Physics
posted by Mary .
The two masses (m1 = 5.0 kg and m2 = 3.0 kg) in the Atwood's machine shown in Figure 1023 are released from rest, with m1 at a height of 0.87 m above the floor. When m1 hits the ground its speed is 1.4 m/s. Assume that the pulley is a uniform disk with a radius of 12 cm. Determine the pulley's mass.

You know the energy gained (mgh)
You know the final KE of all masses, so the rest of the KE must be the pulley.
KE=I*w
I assume you will model the pulley as a disk of some radius r. w=vfinal/r
Solve for masspulley.