Question

How would I answer number 3?

1. A sumo wrestler originally jumps 10 cm above a trampoline but has the same total energy of a small ball that was 200 cm higher than the trampoline. What causes this equivalency?

2. 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.

3. 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

Answer 1

I did #1

#2
potential energy lost = m g h
potential energy gained = (1/2) k x^2

for 40 kg

40 * 9.81 * (1+x) = (1/2)(12,000) x^2

solve quadratic for x

#3
I have no idea because you did not tell me ratio of bounces

Answer 2

how do you do number 1