posted by Alex .
A ball (radius 0.2 m) is rolling on level ground toward an incline. If its velocity is 3 m/s, to what maximum height above the ground does it roll up the incline? The ball is a hollow sphere with a moment of inertia I=(2/3)mr2 (m is the mass of the ball, r its radius).
Kinetic energy = (1/2) I w^2
velocity of surface of ball = w r = .2 w = 3
w = 3/.2 = 15 radians/second
now potential energy at top = kinetic energy at bottom
m g h = (1/2) (2/3) m r^2 (15)^2
m cancels, g = 9.8
h = (1/3) (.04)(225/9.8)