Question

A man pushing against a wall does not do any work. Explain briefly.

Answer 1

The scientific definition of work done by a body is the product of the force exerted by the body on another body and the displacement of the latter body in the direction of that force. If any one of the two, that is, the force or the displacement in the direction of the force is zero, the work done will also be zero.

Complete step by step answer:
Work done in the scientific terms is different from the meaning of work that we use in everyday life. In scientific terms, the work done by a body on another body is defined as the product of the force exerted by the first body on the second body and the displacement of the second body in the direction of the force.
So, the work done $W$ by a body on another body is given by
$W=Fs$ --(1)
Where $F$ is the magnitude of the force exerted by the first body on the second body and $s$ is the magnitude of the displacement of the second body in the direction of the force.
Now, when a man pushes against a wall, even though he applies a force on the wall, the wall does not move and hence, the displacement of the wall is zero. From (1), this would mean that the work done by the man would also be zero.
This is the reason why in scientific terms, a man pushing against a wall does not do any work.

Note:
Students must note that only if the displacement of a body has some component parallel to or anti parallel to the direction of the force applied on it, then only some non zero quantity of work is done by the force. If the force applied and the displacement of the body are in perpendicular directions, this would mean that the displacement has no component along or opposite to the direction of the force and in turn this would mean that the work done by the force is zero, even though the force on the body and its displacement are non zero.