A pulley of radius R1 and rotational inertia I1 is

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Presentation transcript:

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.

1 point for recognition that a = 0 1 point for correct answer (a) Determine the tension T in the cord. T 2mg

(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.

1 point for correct substitution into Newton’s law 1 point for correct solution i. The tension T3 in the section of cord supporting the three blocks on the left. a 3mg T3

1 point for correct substitution into Newton’s law 1 point for correct answer ii. The tension T1 in the section of cord supporting the single block on the right. T1 mg a

I1 = I1 ? 1 point for torque equation 2 points for substitutions 1 point for correct solution iii. The rotational inertia I1 of the pulley. I1 = I1 ?

(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 w1, which in turn causes the larger pulley to rotate. The loop does not slip on the pulleys.

1 point for recognition that the tangential speed of the cord on the pulleys is the same 1 point for correct answer Determine the following in terms of I1, R1, and w1. i. angular speed w2of the larger pulley

Determine the following in terms of I1, R1, and w1. ii. angular momentum L2 of the larger pulley 1 point for correct substitution into the angular momentum equation

Determine the following in terms of I1, R1, and w1. iii. The total kinetic energy of the system 1 point for correct expression for kinetic energy as the sum of kinetic energies 1 point for correct answer