Work done by a force

Work is done when energy is transferred from one store to another. Work is also done when a force causes an object to move. When work is done against frictional forces acting on an object, the object’s temperature increases. For example, a person’s hands warm up when they rub them together repeatedly.

Calculating work done

To calculate the work done on an object when a force moves it, use the equation:

work done = force × distance

This is when:

  • work done is measured in joules (J)
  • force is measured in newtons (N)
  • distance moved along the line of action of the force is measured in metres (m)

Note that one joule of work is done when a force of one newton causes a movement of one metre. This means that work done can also be measured in newton-metres (Nm).

1 J = 1 Nm

It is important not to confuse newton-metres (a unit of work done) with Newton meters (calibrated spring balances used to measure weights).

Example

A doctor weighs 600 N. A lift moves her 40 m to the top floor of a hospital. Calculate the work done on the doctor by the lift.

work done = force × distance

work done = 600 N × 40 m

work done = 24,000 J (or 24 kJ)

Question

In a scrum, a rugby team pushes the other team backwards 5 m using a force of 1,000 N. Calculate the work done moving the other team.

work done = force × distance

work done = 1,000 N × 5 m

work done = 5,000 J (or 5 kJ)