# Homework Help: A little help please what is the mass of the pulley?

1. Nov 12, 2007

### Sucks@Physics

A 4.0 kg mass is hung from a string, which is wrapped around a cylindrical pulley (cylindrical disk I =(1/2)MR^2). If the mass accelerations downward at 4.90m/s^2, what is the mass of the pulley?

I don't even know where to begine, could some1 get me started?

Thanks

2. Nov 12, 2007

### dynamicsolo

Have you worked with rotational kinetic energy yet? Otherwise, this can be done just using torques.

Using torques -- Make a force diagram for the pulley and the hanging mass. What force is acting on the pulley and what is it equal to? What torque does that force apply to the pulley using r x F? The pulley rotates rigidly, so how do you get the angular acceleration of the pulley? What is the tangential acceleration of the pulley at its edge, where the string is wound? Since this has to match the vertical acceleration of the hanging mass, you have the requisite information to solve for the pulley's mass.

Using energy -- Track the total mechanical energy of the system, which includes the linear kinetic energy of the hanging mass, the rotational KE of the pulley, and the gravitational potential energy of the hanging mass. This total is conserved, since we appear to be assuming that there is no friction. This is a subtler approach because you need velocities; but you do know that the linear acceleration of the mass is constant, so you can express its linear velocity in terms of that. Again, from the information in the problem, it will be possible to solve for the pulley's mass.

Incidentally, if you're doing this right, you'll see why you aren't told how big the pulley is...

Last edited: Nov 12, 2007
3. Nov 13, 2007

### Sucks@Physics

I dont know what force is acting on the pully, if you could help me out ther ei think i can get it started

4. Nov 13, 2007

### Astronuc

Staff Emeritus
5. Nov 13, 2007

### Sucks@Physics

So the acceleration of the pully must be the same of the weight correct? But how would u find the raduis of the pulley if you have is the acceleration of it?

6. Nov 13, 2007

### Sucks@Physics

Any help?

7. Nov 17, 2007

### dynamicsolo

If you're still looking at this thread:

You won't need a specific value for the size of the pulley. You can call its radius R for the purpose of the calculation where you need to write something. As I mentioned earlier, it won't matter what the radius is.

As for your other question: yes, the tangential acceleration of the pulley (the linear acceleration at its edge) will be the same as the acceleration of the falling weight.