A disk with a mass of 16.7 kg, a diameter of 25.7 cm, and a thickness of 7.21 cm

Question

A disk with a mass of 16.7 kg, a diameter of 25.7 cm, and a thickness of 7.21 cm is mounted on a rough horizontal axle as shown on the left in the figure. (There is a friction force between the axle and the disk). The disk is initially at rest. A constant force, F = 68.1 N, is applied to the edge of the disk at an angle of 37.0°, as shown on the right in the figure. After 2.00 s, the force is reduced to F = 18.5 N, and the disk spins with a constant angular velocity.

a) What is the magnitude of the torque due to friction between the disk and the axle?

b) What is the angular velocity of the disk after 2.00 s?

c) What is the kinetic energy of the disk after 2.00 s?

Explanation / Answer

a) mass m = 16.7 kg , radius r = 25.7/2 = 12.85 cm = 0.1285 m net force F = 68.1 - 18.5 = 49.6 N torque t = rFsin37 = 3.8357 N.m b) net force F = 68.1 - 18.5 = 49.6 N angle ? = 37 degrees moment of inertia of disk I = mr2 /2 = 0.1378 kg.m2 torque Ia = rFsin37 a = 27.81 rad/s2 intial angular velocity ?1 = 0 , time t = 2s angular velocity at t = 2 s , ?2 = at = 55.63 rad/s c) the kinetic energy of the disk after 2.00 s K = 1/2 I?22 = 213.3 J

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