# If there is a force applied but no work done, what happens to that energy?

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If there is a force applied but no work done, what happens to that energy?

In: Physics

Hi 🙂

If you’d push against a very heavy rock or a mountain, you’d still have mechanics, and/or a stalling motor, and friction turning energy into heat.

What energy? I mean, it’s intuitive, and correct, to say that a table doesn’t need to spend energy holding up a book, isn’t it? Tables don’t need to be plugged in. But the table is applying a force on the book, equal to the force of gravity on it.

Force is actually not carrying any energy by itself, only when it is moving stuff (in physics you have to multiply the force by the distance it moves something to get energy). When you are standing on earth, the gravitational force is pulling you down, but the reactionary force from the ground (which is actually electrons pushing each other away) pushes you up, so the forces cancel out -> nothing moves -> no energy is used

If there is a force applied but no work done, then the net energy is zero.

That energy is cancelled out by an opposing force. Use the gravity example: gravity pulls you down, the earth pushes you back up. These forces *exactly* cancel each other. So there is no net energy and indeed no net force, thus no work done.

This is true for path integrals too. If the forces are conservative then it doesn’t matter what path you take as long as you end where you started then no work is done.

To try to give a clear example of what others have said:

if you compress a spring it has stored energy. If you put it against a wall so that it stays compressed, it will exert a force without releasing any energy. All the potential energy in the spring stays there until the spring is released.