Posted by Kyle on Monday, November 3, 2008 at 9:32am.
What happens is that in the answer the mass and the radius drops out.
The total kinetic energy is:
Ekin = 1/2 m v^2 + 1/2 I omega^2
If the ball rolls without slipping, then:
omega = v/R
The moment of intertial of the ball is:
I = 2/5 m R^2
So, the kinetic energy is:
Ekin = 1/2 m v^2 + 1/5 m v^2 =
7/10 m v^2
The potential energy is mgh, so the total energy of the ball is at height h and velocity v is
E(h,v) = m g h + 7/10 m v^2 =
m [g h + 7/10 v^2]
The total energy is conserved, so you can find the velocity at the top by solving:
E(h=0.76 meter, v ) = E(0, v = 5.40 m/)
The unknown mass m drops out.
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