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This may seem like a silly question, but how can we jump when the ground does no work on us?

When we jump off the ground, the ground does not move. This means the force from the ground on us does zero total work. Since the force does no work, we cannot gain any kinetic energy so we can't jump.

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    $\begingroup$ The ground doesn't do any work on you, so your total energy stays the same. But you use your muscles to convert internal energy (from the food you ate) into kinetic energy. $\endgroup$
    – knzhou
    Commented Dec 1, 2022 at 3:04
  • $\begingroup$ Oh right, chemical potential energy into kinetic energy. Thank you! $\endgroup$ Commented Dec 1, 2022 at 3:06
  • $\begingroup$ @knzhou Actually I guess the ground not doing work on us is an approximation, because from newton's third law, if the ground push's us up then we push the ground down by a very infinitesimal amount due to the inertia of earth. This means that actually the ground dose do a very small amount of work on us increasing our total energy. $\endgroup$ Commented Dec 1, 2022 at 3:09
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    $\begingroup$ It is irrelevant if the ground does or not a little work. You don't need the work of an external force to increase the KE of a system. The work of the internal forces can change the KE. What the internal forces cannot do is to change the momentum of the center of mass. For this, you do need the external force exerted by the ground. But the change in momentum is given by the impulse of the force and this does not need a displacement. So the normal force provides the momentum of the COM. The internal forces take care of the KE (or most of it). $\endgroup$
    – nasu
    Commented Dec 1, 2022 at 4:13

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The ground actually does move, by an infinitesimal amount (c.f. conservation of momentum). But I imagine that's not what you're asking.

The reason you gain energy is because your body converts energy it has already stored (in the form of Adenosine Triphosphate) into mechanical energy that powers your muscles. In other words, you can jump because you are a living being with energy stored, capable of doing work without external input. Put a block of wood on the floor, and you will never see it spontaneously "jump".

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Your muscles are doing work that becomes your kinetic energy associated with the initial speed when jumping. When you jump, some form of chemical energy becomes kinetic energy of you and earth. However, since earth is super heavy, the kinetic energy it receives is essentially zero while you receive essentially all the kinetic energy. The conservation of momentum equation and conversation of energy (KE1+KE2=ChemicalEnergy) equation (with given masses and ChemicalEnergy) will determins the two variables that are the initial speed of you jumping and earth recoil, which is essentially zero when the mass of earth approaches infinity.

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