Energy and Rotational Inertia Question

[ForceSith]

Homework Statement

A pulley of moment of inertia I and radius r is fixed to a wall. A rope is wrapped around it and tied to a block of mass m. The block is initially held at rest, and then it is released. The block drops a distance h. The rope does not slip on the pulley, and the magnitude of the acceleration due to gravity is g. You know I, r, m, h, and g. [NOTE: a diagram wasn't given, but the professor said it was just a simple pulley attached to the wall with a block hanging off of it from a rope).

-What is the work done by gravity on the system?
-What is the change in potential energy of the system? change in kinetic energy of the system?
-What is the speed v of the block in terms of I, r, m, h, and g?
-What is the angular speed (omega) in terms of I, r, m, h, and g?

Homework Equations

These weren't given in the problem, but:
K = (1/2)*I*w^2 + (1/2)*M*v^2
U = mgy

The Attempt at a Solution

Okay, I have no idea about questions 1 and 3, I think it has something to do with conservation of energy? For question number 2, I had:

K1 + U1 = K2 + U2

But the problem is since the whole system starts out at rest, wouldn't there be no initial energy except for potential? Meaning the "change" in potential energy would only be mgh? Or does the block somehow add potential energy as well?

Thanks in advance, I'm quite at a loss right now and my physics textbook isn't helping :(

 

[gamer_x_]

1) think about what needs to happen for gravity to do work. Which parts of the system are affected by this?

2) you're going about it the right way. Don't overthink the potential energy, just use what you know: gravity, springs, electrostatics, chemical, etc . and since all but one of those are not in the question... What are the types of kinetic energy present?

 

[ForceSith]

I guess the only thing affected by gravity is the block? Since the pulley is attached to the wall, does that mean that the only work would be the motion of the block going down the distance h?

So Wg = F*h = m*g*h?

As far as the energy changes, there's no chemical, electrical, or spring...just the .5mv^2 of the block moving and the .5Iw^2 of the pulley?