Question

What determines whether or not work is being done?

Answer 1

Force and displacement

Answer 2

The equation for work is:
\[W=F \Delta r \cos \theta\] where \[\Delta r\] is the displacement

Answer 3

A common and simple example:

You're pushing a rectangular, solid cube. You are applying force to move that cube, and so you are doing work. In contrast, try pushing a wall. Although you are pushing with all your might, the wall does not move. Therefore the displacement \[\Delta r\] is zero. It will not matter what your force is, anything multiplied by zero will be zero, and thus your work is zero.

Answer 4

Also, if we wanted to express work with vectors, then \[\huge W=\vec{F} \cdot \vec{r}\]The dot product can be simplified as\[\huge \vec{F} \cdot \vec{r} = |F||R| \cos(\theta)\]Where \(\theta\) is the angle between the Force vector and the position vector. Note that if the angle between the force applied and its displacement is 90, then the work being done is 0!

Answer 5

An easy way to see it is that every time that energy within the system changes, work was done in the system, so besides W=Fd work is also W= ΔU