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A bowling ball (solid sphere, moment of inertia is (2/5)MR2) of mass M and radius R...

A bowling ball (solid sphere, moment of inertia is (2/5)MR2) of mass M and radius R rolls down a hill without slipping for a distance of L along the hill with slope of angle θ, starting from rest. At that point, the hill becomes frictionless.The ball continues down the hill for another segment of length 2L (thus the total distance travelled on the hill is 3L). The hill levels out into a horizontal area, where the coefficient of friction is μk, which is constant throughout the entire horizontal length. The ball rolls without slipping before it hits a plate attached to a spring with spring constant k.

a) What happens to the ball immediately after it goes onto the frictionless surface (before it reaches the horizontal area)?

b) What is the angular speed of the ball just before it hits the spring?

c) What is the maximum compression of the spring?

d) How much energy is lost to friction from when the ball is released until the spring reaches maximum compression?

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