You are trying to lift a 50 kg box by attaching it to a rope, which hangs over a

ID: 2076763 • Letter: Y

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You are trying to lift a 50 kg box by attaching it to a rope, which hangs over a pulley which has a radius of R = 4.0 cm and mass of 1.5 kg, and pulling the other end. Unfortunately, you lose your grip, and the box starts to fall again. If the box starts from rest, what is the angular velocity wof the pulley after the box has fallen 1.0 m? Assume there is no “slippage” between the rope and pulley. (Solve with conservation of energy, not Kinematics!) You are trying to lift a 50 kg box by attaching it to a rope, which hangs over a pulley which has a radius of R = 4.0 cm and mass of 1.5 kg, and pulling the other end. Unfortunately, you lose your grip, and the box starts to fall again. If the box starts from rest, what is the angular velocity wof the pulley after the box has fallen 1.0 m? Assume there is no “slippage” between the rope and pulley. (Solve with conservation of energy, not Kinematics!)

Explanation / Answer

Applying energy conservation for pulley-mass system,

PEi + KEi = PEf + KEf

m g h + 0 = 0 + (m v^2 /2 + I w^2 /2)

50 x 9.8 x 1 = ( 50 v^2 /2) + (1.5 r^2 / 2)( v / r)^2 / 2

490 = 25 v^2 + 0.375 v^2

v = 4.39 m/s

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You are trying to lift a 50 kg box by attaching it to a rope, which hangs over a

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