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When a body on which a force is acting moves in the direction of the force work is done and energy is transformed.

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:

Work done = Fs cosq

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.

Example problems
1. A truck is pulled along a track a distance of 3 m by force of 25 N acting at 30o to the direction of the track.
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 20o to the horizontal. If he uses a force of 150 N. calculate:
(a) the work done by the man
(b) the frictional drag on the slope
(Take g = 9.8 Nkg-1)

(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

© Keith Gibbs 2020