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In every formula I've seen that involves energy, I've also seen a distance element. Is there nothing that doesn't involve movement? For instance if I hold my arm out parallel to the ground with a weight in it, my arm will get tired very quickly but according to the formulas I've done no work (force * distance) since distance is 0 and I'm not even applying any force (mass * acceleration) because the mass is not accelerating.

Where's the flaw in my understanding?

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This exact problem was rose also by Feynman in his lectures. In particular at the beginning of chapter 14 in the first volume.

It is a fact that when one holds a weight he has to do “physiological” work. Why should he sweat? Why should he need to consume food to hold the weight up? Why is the machinery inside him operating at full throttle, just to hold the weight up? Actually, the weight could be held up with no effort by just placing it on a table; then the table, quietly and calmly, without any supply of energy, is able to maintain the same weight at the same height! The physiological situation is something like the following. There are two kinds of muscles in the human body and in other animals: one kind, called striated or skeletal muscle, is the type of muscle we have in our arms, for example, which is under voluntary control; the other kind, called smooth muscle, is like the muscle in the intestines or, in the clam, the greater adductor muscle that closes the shell. The smooth muscles work very slowly, but they can hold a “set”; that is to say, if the clam tries to close its shell in a certain position, it will hold that position, even if there is a very great force trying to change it. It will hold a position under load for hours and hours without getting tired because it is very much like a table holding up a weight, it “sets” into a certain position, and the molecules just lock there temporarily with no work being done, no effort being generated by the clam. The fact that we have to generate effort to hold up a weight is simply due to the design of striated muscle. What happens is that when a nerve impulse reaches a muscle fiber, the fiber gives a little twitch and then relaxes, so that when we hold something up, enormous volleys of nerve impulses are coming in to the muscle, large numbers of twitches are maintaining the weight, while the other fibers relax. We can see this, of course: when we hold a heavy weight and get tired, we begin to shake. The reason is that the volleys are coming irregularly, and the muscle is tired and not reacting fast enough. Why such an inefficient scheme? We do not know exactly why, but evolution has not been able to develop fast smooth muscle. Smooth muscle would be much more effective for holding up weights because you could just stand there and it would lock in; there would be no work involved and no energy would be required. However, it has the disadvantage that it is very slow-operating.

From: 14–1 Work

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  • $\begingroup$ So, to answer the question more directly: There is movement, but it's on a small scale that isn't obvious. $\endgroup$ – Adam Davis Jun 2 '15 at 14:11
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Potential energy doesn't seem to require movement, but it required movement to become potential.

For example an object resting on a table edge has potential energy, PE = m * g * h, where m is the object's mass, g is Earth's gravitational acceleration, and h is height of the table. The object isn't moving, but someone placed it on the edge of the table, and that required expenditure of kinetic energy. KE = (m * v^2) / 2, where m is the object's mass, and v is it's velocity on it's way to the table edge.

The table is dependent on charges moving inside its atoms to keep it from collapsing into the Earth's gravity.

Energy contained in a magnetic field doesn't seem to require movement, but the field is caused by spinning electrons in atoms aligned in magnetic domains. Without the motion of electric charges, there is no magnetic field and no energy.

The binding energy of an atomic nucleus doesn't seem to require movement, but that's because it already has been removed from the nucleus. The mass of a nucleus is always less than the individual masses of the protons and neutrons in it. Nuclear fusion produces gamma rays which carry away the binding energy, and leave the nucleons in a lower energy state than they'd be if separate. That's why they hold together as a nucleus. To separate them again, you need to replace the enormous binding energy they lost.

Energy itself is movement. All particles vibrate. If you have a string theory outlook, the nature of the universe is the vibration of strings. To have energy, you need movement.

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