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

Question

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

In: Physics

Answer 1

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.