Question

A body constrained to move along the z-axis of a coordinate system is subject to a constant force F given by $\text F$ = $-\hat{i}+2\hat j+3\hat k$ where $\hat i,\hat j,\hat k$ 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

Force exerted on the body,$\text F$ = $-\hat{i}+2\hat j+3\hat k$ $\text N$
Displacement, $s$ = $4\,\hat k\,m$
Work done, $W$ = $\text F.s$ = ($-\hat{i}+2\hat j+3\hat k$) . ($4\,\hat k$) = $0+0-3\times 4$ = $12 \,\text J$

Hence, $12 \,\text J$ of work is done by the force on the body.