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.

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.

anonymous · Answer

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 $$\left( 0, 0, 96 \right)$$