Work is defined as
$$W = \vec{F}\cdot\vec{s}$$
But what what exactly is $\vec{s}$? Is it the displacement of the body on which the force is being applied? Or is it the displacement of the point of application of the force?
If you look at the derivation for the definition of work from kinetic energy (the way many textbooks do it), it would seem to be the former, but I'm not sure since I can think of many examples that contradict the fact.
Or is it something else entirely?
Best Answer
Here's a way to argue it isn't the displacement of the (center of mass) of the body.
Take a spring that's at rest. Apply two forces on either end so it compresses. You can do this in such a way that the center of mass of the spring doesn't move. However, the energy of the spring system has changed (the potential energy increased). In order to satisfy the work energy theorem $$W_\text{net, external} = \Delta E_\text{total},$$ it would seem that the work must be non-zero. If you used the center of mass displacement, then $W=0$, which is inconsistent. The solution is to use the displacement of the point of application of the (two) force(s): $$W=W_1^\text{app} + W_2^\text{app}.$$