If I push my hand against a wall, the wall doesn't move, so there is no displacement and so no work done. But energy is being used to generate the force, so what is happening to the energy? Does that mean the total energy is being lost as heat? If so how would you calculate this energy? I though of a way to do it, but I'm not sure if its correct, and would like to know that. Work done i.e. W = F x s can be converted to a function of time and so it becomes W = F^2 * s^2 / 2m. And then if I knew the force I applied, the duration for which I applied it, and the mass of my hand, I can calculate the total energy lost as heat, based on the potential distance my hand would have gone if there was no wall. Will this give an accurate result for the energy being transferred to heat?
2 Answers
remember, work done is defined as the (dot) product of force and distance moved by the point of application. Take the example of someone doing pushups. His hands clearly dont move during the process, so the work done by the hands on the floor is clearly 0. But its pretty obvious from observation that the person soon gets tired and therefore loses energy. Where did this energy come from and go?
Basically, whats happening is that although your hands are stationary, muscles all over the body ARE moving and exerting forces on each other. Thus, the work is being done by internal spring like muscular forces. Since muscles are doing the work, they are losing (chemical) energy, which is being converted the body's kinetic energy and heat.
Note: since no force exerted by the body on an external object is doing work, there is no external transfer of energy. Since internal muscular forces are doing work on objects inside the body, the transfer of energy is purely internal; no energy s atually leaving the body (at least initially)
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Your intuition is partially correct but also misleading you somewhat.
Consider a simpler example. Imagine a heavy weight sitting at rest on a hard concrete floor. The weight exerts a force on the floor but there is no displacement. In this example no work is done and clearly no energy is used. There's certainly no heat generated, otherwise we could get free heat just by putting heavy things on the ground!
On the other hand you know from experience that if you were to push against a wall for a long time you would get tired and you would need to eat food to replenish your energy.
This tells us that the rate of energy usage has something to do with the human body, not with force in general. See the answers linked in the comments above for an explanation of what's going on.
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