# Work

### Work done by a constant force

Only the component of a force in the direction of the displacement does work. If the force is constant, then we can simplify the general work equation to the following.

U_{1-2} = F⋅Δr_{1-2} or U_{1-2} = Fcosθ d_{1-2}

### Work done by a non-constant force

The general work equation may be applied in the individual coordinate directions.

U_{1-2} = ∫F_{x}dx + ∫F_{y}dy

### Work in the n-t coordinate system

Since motion only occurs in the t-direction, only the t-component of the force does work.

U_{1-2} = ∫F_{t}ds