A block of mass m = 3.1 kg is attached to a string that is wrapped around the ci

Question

A block of mass m = 3.1 kg is attached to a string that is wrapped around the circumference of a wheel of radius R = 7.1 cm . The wheel rotates freely about its axis and the string wraps around its circumference without slipping. Initially the wheel rotates with an angular speed , causing the block to rise with a linear speed v = 0.40 m/s .(Figure 1)Part A Find the moment of inertia of the wheel if the block rises to a height of h = 8.4 cm before momentarily coming to rest. Express your answer using two significant figures.

Explanation / Answer

v = R w

w = v / R = 0.40 / 0.071 = 5.63 rad/s

initial energy = 1/2 m v2 + 1/2 I w2

= (1/2 * 3.1 * 0.42) + (1/2 * I * 5.632)

= 0.248 + 15.85 I

final energy = m g h = 3.1 * 9.8 * 8.4 * 10-2 = 2.55

initial energy = final energy

0.248 + 15.85 I = 2.55

moment of inertia I = 0.145 kg.m2

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