Why Does a Rolling Sphere Climb Higher Than a Sliding Particle?

[connorc234]

Homework Statement

A uniform sphere and a particle are sent one-by-one with the same initial speed up the same incline. Each rises to a maximum height before falling back towards the starting point. The sphere rolls without slipping; the particle slides without friction. Use conservation of energy to show that the maximum height gained by the sphere is a factor 7/5 times that gained by the particle

Homework Equations

I = (2/5)MR^2

The Attempt at a Solution

In the first part of the question I'm asked to prove the moment of inertia for a hollow sphere and then a uniform sphere. I've done that and gotten the above equation for uniform sphere. But I don't know to apply it in this case. I'm not given any masses for either body. Any help?[/B]

 

[haruspex]

I'm not given any masses for either body. Any help?

So plug in a (different) unknown for each mass and see where it goes. Just maybe the masses will cancel out later.

 

[lordianed]

Like haruspex said, the masses don't matter, they'll cancel out. Keep in mind that the total initial energy possessed by the sphere will be comprised of rotational and translational kinetic energy.