Work

Definition

The work done by a force on a body is a scalar quantity defined as the dot product integral of the force with respect to the instantaneous displacement vector of the body. In other words, the work done by a force ${\overline {F}}$ is defined as the integral:

$\int {\overline {F}}\cdot d{\overline {s}}$.

A special case of this is when the force is constant in magnitude and direction, the work done by it is defined as the dot product of that force and the total displacement of the body.

When ${\overline {F}}$ is the only external force acting on the body, the work done by ${\overline {F}}$ equals the change in kinetic energy of the body. In general, the sum of the works done by all the external forces acting on the body equals the change in kinetic energy of the body.

Units and dimensions

The MLT dimensions of work are $ML^{2}T^{-2}$ and the SI unit is $J$ (Joules) which is the same as $kgm^{2}/s^{2}$ (kilograms meters squared per second squared). These are the same as the units of energy (both kinetic energy and potential energy and forms of energy other than mechanical energy).