(Figure Included Here) A bucket hangs from a rope that is attached to a cylindri
ID: 1791332 • Letter: #
Question
(Figure Included Here) A bucket hangs from a rope that is attached to a cylindrical, massive pulley with a radius of 0.420 m and a mass of 3.10 kg. The bucket starts at rest and falls a distance 4.33 m before hitting the water. During this time the pulley undergoes an angular acceleration of 4.17 rad/s2, which means the bucket is falling with a linear acceleration of 1.75 m/s2 (a=r). What is the moment of inertia of the pulley? (remember, this is a solid cylinder.) Submit Answer Tries 0/10 What is the magnitude of the torque that the rope exerts on the pulley? (Think about the rotational version of Newton's Second Law.) Submit Answer Tries 0/10 Since you know the torque, what is the force that the rope is exerting on the pulley? Submit Answer Tries 0/10 How much time elapses between when the bucket is released and when it hits the water?
Explanation / Answer
a) I = 1/2 m R2
= 1/2 * 3.10 * 0.4202= 0.273 kg.m2
b) Torque = I * alpha
= 0.273 * 4.17 = 1.14 N.m
c) Tension = torque / R
= 1.14 / 0.420 = 2.71 N
d) t = sqrt [2 d / a]
= sqrt [2 * 4.33 / 1.75] = 2.22 s
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