l Verizon 9:53 PM a capa9.phy.ohio.edu The Pulley and the Falling Bucket e this

Question

l Verizon 9:53 PM a capa9.phy.ohio.edu The Pulley and the Falling Bucket e this Friday, Mar 23 at 11:59 pm (EDT) A bucket hangs from a rope that is attached to a cylindrical, massive pulley with a radius of 0.380 m and a mass of 2.26 kg. The bucket starts at rest and fals a distance 7.70 m before hitting the water. During this time the pulley undergoes an angular acceleration of 4.42 rad/s2, which means the bucket is falling with a linear acceleration of 1.68 m/s (a ra). What is the moment of inertia of the pulley? (remember, this is a solid cylinder.) Submi 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 AnswerTries 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? Submit Answer Tries 0/10

Explanation / Answer

a) I = 1/2 m R2 = 1/2 * 2.26 * 0.3802= 0.163 kg.m2

b) Torque = I * alpha = 0.163 * 4.42 = 0.72 N.m

c) torque = F R

F = torque / r = 0.72 / 0.380 = 1.89 N

d) y = 7.70 m

y = voy t + 1/2 ay t2

7.70 = 0 + (0.5 * 1.68 * t2)

t = 3.03 s

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