Exam question, rotational motion.

[Kelschul]

Homework Statement

Two identical soccer balls are released from rest from the top of ramp consisting of a straight section connected to a circular section having the shape shown at right (height of ramp from where ball is released to bottom of curve is 4.0m. The radius of the curve is 1.5m). The end of the circular section of track is vertical. One ball slides down the ramp, while the other ball rolls without slipping. A soccer ball can be considered a thin-walled spherical shell. What is the speed of each ball at the bottom of the curve?

Homework Equations

I=(2/3)MR(^2)

The Attempt at a Solution

I have to solve one ball using rotational motion concepts, and one just regularly, right?
I think this is what I have to do, but without having mass, or any other variable I just can't figure out what equation to start with.
The only equation I can find that has height in it, which seems the only logical place to start for me is the equation for work done by non-conservative forces. I started to use this equation, but then I realized it still wouldn't help me find the speed at the bottom of the hill because I don't know mass, velocity, or the Wnc.
I'm scanning my notes like crazy trying to find an equation!

Maybe I just found something...
PE=mgh
Initial Pe is m(9.8)(4.0), Final is 0 because there is no height...
39.2m=.5mvf(^2)-0 (no initial velocity)
vf=8.9m/s for the sliding ball? right?

 

[Kurdt]

Its definitely to do with energy considerations. One ball will have all its energy transferred to kinetic energy while the other will have a sum of kinetic energy and rotational energy. I think the last part of your attempt has touched on what you need to do and also shows that the masses cancel. Do you know the equation for rotational energy? It is very similar to translational kinetic energy.