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.

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Presentation transcript:

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.

(a) Determine the rotational inertia of the rod-and-block apparatus attached to the top of the pole. 1 point - Correct formula for inertia 1 point - Summing the mL2’s 1 point - Correct answer

1 point - Newton’s 2nd law 1 point - Correct substitution 1 point - Torque formula 1 point - Substitution 1 point - angular acceleration to linear acceleration 1 point - Correct answer (b) Determine the downward acceleration of the large block. T 4mg

Check the appropriate space below. 1 point - Correct selection (c) 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 ? Check the appropriate space below. 1 point - Correct selection 2 points - Justification ___Greater than 4mgD ___Equal to 4mgD ___Less than 4mgD Justify your answer. Total energy is conserved

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 l. 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.

1 point - Correct selection D 4m (d) 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) ? Check the appropriate space below. ___Greater ___Equal ___Less Justify your answer. 1 point - Correct selection 2 points - Justification The two blocks (m) gain gravitational potential energy as they rise.