AP Free Response Question
2001 C3
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A light string that is attached to a large block of mass 4m passes over a pulley with negligible rotational inertia and is wrapped around a vertical pole of radius
r
, as shown in Experiment A above.
The system is released from rest, and as the block descends the string unwinds and the vertical pole with its attached apparatus rotates. The apparatus consists of a horizontal rod of length
2L
, with a small block of mass
m
attached at each end. The rotational inertia of the pole and the rod are negligible.
Determine the rotational inertia of the rod and block apparatus attached to the top of the pole.
Determine the downward acceleration of the large block.
When the large block has descended a distance D, how does the instantaneous total kinetic energy of the three blocks compare with the value 4mgD?
___ Greater than 4mgD ___ Equal to 4mgD ___ Less than 4mgD
Check the appropriate space and justify your answer.
The system is now reset. The string is rewound around the pole to bring the large block back to its original location. The small blocks are detached from the rod and then suspended from each end of the rod, using strings of length
.
The system is again released from rest so that as the large block descends and the apparatus rotates, the small blocks swing outward, as shown in Experiment B above. This time the downward acceleration of the block decreases with time after the system is released.
When the large block has descended a distance D, how does the instantaneous total kinetic energy of the three blocks compare to that in part c?
___ Greater before ___ Equal to before ___ Less than before
Check the appropriate space and justify your answer.
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
torque
uniform acceleration - displacement and instantaneous velocity
uniform acceleration - instantaneous position
uniform acceleration - instantaneous velocity
work (dot product)
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