Question

1. An object moves along a straight track from the point (1,−2,1) to the point (0,−7,5). The only force acting on it is a constant F=2i−3j−5k newtons. Find the work done if the distance is measured in meters.

2. A wrench 0.5 meters long lies along the positive y-axis, and grips a bolt at the origin. A force is applied in the direction of <0,1,4> at the end of the wrench. Find the magnitude of the force in newtons needed to supply 100 newton-meters of torque to the bolt.

Answer 1

since F is conservative, the work is independent of the path, so it is

∫[(1,-2,1),(0,-7,5)] 2dx-3dy-5dz
= 2x-3y-5z [(1,-2,1),(0,-7,5)]
= (0+21-25)-(2+6-5)
= -4-3
= -7

You can work the other the same way, but it's easier since only y is involved.