Sphere Rolling vs. Sliding Down a Ramp

[oranim2]

Homework Statement

Let there be two spheres, of equal radius but unknown masses (mass isn't important).
Both move down a ramp of angle $$\theta$$, where $$\theta$$ can be any angle but 90 deg. or 0 deg.
The first sphere slides down the ramp with no (negligible) friction. This sphere does not roll at all.
The second sphere rolls down the ramp. This sphere does not slip, and thus, its only movement is caused by the rolling, not a sliding motion.

If both spheres are released from the same displacement up the ramp from the ramp's end, at the same time, which will reach the bottom of the ramp first?
Prove that this is so

Homework Equations

Moment of inertia equations. F=MA. Motion with constant acceleration equations.

The Attempt at a Solution

I tried manipulating some of the formulas, but was not able to get very far. I didn't find a way to relate time to the rolling (not sliding) ball.

 

[Doc Al]

Compare the forces acting on each. Then apply Newton's 2nd law.

 

[just__curious]

You can also use energy, might be easier.

 

[oranim2]

Any other help?... I still am a bit stuck.

 

[jgens]

Sure, let's examine the energy transformations of the sliding ball. We start out with purely potential energy; however, as the ball reaches the end of the incline, all the potential energy has subsequently been converted into kinetic energy. Hence, PE = KE.

Now apply similar logic to the rolling ball and interpret the results.