a) Two identical spring scales are each attached to a cord that is wrapped around a pulley, as shown in Figure 1. The two pulleys have identical mass Mp and radius Rp. However, Pulley A is a solid disk, whereas Pulley B has most of its mass located at its outer rim. Both pulleys can rotate about their centers with negligible friction in their axles.

The pulleys are initially at rest when the two spring scales are pulled with the same constant force Fs, causing both pulleys to rotate. Predict which of the pulleys, if either, will complete one revolution first.

____ Pulley A ____ Pulley B ____ Both pulleys will complete one revolution at the same time.

Without writing or manipulating equations, provide reasoning for your selection.

(b)

i. Derive an equation for the time tA it takes Pulley A to complete one revolution. Let IA be the pulley’s rotational inertia. Express your answer in terms of FS, IA, Mp, Rp, and physical constants, as appropriate.

ii. Is your answer to part (b)(i) consistent with your answer to part (a)?

____ Yes ____ No

Provide reasoning for whether the two answers are or are not consistent.

(c) A block of mass M is attached to Pulley A , as shown in Figure 2. The block is released from rest. Describe how the net torque exerted on the pulley and the magnitude of the angular momentum of the pulley are changing, if at all, a short time after the block is released.

Net torque: ____ Increasing ____ Decreasing ____ Not changing

Angular momentum: ____ Increasing ____ Decreasing ____ Not changing

Briefly describe how you arrived at your answers.

(d) A long cord of negligible mass is wrapped around a third pulley, Pulley C, and attached to a spring scale, as shown in Figure 3. The spring scale is pulled downward so that it exerts a constant force of magnitude FS on the cord. As the spring scale moves down a significant distance, the vertical portion of the cord moves closer and closer to the center of the pulley.

Predict how the net torque exerted on the pulley and the rotational kinetic energy of the pulley will be changing, if at all, as the spring scale moves downward and the vertical portion moves closer to the center of the pulley.

Net torque: ____ Increasing ____ Decreasing ____ Not changing

Rotational kinetic energy: ____ Increasing ____ Decreasing ____ Not changing

Briefly provide reasoning for your predictions.
 
 

Transcribed Image Text:

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Answer rating: 100% (QA)

1 a Pulley A Moment of inertia is give... View the full answer