Question

A body constrained to move along the z-axis of a coordinate system is subject to a constant force F given by F = −i + 2 j + 3 k N where i, j, k are unit vectors along the x-, y- and z-axis of the system respectively. What is the work done by this force in moving the body a distance of 4 m along the z-axis?

Answer 1

Displacement $\vec{r} = 4 \vec{k}$ is directed along z-axis.

work done by this force is

$W = \vec{F}\cdot \vec{r} = (-1)\cdot 0 + 2 \cdot 0 + 3 \cdot 4 = 12 \text{ J}$