What is the amount of work that the floor does when you jump if the floor is compressive?

Question

If the floor isn't compressive and the Earth's mass is too big to consider, the floor does not do work on you. What if it's like the real world, where the floor compresses a little and the Earth moves because of your jump? If you jump to a height h, Will it do exactly mgh work, 0 work, or somewhere in between?

Answer 1

Without doing the calculations I can confidently say that with the mass ratio between a person and the earth that the earths movement effected by your jump is so miniscule that work would be equivalent to zero, there would though be some work though.

you might want to see how this scales such that what if everyone jumped at the same time really close together? this is a great book/video that answers this I recommend grabbing the book if you like weird physics questions.

as for calculations I don't have the time at the moment to run thru them but if I remember I'll revisit this question.

Answer 2

Either 0 (in an idealized case) or neither of those things. You will actually do work on the floor. You compress it; some of the energy stored in the ATP in your body and released in your muscles during the jump is spent on deformation. This deformation is not perfectly elastic: otherwise you wouldn't hear the sound of the jump. Even if on large scale you don't deform the floor, you make it oscillate. Those are dumped oscillations: energy goes into some kind of friction, i.e. ultimately into heat, so you heat the floor up a bit by jumping on it. If the floor gets deformed permanently, that again means you spent some energy on deforming it, i.e. performed some work on the floor.

Answer 3

The Earth does no work on (transfers no energy to) your body when you jump. In order for a force to do work on an object it must displace the material of the object at the point of contact with the force. That doesn’t happen when you jump. The bottom of your feet are vertically displaced after they lose contact with the Earth. Instead, jumping essentially involves the conversion of chemical potential energy of the cells in the muscles of your body enabling them to giving your body kinetic energy.

It’s somewhat analogous to considering your legs as compressed springs before jumping with the mass of your body on top. The springs are suddenly unlatched propelling the mass upward. Only in this case it involves the conversion of elastic potential energy of the spring, instead of chemical potential energy of your muscles, into kinetic energy of the mass.

Hope this helps.

Answer 4

You had zero velocity at first, and after flexing legs, reach a velocity $v$ just when losing contact with the ground. Your centre of gravity went up during that period from A to B.

Gravity and the force that the ground does on you are the only external force responsible for that increase in your kinetic energy. So, the work of that forces equals the change of your kinetic energy.

After losing contact with the ground, and neglecting air resistance, the only external force is gravity. As a conservative force, all kinetic energy is transformed in potential energy at the maximum height $h$, when your velocity is zero again. So, we can calculate the work from the ground force on you, responsible for your initial velocity:$$w = \int_A^B (F_g-mg)dz = \int_A^B F_gdz - mg(B-A) = \frac{1}{2}mv^2 = mgh$$ or $$w = mg(h + (B-A))$$