A light rope is wrapped several times around a large wheel with a radius of 0.42
ID: 1291585 • Letter: A
Question
A light rope is wrapped several times around a large wheel with a radius of 0.425m . The wheel rotates in frictionless bearings about a stationary horizontal axis, as shown in the figure. The free end of the rope is tied to a suitcase with a mass of 20.0kg . The suitcase is released from rest at a height of 4.00m above the ground. The suitcase has a speed of 3.35m/s when it reaches the ground.
1. Calculate the angular velocity of the wheel when the suitcase reaches the ground.
____ rad/s
2. Calculate the moment of inertia of the wheel.
I = _____ kg x m^2
A light rope is wrapped several times around a large wheel with a radius of 0.425m . The wheel rotates in frictionless bearings about a stationary horizontal axis, as shown in the figure. The free end of the rope is tied to a suitcase with a mass of 20.0kg . The suitcase is released from rest at a height of 4.00m above the ground. The suitcase has a speed of 3.35m/s when it reaches the ground. 1. Calculate the angular velocity of the wheel when the suitcase reaches the ground. ____ rad/s 2. Calculate the moment of inertia of the wheel. I = _____ kg x m^2Explanation / Answer
The total kinetic energy = 1/2 * I*w^2 + 1/2 *m*v^2
According to law of conservation of energy
mgh =1/2 * I*w^2 + 1/2 *m*v^2
mgh-1/2 *m*v^2 =1/2 *( m*r^2 /2)*w^2
gh-v^2 =1/4*r^2w^2
w^2=4(gh-v^2 )*r^2
w^2=4*(9.8*4-3.35^2)*0.425
w^2=47.56
w=6.89 rad /s
2) I =M*R^2/2
=1.80625 kg.m^2
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