No work done and no energy spent?

Imagine there's some body and a force F trying to move that body. In that case the force will do a work and the body will start to accelerate (obtain a kinetic energy). Now also imagine that I'm applying a force -F right in the opposite direction of the existing force, when the body is still standing. Then it will remain standing as long as the 2 opposite forces are applied and cancel each other.

Question: Do I do some work or spent some energy while applying that force -F? If yes, then is there a formula for it, if no, then does that mean, that it's the same whether I do nothing or try to hold the body from moving by applying an equal force to the existing one but in opposite direction?

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Matterwave
Gold Member
No, if there is no displacement, there is no work done by either force (assuming the body is rigid). No energy is transferred. All you're doing is not allowing the energy to be transferred from the first object applying that force.

If the object is not rigid, and can deform (like all objects on this earth) you would be transferring some of the energy into deforming the object and would be doing work.

Imagine there's some body and a force F trying to move that body. In that case the force will do a work and the body will start to accelerate (obtain a kinetic energy). Now also imagine that I'm applying a force -F right in the opposite direction of the existing force, when the body is still standing. Then it will remain standing as long as the 2 opposite forces are applied and cancel each other.

Question: Do I do some work or spent some energy while applying that force -F? If yes, then is there a formula for it, if no, then does that mean, that it's the same whether I do nothing or try to hold the body from moving by applying an equal force to the existing one but in opposite direction?
There is no work done if there is no motion. So yes, your scenario is the same as doing nothing. You are performing no work on the body...unless, of course, the forces you are using are so great that you end up crushing the thing. Then you did do some work on it.

Also, you're not doing any work on the body, but if you're the one applying the force, then obviosuly you will get tired and have expended some work, on some level deep within your muscles. Unfortunately you got tired for nothing and all your work will have been wasted. But, that's just a limitation of the human body...

A more efficient way to accomplish the same thing is to simply put a clamp around the body, and let it squeeze it. You can then go watch 25 consecutive episodes of the Simpsons while applying your opposite forces without getting anyone tired.

A.T.
Question: Do I do some work or spent some energy while applying that force -F? If yes, then is there a formula for it, if no, then does that mean, that it's the same whether I do nothing or try to hold the body from moving by applying an equal force to the existing one but in opposite direction?
There is no work done by you on the object. Instead of your muscles you could just as well use two walls to apply that opposite forces to the object: no energy transfer, no work done. However, if you use your muscles, you convert energy internally to produce the force. But this energy doesn't go into the object, but dissipates as heat. Therefore no work is done on the object.

Think of a helicopter hovering at constant height. The engine uses energy but does no work on the helicopter chassis. Yet it still creates a force upward on the helicopter chassis.

TYou can then go watch 25 consecutive episodes of the Simpsons while applying your opposite forces without getting anyone tired.
And while watching and flicking through the adds, you are putting a downwards force on your settee and could even fall asleep doing all this downward forcing.

thanks to all for detailed replies, got it :)

As mentioned above, if the body is not rigid, there is some deformation of its shape, so it stores energy like a spring when deformed by external forces. These types of work are relevant in structural engineering, architecture, and strengths of materials.

thanks SystemTheory