- #1
woodie37
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Homework Statement
A ball is rolled down a rough hill with coefficient of [tex]\mu[/tex]<tan[tex]\theta[/tex]. The hill has a height of h. The ball has moment of inertia of I, mass of m, and radius of r, which are all constant. What is the final velocity of the ball at the bottom of the hill?
P.S. I made this question up, so I can't find an answer anywhere except from physics experts =D
Homework Equations
W = [tex]\Delta[/tex]K + [tex]\Delta[/tex]U where W is the work done by friction, K is the kinetic energy and U is potential energy.
The Attempt at a Solution
As the ball rolls down the hill it slips due to the fact that the frictional force is not strong enough. From an FBD, gravitational force acts on its center, and frictional force rotates the ball a little bit but the ball slips at a constant rate of slippage (idk if that's the right word).
As the ball is accelerated down wards by gravity, the frictional force decelerates the ball such that it slows down the gravitational acceleration and slightly rotates the ball...
and I have no idea how to do this...I attempted it and got an answer slightly greater than if the friction is strong enough to prevent slippage, where no energy is lost to friction.
Can someone help me solve this please? lol