AP? Physics C
2000 Free response Questions
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(2000 M1) You are conducting an experiment to measure the acceleration due to gravity gu at an unknown location. In the measurement apparatus, a simple pendulum swings past a photogate located at the pendulum's lowest point, which records the time t10 for the pendulum to undergo 10 full oscillations. The pendulum consists of a sphere of mass m at the end of a string and has a length l. There are four versions of this apparatus, each with a different length. All four are at the unknown location, and the data shown below are sent to you during the experiment.
t10 T T2 ? (s) (s) (s2) (cm) 12 7.62 18 21 32 8.89 10.09 12.08 a. For each pendulum, calculate the period T and the square of the period. Use a reasonable number of significant figures. Enter these results in the table above.
b. On the axes below, plot the square of the period versus the length of the pendulum. Draw a best-fit straight line
for this data. c. Assuming that each pendulum undergoes small amplitude oscillations, from your fit determine the experimental value gexp of the acceleration due to gravity at this unknown location. Justify your answer.
d. If the measurement apparatus allows a determination of gexp that is accurate to within 4%, is your experimental
value in agreement with the value 9.80 m/s2 ? Justify your answer.
e. Someone informs you that the experimental apparatus is in fact near Earth's surface, but that the experiment has
been conducted inside an elevator with a constant acceleration a. Assuming that your experimental value g is exact, determine the magnitude and direction of the elevator's acceleration.
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2000M2. A rubber ball of mass m is dropped from a cliff. As the ball falls, it is subject to air drag (a resistive force caused by the air). The drag force on the ball has magnitude bv2, where b is a constant drag coefficient and v is the instantaneous speed of the ball. The drag coefficient b is directly proportional to the cross-sectional area of the ball and the density of the air and does not depend on the mass of the ball. As the ball falls, its speed approaches a constant value called the terminal speed.
a. On the figure below, draw and label all the forces on the ball at some instant before it reaches terminal speed.
b. State whether the magnitude of the acceleration of the ball of mass m increases, decreases, or remains the same
as the ball approaches terminal speed. Explain.
c. Write, but do NOT solve, a differential equation for the instantaneous speed v of the ball in terms of time t, the
given quantities, and fundamental constants.
d. Determine the terminal speed vt in terms of the given quantities and fundamental constants.
e. Determine the energy dissipated by the drag force during the fall if the ball is released at height h and reaches
its terminal speed before hitting the ground, in terms of the given quantities and fundamental constants.
2000M3. A pulley of radius R1 and rotational inertia I1 is mounted on an axle with negligible friction. A light cord passing over the pulley has two blocks of mass m attached to either end, as shown above. Assume that the cord does not slip on the pulley. Determine the answers to parts (a) and (b) in terms of m, R1, I1, and fundamental constants. a. Determine the tension T in the cord.
b. One block is now removed from the right and hung on the left. When the system is released from rest, the three
blocks on the left accelerate downward with an acceleration g/3 . Determine the following. i. The tension T3 in the section of cord supporting the three blocks on the left ii. The tension Tl in the section of cord supporting the single block on the right iii. The rotational inertia I1 of the pulley
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c. The blocks are now removed and the cord is tied into a loop, which is passed around the original pulley and a
second pulley of radius 2R1 and rotational inertia 16I1. The axis of the original pulley is attached to a motor that rotates it at angular speed ?1, which in turn causes the larger pulley to rotate. The loop does not slip on the pulleys. Determine the following in terms of I1, RI, and ?1. i. The angular speed ?2 of the larger pulley
ii. The angular momentum L2 of the larger pulley iii. The total kinetic energy of the system
2000E1. Lightbulbs A, B, and C are connected in the circuit shown above.
a. List the bulbs in order of their brightness, from brightest to least bright. If any bulbs have the same brightness,
state which ones. Justify your answer.
Now a switch S and a 5.0 mH inductor are added to the circuit; as shown above. The switch is closed at time t = 0.
b. Determine the currents IA, IB, and IC for the following times. i. Immediately after the switch is closed ii. A long time after the switch is closed
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c. On the axes below, sketch the magnitude of the potential difference VL across the inductor as a function of time,
from immediately after the switch is closed until a long time after the switch is closed.
d. Now consider a similar circuit with an uncharged 5.0 ?F capacitor instead of the inductor, as shown above. The
switch is again closed at time t = 0. On the axes below, sketch the magnitude of the potential difference Vcap across the capacitor as a function of time, from immediately after the switch is closed until a long time after the switch is closed.
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College Board, Advanced Placement Program, AP, SAT, and the acorn logo are registered trademarks of the College Entrance Examination Board.