Work done

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 are rubbed 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

W = F~s

This is when:

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

Note that one joule of work is done when a force of 1 N causes a movement of 1 m. This means that work done can also be measured in newton-metres (Nm):

  • 1 J = 1 Nm

Take care 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.

W = F~s

W = 600~N \times 40~m

W = 24,000~J (or 24~kJ)

Question

In a scrum, a rugby team pushes the other team backwards 5 m using a force of 1000 N. Calculate the work done moving the other team.

W = F~s

W = 1000~N \times 5~m

W = 5000~J (or 5~kJ)