Question

A hollow ball, made of a thin plastic shell, rolls down a rough hill (no slipping) of height h? from rest and across a level ground. It then approaches another hill, but this one is smooth and frictionless.

1. a) Draw a diagram of this situation. (4 points)

2. b) Write down the energy equation which represents the first half of the journey and simplify it to find an expression for the maximum linear velocity of the ball. (4 points)

3. c) Write down the energy equation which represents the second half of the journey and simplify it to find an expression for the maximum height reached. (4 points)

4. d) How high, in terms of h? will the ball go up on the smooth hill? (8 points)

5. e) Does the ball return to its original height, if not, what has happened to the initial potential

   energy of the ball? (6 points)

6. f) If the ball was replaced by a solid disk and a hoop, which of the three shapes would reach the

   highest, which the lowest, justify your answer. (4 points)

Answer 1