Work done by a force

Work is done whenever a force moves something over a distance. You can calculate the energy transferred, or work done, by multiplying the force by the distance moved in the direction of the force.

Energy transferred = work done = force x distance moved in the direction of the force

When energy is transferred from energy stored chemically in muscles to energy in a raised load, or to energy stored elastically in a stretched spring, the energy transferred is a measure of how much work has been done.

Energy transferred = mgΔh

This second equation is illustrated by raising kilograms onto different height shelves. You can show that the equation is a good summary of what happens. It takes account of the mass, the height raised and whether the kilogram is raised on the Earth or the Moon.

The useful thing which you get from fuels by burning them is a transfer of energy, so that a load can be raised, or an object accelerated.

However, not all the energy available does a useful job. If you lift a lot of bricks, you can get too hot. As well as transferring energy to the raised bricks, some of the energy in your muscles warms you up. The transfer of energy is not 100% efficient and not all the energy transferred is represented by mgh. Nor do you know how much total energy is stored gravitationally. You can only calculate energy that is transferred.

Concepts develop with steam engines

Humans first domesticated animals to do useful work and later found other ways of exploiting energy from natural sources, such as falling water and wind. But the abstract idea of an ‘engine’ really developed with steam engines.

By the 1820s the concept of ‘work’ as mechanical effect had been introduced into discussions about what are now called power technologies. Early on, a major use of steam engines was pumping water out of mines. Manufacturers such as Boulton & Watt persuaded mine owners in Cornwall to buy a steam engine in place of their pit ponies, by comparing the amount of work each could do.

Watt went even further, developing the concept of rate of working, or power, with his steam engines described in ‘horsepower’. Steam engines enabled the output of many Cornish mines to quadruple.

An analogy to use when teaching about energy transfers

Consider two bank accounts. If I transfer a £1 cheque from my account to yours then my account goes down by £1 and yours will go up by £1. But a cheque is not cash of any kind. It is an instruction to my bank to pay out £1 into your account. We have to pay the banks for doing the job for us and so although my account falls by £1 yours may only gain 95p because you have to pay bank charges. It is also impossible in this transaction to know how much is stored in each account.

Pushing this analogy to its limits helps to show that whilst you can store real cash in the bank (the energy stored, for example, in a fuel + oxygen mixture), the cheque which passes between accounts is something different. The cheque is a means of transferring the cash value (the work done for example when a brick is raised). Work is energy being transferred.