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_xdx + ∫F_ydy

 

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_tds