[Physics] How to calculate the work without displacement?


For example, I hold an item in my hand at arm's length. There are forces of gravity and elasticity. And obviously I use some amount of energy to keep holding. Is it possible to calculate the work without displacement?
I've finished high school years ago, it's just my curiosity.

Best Answer

If there's no displacement, there's no work done. Work without displacement is zero.

The force of gravity pulls down on the item, you are holding. But in general, no, you do not spend energy to keep it up.

  • If the item is on a shelf, this shelf is not continuously spending energy to keep it up. It spends no energy and does do work.
  • When you hold the item still in a certain height, that's the same situation. No work is done on the item.

But your body is a strange thing and always tricky to see in this context. Because of muscle expansion and compression and other processes within your body, your body spends energy of many reasons in order to create the force that holds up the item. Work is done internally on that, but no work done on the item.

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