A force is said to do work on an object when the body it acts on has a displacement of the point of application. Force does work when it results in movement. The SI unit of work is a newton-metre or joule (J).

Work was introduced in 1826 by a French mathematician Gaspard-Gustave Coriolis. [1] He described work as the “weight lifted through a height”. This was based on the early steam engines ability to life buckets of water out of flooded mines.

Work done by a constant force of magnitude F on a point that moves a displacement d is:

W=Fd

For moving objects, the quantity of work/time is calculated as a distance/time, or velocity. Thus at any instant, the rate of work done by a force is the scalar product of the force and the velocity vector of the point of application. The small amount of work done over an instant of time is calculated as:

δW=F*vδt

To calculate the work over a distance can be calculated by integration. The derivation leads to:

W=Fd cosθ