# Force, work and the apparent disappearance of Mechanical Energy [duplicate]

A man exerts force on a wall of bricks. The man must have consumed the energy he possessed (mechanical energy?) to exert the force. The man sweats and tires himself out but the wall does not move.

The force is given as $F = ma$ but no acceleration was produced in the wall. So, the force is zero even though force was exerted. The definition of force says that it moves, tends to move, stops or tends to stop the motion of a body. How can the force be zero?

The work done is zero since displacement is zero. The Work-Energy principle says that work done on a body appears as a change in its kinetic or potential energy. Since work done is zero, no change in the energy of the wall occurs. Where did all of the energy the man spent go?

## marked as duplicate by user191954, John Rennie, Kyle Kanos, Community♦Sep 10 '18 at 17:50

First, it does not require energy to produce a force. A ladder can lean against a wall, exerting a force on it indefinitely without the expenditure of energy. A man exerting the same force sweats and gets tired, not because energy is required to produce force but simply because the human body is a very inefficient machine.

Your second paragraph makes the same mistake as in your previous question. As I explained there, the proper form of Newton’s 2nd law is $\Sigma F = ma$. You are neglecting the other forces acting on the wall. So the force exerted by the man is not zero, but there are other forces acting on the wall such that $\Sigma F=0$

For your third paragraph, the energy the man spent went to thermal energy. This is where energy usually goes for inefficient machines.

• But doesn't the ladder have gravitational potential energy and that the force exerted on the wall is due to gravity? If there were no gravity, there would be no force. – Muhammad Inam Sep 10 '18 at 17:57
• The ladder has gravitational potential energy but it does not “consume the energy” to produce the force. That is the point. Energy is not expended to produce a force, even if that force has an associated potential energy – Dale Sep 10 '18 at 19:36

In short, the energy is lost as heat generated by the muscle fibers as they contract to exert a force. It ultimately boils down to the chemical reactions involved in the muscle to exert that force. You are correct that no work is being done.