# Work, Energy and Power

### Work, Energy and Power

#### 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.

The unit of work is the joule, 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, 1 J = 1 Nm

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 20.1. The area under the graph, shown shaded, represents the work done. Hence

In another example, a spring extended by 20 mm by a force of 500 N may be represented by the work diagram shown in Figure 20.2, where

It is shown in chapter 9 that force D mass ð acceleration, and that if an object is dropped from a height it has a constant acceleration of around 9.81 m/s2.

For example, if a mass of 8 kg is lifted vertically 4 m, the work done is given by:

The work done by a variable force may be found by determining the area enclosed by the force/distance graph using an approximate method (such as the mid-ordinate rule)

#### Energy

Energy is the capacity, or ability, to do work. The unit of energy is the joule, the same as for work. Energy is expended when work is done. There are several forms of energy and these include:

(i) Mechanical energy (ii) Heat or thermal energy

(iii) Electrical energy (iv) Chemical energy

(v) Nuclear energy (vi) Light energy

(vii) Sound energy

Energy may be converted from one form to another. The principle of conservation of energy states that the total amount of energy remains the same in such conversions, i.e. energy cannot be created or destroyed.

##### Some examples of energy conversions include:

(i) Mechanical energy is converted to electrical energy by a generator

(ii) Electrical energy is converted to mechanical energy by a motor

(iii) Heat energy is converted to mechanical energy by a steam engine

(iv) Mechanical energy is converted to heat energy by friction

(v) Heat energy is converted to electrical energy by a solar cell

(vi) Electrical energy is converted to heat energy by an electric fire

(vii) Heat energy is converted to chemical energy by living plants

(viii) Chemical energy is converted to heat energy by burning fuels

(ix) Heat energy is converted to electrical energy by a thermocouple

(x) Chemical energy is converted to electrical energy by batteries

(xi) Electrical energy is converted to light energy by a light bulb

(xii) Sound energy is converted to electrical energy by a microphone.

(xiii) Electrical energy is converted to chemical energy by electrolysis.

Efficiency is defined as the ratio of the useful output energy to the input energy. The symbol for efficiency is 1 (Greek letter eta). Hence

Efficiency has no units and is often stated as a percentage. A perfect machine would have an efficiency of 100%. However, all machines have an efficiency lower than this due to friction and other losses.

For example, if the input energy to a motor is 1000 J and the output energy is 800 J then the efficiency is:

In another example, if a machine exerts a force of 200 N in lifting a mass through a height of 6 m, the efficiency of the machine if 2 kJ of energy are supplied to it is calculated as follows:

Power

Power is a measure of the rate at which work is done or at which energy is converted from one form to another.

The unit of power is the watt, W, where 1 watt is equal to 1 joule per second. The watt is a small unit for many purposes and a larger unit called the kilowatt, kW, is used, where 1 kW = 1000 W

The power output of a motor that does 120 kJ of work in 30 s is thus given by

For example, if a lorry is travelling at a constant velocity of 72 km/h and the force resisting motion is 800 N, then the tractive power necessary to keep the lorry moving at this speed is given by: