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This is kind of a complicated question that deals with the conservation of energy.

If I push against a wall it requires energy, but since the wall doesn't move, no energy has been transferred, so where does it go to?

If you say it is lost to heat, then if the wall moves while I'm pushing with the same amount of force that would mean my body would produce less heat since now some of the energy I'm expending is being transferred to the moving wall, but how would my body know that the wall is moving so that it then produces less heat?

This is just a hypothetical experiment, since if the wall moves my body would have to move with it after it moves beyond the reach of my arms, so the experiment might not be technically possible beyond a very short distance. But the point is that I'm expending the same exact amount of energy regardless if the wall is moving or not, and if that is the case, then my body should produce less heat if the wall is moving due to the conservation of energy, right? But if so, how would my body "know" the wall is moving?

Dale
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2 Answers2

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First, a general piece of advice: the human body is messy and complicated. It is rarely a good idea to learn physics concepts based on the human body. Instead, learn the physics concepts on simple systems first and then once you have learned the physics on the simple system you can come back to the human.

Here, let’s consider a spring instead of a human. Suppose that the spring is initially compressed, thus storing elastic potential energy. In its compressed state it exerts a force on the wall and since the wall does not move the spring remains compressed and continues to exert that force without losing any potential energy. So indeed, for a simple system we can clearly see that there is no work done and no energy loss in exerting a force.

Now that we understand the simple system, let’s go to the human. The difference between the human and the spring is that the human does not use springs for muscles. Forces are primarily generated in a muscle by using chemical potential energy, not elastic energy. This means that generating a force at constant distance requires continual use of chemical potential energy, unlike the case of a spring. Because no external work is being done, all of the energy goes to heating the muscle tissue (through repeated ratcheting of the actin and myosin and all of the supporting metabolic processes).

If you say it is lost to heat, then if the wall moves while I'm pushing with the same amount of force that would mean my body would produce less heat since now some of the energy I'm expending is being transferred to the moving wall, but how would my body know that the wall is moving so that it then produces less heat?

Yes, that is correct. Less heat will be dissipated in your muscles if you spend the same amount of energy in isometric exercise than in non-isometric exercise. Note that spending the same amount of energy is a strong restriction because that is not the same as exerting the same force for the same amount of time.

The body is very aware of whether or not the limbs are moving, both on a proprioceptive level and also on the actin and myosin level. We are poorly designed (in terms of efficiency) for isometric exercise (0% efficiency) and even worse for eccentric exercise (negative efficiency). On the level of the actin and myosin isometric exercise generates more heat for the same energy expenditure because the neighboring actin and myosin are randomly “jiggling” back and forth instead of pulling together.

Dale
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Lets start simple, a cupboard on the floor

cupboard

Push it on the floor . The chemistry of the muscles collectively gives momentum and energy and the cupboard slides ,it has the kinetic energy $1/2{mv^2}$. You have spent more than that in muscle power and there is the friction on the floor dissipating part of the energy, and the friction of your hands on the cupboard.

Make $m$ larger and larger. At some point the cupboard will not move. Where does the energy go? to the frictional contact with the floor, that does not allow motion, there should be heat generated, and the frictional contact of your hands on the cupboard, possibly to vibrations of the mass.

Let $m$ be the mass of the wall, rooted to the floor. Where will the energy you supply go? Vibrations of the wall molecular lattice , but due to the very large mass not discernible, and frictional heat of your hands on the wall where you are trying to push it.

anna v
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