Problem 3 A block is attached to a diskshaped pulley The mas

A block is attached to a disk-shaped pulley. The mass of the pulley is M = 0.10 kg and its radius is R = 0.4 m. The mass of the block is m = 0.25 kg. If the block starts at rest, what is the speed of the block after it drops by 4.0 m?

Solution

Let speed be v after it drops by 4 m.

loss in potential energy = gain in kinetic energy.

mgh= KE of block + rotational KE of disk

mgh= 1/2mv^2 + 1/2 MR^2 (V/R)^2 = 1/2 mv^2 + 1/2 Mv^2 = 1/2(m+M) v^2

v= (2mgh/(m+M))^1/2 = 7.483 m/s