Need answer to this Energy and Rotation problem.

A block of 5.0 kg rests on a frictionless plane. It is connected to a rope which runs over a disk, and the other end of the rope is attached to a hanging block of 2.0 kg. The disk is homogeneous,it is free to rotate, and has a radius of 8.0 cm and a mass of 600 g.The rope runs over the disk without slipping.

i) Calculated the velocity of the 2kg block after it has fallen 2.5 m.

ii) What is then the angular velocity of the disk?

Question

Need answer to this Energy and Rotation problem.

A block of 5.0 kg rests on a frictionless plane. It is connected to a rope which runs over a disk, and the other end of the rope is attached to a hanging block of 2.0 kg. The disk is homogeneous,it is free to rotate, and has a radius of 8.0 cm and a mass of 600 g.The rope runs over the disk without slipping.

i) Calculated the velocity of the 2kg block after it has fallen 2.5 m.

ii) What is then the angular velocity of the disk?

anonymous · Answer

|dw:1318802112131:dw|

the initial potential energy of the system is PE = mgh=2kg * 9.8 * 2.5m

this will be converted to kinetic energy after it has fallen by 2.5 meters. 
KE of 5kg block is 5/2 v^2
KE of Disk is 1/2 Iw^2 = 1/4 mr^2 w^2 = 1/4 (mr/v) = 1/4 (0.6*0.08/v)
KE of 2kg block is 1/2 mv^2= v^2

add all this KE up and Equate it to the initial PE and you will get the velocity :D

2.) angular velocity = omega = w = v/r