It's easy to understand that as an object is lifted, it gains gravitational potential energy; as it falls, that potential energy is converted into kinetic energy. But what about when it's at rest? If a book sits on a table at rest, gravity exerts a force on the book. But the exertion of force requires energy, right? And what about the normal force? It exerts force as well; where does the energy to exert THAT force come from? Am I misunderstanding what energy is?

EDIT: Question answered - humans have a flawed understanding of force, and force actually isn't conserved in nature like energy is.


But the exertion of force requires energy, right?

Actually, no.

When you push on something, it consumes energy, but that's because you are a complicated and inefficient chemical machine, with lots of stuff going on besides the actual force exerted on whatever you're pushing. When two masses exert gravitational force on each other, none of that happens and energy is only transferred if one of the masses moves. Same story if two electric charges exert force on each other.

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    $\begingroup$ Oh, so... are you saying that my intuitive understanding of force, as a human, is incorrect, and that conservation of energy is a thing but conservation of force isn't? $\endgroup$ – Somniad Jul 28 '17 at 3:04
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    $\begingroup$ Correct, force is not a conserved quantity. $\endgroup$ – The Photon Jul 28 '17 at 4:31
  • $\begingroup$ @Somniad To make it more explicit, for "conservative forces" such as gravity the work done is $\int \mathbf{F}\cdot d\mathbf{s}$, which implies to do work the object must not only move, but move in a direction that's not perpendicular to the force. (Forces are parallel to acceleration, not motion. Magnetism causes charges to move perpendicular to the force, so it does no work on them!) $\endgroup$ – J.G. Jul 30 '17 at 9:20
  • $\begingroup$ Thanks for the explicit clarification! It's definitely very helpful for understanding the problem. $\endgroup$ – Somniad Jul 30 '17 at 9:40

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