A hollow ball of mass M and radius R rolls up a hill without slipping. At the bo

A) vf = sqrt( v0^2 + 2*g*h) m/s B) Angular velocity, w = vf/R = sqrt( v0^2 + 2*g*h)/R rad/s C) NO D) same as vf , that is sqrt( v0^2 + 2*g*h) m/s

ID: 1487355 • Letter: A

Question

A hollow ball of mass M and radius R rolls up a hill without slipping. At the bottom of the hill, it is moving with a velocity v0 .

Part A

What is the ball's velocity at the top of the hill (which has a height h )?

Part B

What is the angular velocity of the ball at the top of the hill?

Part C

At the top of the hill, the ball rolls off a cliff. While the ball is in the air, does its angular velocity change? (You may ignore air resistance.)

Part D

The ball is moving horizontally when it leaves the cliff. What is the vertical velocity of the ball when it lands?

Part E

What is the speed of the ball when it strikes the ground?

Part F

What is the total kinetic energy of the ball when it strikes the ground? (Since the ball is NOT rolling without slipping, you cannot use ?=v/R!)

vf =

vf = sqrt( v0^2 + 2*g*h) m/s

Angular velocity, w = vf/R = sqrt( v0^2 + 2*g*h)/R rad/s

same as vf , that is sqrt( v0^2 + 2*g*h) m/s

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