Rotational kinetic energy of falling mass

[kyin01]

Homework Statement

Engineers are designing a system by which a falling mass {m} imparts kinetic energy to a rotating uniform drum to which it is attached by thin, very light wire wrapped around the rim of the drum ( View Figure ). There is no appreciable friction in the axle of the drum, and everything starts from rest.

That is top part of the problem

Homework Equations

mgh = rotational + translation kinetic energy

The Attempt at a Solution

I've tried various methods mainly using energy conservation laws, but I can't get it right. the problem didn't give I or R so I've been using .200J as the total rotational energy.

Any hits on how I should be going on this problem?

thanks

 

[Dick]

The presentation of your problem is headache inducing. Can you maybe just include the diagram, and the problem statement and leave off the irrelevant blank graphic parts. Just type out what the question is. You also left out any description of how you attempted to use those conservation laws. There is a relation between the velocity of the descending weight and the rotational velocity of the disk. v=omega*r. Did you use that? No way to know, is there?

 

[kyin01]

that was all that's given in the problem. The question is under Part A.

 

[Dick]

You don't need I or R. The question is to compare the operation of the thing on Earth and on Mars. The only difference is 'g'. If you don't know something leave it as a letter. Now, write down one of these conservation laws.

 

[kyin01]

In this situation there are no non conservative forces so

Kinetic energy = potential energy.

So in our situation we have
(Point 1 to be taken at before the system is released and point 2 to be taken just before it hits the ground)

mgh= .200 (which is the rotational kinetic energy that was given to us)

so in mars, just replace 9.8 with the given 3.71 (mass is the same) and solve for h. But when I tried that, they told me it's wrong.
I got h to be .003594m

 

[Dick]

Absolutely right. But how did you get that silly answer? If m*(9.8m/s^2)*h_earth=m*(3.7m/s^2)*h_mars, then h_mars must be LARGER than h_earth. Can you post the details of how you did it?

 

[kyin01]

ah, I got it. Forgot to take account linear kinetic energy also

so the system is actually

Potential energy = Kinetic rotational + kinetic linear

thanks.