Work & Power: Using the Equations

Explained

Working through the two equations

Work done equals force times distance, W equals F times d. Power equals work done divided by time, P equals W over t.

Work and energy are the same quantity measured the same way, both in joules, so a question about energy transferred is a question about work done. Power is in watts, and one watt is one joule per second.

The three forms of each

From W equals F times d: to find work, multiply. To find force, divide the work by the distance. To find distance, divide the work by the force.

From P equals W over t: to find power, divide. To find work, multiply the power by the time. To find time, divide the work by the power.

Rather than memorising six versions, write the original equation, substitute the two values you have, and solve for the letter left over.

A worked example

A crane lifts a 500 N load through 12 m in 20 s.

Work done is 500 times 12, which is 6000 J.

Power is 6000 divided by 20, which is 300 W.

Two steps, in that order. You cannot find the power without the work done first, which is why most questions of this kind are worth three or four marks rather than two.

Lifting problems need a step before that

If the question gives a mass rather than a force, the force is the weight, so multiply by g first.

Lifting a 60 kg load through 3 m: the weight is 60 times 10, which is 600 N. The work done is 600 times 3, which is 1800 J. Going straight to 60 times 3 gives 180, which is not work done and not anything else either.

Watch for the same trap in a stair climbing question, where the mass of the person and the vertical height of the stairs are given, and the horizontal distance walked is irrelevant.

Distance means the vertical distance for lifting

Work done against gravity uses the vertical height gained. A ramp 5 m long that rises 2 m involves 2 m of vertical distance, so the work done against gravity uses 2, not 5.

The extra distance along the ramp is why a ramp needs less force for the same work, which is the point of using one.

Units, and a check

Newtons and metres give joules. Joules and seconds give watts. A mass in grams must become kilograms and a distance in centimetres must become metres before anything else happens.

Kilowatts and megawatts appear in real contexts, so a power in kW must be multiplied by a thousand before being used with joules and seconds.

Then check the size. A person climbing stairs works at a few hundred watts; a kettle is a couple of thousand. An answer in the millions for a human activity means a conversion has gone wrong.

Efficiency, if the question asks

Efficiency is the useful energy or work out divided by the total energy in, expressed as a percentage.

It cannot exceed one hundred per cent. If yours does, the two figures have been divided the wrong way round, and dividing the larger by the smaller is the usual cause.