Question

A constant force\({\rm{F = 3i + 5j + 10k}}\) moves an object along the line segment from \({\rm{(1,0,2)}}\)to\({\rm{(5,3,8)}}\). Find the work done if the distance is measured in meters and the force in Newton.

Short answer

The work done is\({\rm{87Nm}}\).

Step-by-step solution

To find distance \({\rm{D}}\).

The following is the work formula:

\({\rm{W = F}} \cdot {\rm{D}}\)

\(\begin{aligned}{c}{\rm{D = }}\langle {\rm{5 - 1,3 - 0,8 - 2}}\rangle \\{\rm{ = }}\langle {\rm{4,3,6}}\rangle \end{aligned}\)

To find work done\({\rm{W}}\).

\(\begin{aligned}{c}{\rm{W = }}\langle {\rm{3,5,10}}\rangle \cdot \langle {\rm{4,3,6}}\rangle \\{\rm{ = 3(4) + 5(3) + 10(6)}}\\{\rm{ = 12 + 15 + 60}}\\{\rm{ = 87}}\end{aligned}\)

Therefore, the work done is\({\rm{87Nm}}\).