Work is defined as the product of force and displacement and although force is a vector work itself is a scalar quantity.

Work | = | Force | x | Displacement |

(a scalar) | = | (a vector) | x | (a vector) |

A more general case is shown by Figure 1

This shows that:

where q is the angle between the line of action of the force and the direction of motion.

The unit of work and energy is the joule, which is defined as follows:

One joule of work is done, and one joule of energy transformed from one form to another if a force of one Newton is moved a distance of one metre along the line of action of the force.

1. A truck is pulled along a track a distance of 3 m by force of 25 N acting at 30

Calculate the work done by the force.

Work done = 3 x 25 x cos30 = 65 J

2. A man pulls heavy case of mass 30 kg a distance of 6 m up a rough slope which is inclined at 20

(a) the work done by the man

(b) the frictional drag on the slope

(Take g = 9.8 Nkg

(a) work done = 150 x 6 = 900 J

(b) total work done = 900 = F x 6 + mgsin20 x 6 = 6F + 101x6 = 6F + 606

Frictional drag (F) = [900 – 606]/6 = 49 N