Mechanical Engineering Principles

14

Work, energy and power

At the end of this chapter you should be

able to:

• define work and state its unit


• perform simple calculations on work done


• appreciate that the area under a force/
  distance graph gives work done


• perform calculations on a force/distance
  graph to determine work done


• define energy and state its unit


• state several forms of energy


• state the principle of conservation of
  energy and give examples of conversions


• define and calculate efficiency of systems


• define power and state its unit


• understand that power=force×velocity


• perform calculations involving power,
  work done, energy and efficiency


• define potential energy


• perform calculations involving potential
  energy=mgh


• define kinetic energy


• perform calculations involving kinetic
  energy=^12 mv^2


• distinguish between elastic and inelastic
  collisions


• perform calculations involving kinetic
  energy in rotation=^12 Iω^2

14.1 Work

If a body moves as a result of a force being applied
to it, the force is said to do work on the body. The
amount of work done is the product of the applied

force and the distance, i.e.

work done=force×distance moved in

the direction of the force

The unit of work is thejoule, J, which is defined as

the amount of work done when a force of 1 Newton

acts for a distance of 1 m in the direction of the

force. Thus,

1J=1Nm

If a graph is plotted of experimental values of force

(on the vertical axis) against distance moved (on

the horizontal axis) a force/distance graph or work

diagram is produced.The area under the graph

represents the work done.

For example, a constant force of 20 N used to

raise a load a height of 8 m may be represented on

a force/distance graph as shown in Figure 14.1. The

area under the graph shown shaded represents the

work done. Hence

work done=20 N×8m=160 J

20

10

04

Distance / m

8

Force / N

Figure 14.1

Similarly, a spring extended by 20 mm by a force

of 500 N may be represented by the work diagram

shown in Figure 14.2, where

work done=shaded area

=^12 ×base×height