AP Free Response Question
2004 C2
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A solid disk of unknown mass and known radius
R
is used as a pulley in a lab experiment, as shown below.
A small block of mass
m
is attached to a string, the other end of which is attached to the pulley and wrapped around it several times. The block of mass
m
is released from rest and takes a time
t
to fall the distance
D
to the floor.
(a) Calculate the linear acceleration
a
of the falling block in terms of the given quantities.
(b) The time
t
is measured for various heights
D
and the data are recorded in the following table.
i. What quantities should be graphed in order to best determine the acceleration of the block? Explain your reasoning.
ii. On the grid below, plot the quantities determined in (b)i., label the axes, and draw the bestfit line to the data.
iii. Use your graph to calculate the magnitude of the acceleration.
(c) Calculate the rotational inertia of the pulley in terms of
m
,
R
,
a
, and fundamental constants.
(d) The value of acceleration found in (b)iii, along with numerical values for the given quantities and your answer to (c), can be used to determine the rotational inertia of the pulley. The pulley is removed from its support and its rotational inertia is found to be greater than this value. Give one explanation for this discrepancy.
Topic Formulas
Description
Published Formula
angular displacement
angular momentum
angular velocity
center of mass
centripetal acceleration
friction
gravitational force (vector)
gravitational potential energy
Hooke's Law
impulse
kinetic energy
linear momentum
linear velocity and angular velocity
moment of inertia
net torque
Newton's 2nd Law
Newton's Law of Universal Gravitation
period and frequency
period of a simple pendulum
period of a spring
potential elastic energy
potential energy
power (dot product)
rate of change of momentum
rate of change of work
rotational kinetic energy
torque
uniform acceleration  displacement and instantaneous velocity
uniform acceleration  instantaneous position
uniform acceleration  instantaneous velocity
work (dot product)
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