# Note: Use g=10 N/kg in this assignment.?

1. What is the gravitational energy (relative to the unstretched surface of the trampoline) of the 20 kg ball at its apex 2 m above the trampoline?

2. What is the kinetic energy of the ball just before impacting the trampoline?

3. At maximum stretch at the bottom of the motion, what is the sum of the elastic and gravitational energy of the ball?

4. What conclusions can you draw from the answers found above?

5. The sumo wrestler originally only jumps 10 cm above the trampoline but he has the same total energy as the ball which was 200 cm higher than the trampoline. What causes this equivalence?

6. If a 40 kg gymnast and a 400 kg sumo wrestler each dropped from 1 m above the trampoline, find the final position of each athlete. Assume the trampoline is a simple spring obeying Hooke's law with a k value of 12 000 N/m.

7. Each push of the legs drives the sumo wrestler 10 cm higher in the air. If on the first push, the trampoline went from 8 cm below its normal surface plane, find the average force exerted by his leg muscles?

8. Real world trampolines lose energy since they are damped springs with much internal friction. How much energy does the sumo wrestler lose on each bounce in this situation?

9. How can a gymnast keep a constant bounce height in a real world trampoline?