Question

A force F=(3,5,12) in newtons is applied to lift a box with displacement S=(0,0,8).

Calculate the work against gravity and the work in the direction of travel.

Answer 1

Gravity is (0,0,-g) so therefore the dot product of \[F_g\] and \[S\] is -8g. This means the work done against gravity is +8g. The work in the direction of travel is the dot product of the force and displacement vectors, or just \[\left( 0, 0, 96 \right)\]