A bucket of water with total mass 20.0 kg is attached to a rope,which in turn is wound around a 0.050-m radius cylinder,with crank,at the top of a well.The moment of inertia of the cylinder and crank is 0.21 kg
M².The bucket is raised to the top of the well and released to fall back into the well.What is the kinetic energy of the cylinder and crank at the instant the bucket is moving with a speed of 7.0 m/s?

Question

A bucket of water with total mass 20.0 kg is attached to a rope,which in turn is wound around a 0.050-m radius cylinder,with crank,at the top of a well.The moment of inertia of the cylinder and crank is 0.21 kg

M².The bucket is raised to the top of the well and released to fall back into the well.What is the kinetic energy of the cylinder and crank at the instant the bucket is moving with a speed of 7.0 m/s?

Quizplus · Accepted Answer

The potential energy of the bucket in the initial position is equal to the work done on it by the force of gravity as it falls back into the well. Thus, 
mgh = (1/2)mv^2 + (1/2)Iω^2
where m is the mass of the bucket and water, g is the acceleration due to gravity, h is the height of the well, v is the speed of the bucket at the bottom of the well, I is the moment of inertia of the cylinder and crank, and ω is the angular velocity of the cylinder and crank. 
Solving for the kinetic energy, we get 
(1/2)mv^2 + (1/2)Iω^2 = mgh 
(1/2)(20.0)(7.0)^2 + (1/2)(0.21)(7.0/0.050)^2 = (20.0)(9.81)(0.0) 
= 2 058 J.

A Bucket of Water with Total Mass 20