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.

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?

Question

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.

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?

Narad · Answer

At the beginning, both of them will have potential energy

PE=mgy

Where y=h+x (x is the compression of the spring)

And the PE will be stored in the spring as

E= 1/2kx^2

So the equation is

1/2kx^2=mg(h+x)

You will have 2 equations to solve and you will find 2 values for x (one for the gymnast and one for the sumo)