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.