Work done by a force

The definition of work done by a force is the scalar quantity given by the force multiplied by the distance moved by its point of application in the direction of the force. Thus, if you carry the shopping home along a horizontal path, the force from your hand which holds up the basket does no work since there is no movement in the vertical direction. The unit of work is the joule, which is the same as a newton metre.

If the force is F and the distance moved by its point of application is a at angle α to F, as shown in Figure 9.1, then the work done by F is W = Fa cos α. In fact, this is the scalar product of the two vectors F and a, i.e. W = F.a.

EXERCISE 1

Find the work done by a force F = (20i + 30j + 40k) N when its point of application moves from A(4, 3, 2) to B(1, 2, 3) where the Cartesian coordinate distances are given in metres.

Problems 67 and 68.

Work done by a couple

Firstly, consider movement of a body in the plane of a couple acting on it which involves a translation a and a small rotation through angle δϕ radians. Referring to Figure 9.2, let the couple consist of two forces F and −F, a perpendicular distance b apart. In the translation, the work done by the couple is W = F.a − F.a = 0.