I know you will all say no energy has been transferred across so the
$ Work$ $Done = Force$ x $Distance = 0$ $joules $
But I am thinking, surely energy is required to mechanically apply a force? It could be a motor vehicle trying to pull an immovable object or me simply pushing against a brick wall. I might simply be holding a heavy weight in position with my arms. In all these case, surely energy is being used. so how do I calculate that energy, given there is no displacement? Such scenarios seem to suggest that energy should be a measure of $Force$ x $Time$ it is is applied for. I cannot conceptualise why this is not the case.
The equations of classical physics seem to suggest no energy is expended.
I can only guess that what is happening is that energy is being consumed (burnt) internally. So for example, chemical energy is created to contract my muscles to push, and that energy is lost as heat. What about electrical energy to power a motor attached to a cable pulling a mountain say? Surely, energy is being used to create the force via the motor. WHY can energy not be quantified by multiplying Force by the duration that force is applied? Please try to avoid answering this by saying something abstract like the units or dimensions of $Force$ x $Time$ do not yield that of energy. I am seeking an intuition to help me understand why $Energy$ is not $Force$ x $Time$ in general.
