- #1

Watney

- 7

- 0

## Homework Statement

A sphere of mass M and radius R is not necessarily solid or hollow. It has moment of inertia I = cMR^2 . The sphere starts from rest and rolls without slipping down a ramp from height H. It then moves back up the other side with height h, but now with no friction at all between the sphere and the ramp.

What height h does the sphere reach?

(Answer should only include H and c.)

## Homework Equations

I = cMR^2

KE = 1/2Iω^2

PEg = mgH

## The Attempt at a Solution

So I tried setting up a conservation of energy for both sides of the ramp. For the first half I got

mgH = 1/2mv^2 + 1/2Iω^2. I then solved for v^2.

For the second half of the ramp (one without friction), I got

1/2mv^2 + 1/2Iω^2 = mgh + 1/2Iω^2.

I solved for h then plugged in v^2 from the first equation and got g^2H/c but my answer can't have g so I know this is wrong. Any pointers? I've never done a problem like this so I'm pretty sure I'm way off.