Engineering Mechanics

(^600) „„„„„ A Textbook of Engineering Mechanics
Then work done by the force P
= Component of the force in the direction of motion × Distance
= P cos θ × s
Fig. 30.1. Work done by a force
30.2. UNITS OF WORK
We have already discussed that the work is the product of force and distance, through
which the body moves due to action of the force. Thus the units of work depend upon the units of
the force and distance. The units of work (or work done) are :

1. One N-m. It is the work done by a force of 1 N, when it displaces the body through 1 m.
   It is called joule (briefly written as J), Mathematically.
   1 joule = 1 N-m


2. One kN-m. It is the work done by a force of 1 kN, when it displaces the body through 1 m.
   It is also called kilojoule (briefly written as kJ). Mathematically.
   1 kilo-joule = 1 kN-m
   Note. Sometimes, the force stretches or compresses a spring or penetrates into a body. In such
   a case, the average force is taken as half of the force for the purpose of calculating the work done.

30.3. GRAPHICAL REPRESENTATION OF WORK

Fig. 30.2. Graphical representation of work.

The work done, during any operation, may also be represented by a graph, by plotting distance

along X-X axis and the force along Y-Y axis as shown in Fig. 30·2 (a) and (b).

Since the work done is equal to the product of force and distance, therefore area of the figure

enclosed, represents the work done to some scale. Such diagrams are called force-distance diagrams.

If the force is not constant, but varies uniformly with the distance, the force distance diagram is not a

rectangle; but a trapezium as shown in Fig. 30·2 (b).

Example 30.1. A horse pulling a cart exerts a steady horizontal pull of 300 N and walks at

the rate of 4·5 km.p.h. How much work is done by the horse in 5 minutes?

Solution. Given : Pull (i.e. force) = 300 N ; Velocity (v) = 4·5 km.p.h. = 75 m/ min and time

(t) = 5 min.