Physics HELP!!?

Question

A uniform solid sphere with a mass of M = 5.0 kg and radius R = 20 cm is rolling without
slipping on a horizontal surface at a constant speed of 5.0 m/s. It then encounters a ramp, and
proceeds to roll without slipping up the ramp. The goal of this problem is to determine the
maximum height reached by the sphere on the ramp before it turns around, and to use
conservation of energy to do so. Use g = 10 m/s2.

(a) Write out expressions for the remaining terms. Remember to account for both
translational kinetic energy and rotational kinetic energy, if appropriate. Keep everything in
terms of variables.

(b)How far does the sphere roll up the ramp (measuring the vertical distance)? First
find an expression for this distance in terms of variables, simplified as much as possible, and
then plug in the appropriate values.

(c) If a block slides without friction up the ramp, starting at the bottom with the same
initial speed as the sphere, which object travels farther up the ramp

Thanks jgoulden....

thats exactly how i did it. now i know i did it right. I'll give you the points as soon as i can.

Answer 1

The initial kinetic energy is 1/2 m v^2 + 1/2 I w^2 where

m is the mass
v the velocity
I the moment of inertia = 2/5 m r^2 for a uniform solid sphere
w the angular velocity = v/r since it rolls without slipping

When the sphere moves up the ramp and stops, for a split second all of the energy is potential, mgh

So solve 1/2 m v^2 + 1/2 I w^2 = mgh to find the height h

The block is solved the same way; 1/2 m v^2 = m g h
You don't need to know the mass, it cancels out ;)