____ Less than _____ Equal to Justify your claim.)

10 GO ON TO THE NEXT PAGE. Use a pencil or pen with black or dark blue ink only. Do NOT write your name. Do NOT write outside the box. 2021 College Board. Visit College Board on the web: 5. 166 V Front Bklt AP Physics C: Mechanics 2021 Free-Response Questions Begin your response to QUESTION 2 on this page. 2. Object A is a long, thin, uniform rod of mass M and length 2L that is free to rotate about a pivot of negligible friction at its left end, as shown above. (a) Using integral calculus, derive an expression to show that the rotational inertia IA of object A about the 4. pivot is given by ML 2 . 3. Object B of total mass M is formed by attaching two thin, uniform, identical rods of length L at a right angle to each other. Object B is held in place, as shown above. Express your answers in part (b) in terms of L . (b) Determine the following for the given coordinate system shown in the figure.