Energy stores and systems: work done by forces

The idea

When a force moves an object, energy is transferred mechanically and we say work is done. The work done equals the force multiplied by the distance moved along the line of the force: W = F s. If a 20 N force pushes a box 3 m in the direction of the force, the work done is 20 × 3 = 60 J. One joule is one newton metre. If the force acts at an angle to the motion, only the component along the motion does work, so the full force does not transfer energy. Work done is a measure of energy transferred, so it is measured in joules, the same unit as energy. A force at right angles to motion, such as the normal contact force on a sliding box, does no work because there is no movement along the force.

What earns the marks

• State that work is done when a force causes an object to move through a distance.
• Recall and apply the relationship work done = force × distance moved along the line of the force, W = F s.
• Use the correct units: force in newtons (N), distance in metres (m) and work done in joules (J).
• Recognise that work done equals energy transferred, so a 60 J transfer means 60 J of work done.
• Explain that a force perpendicular to the direction of motion does no work because distance moved along the force is zero.
• Calculate a missing quantity by rearranging W = F s when the work done and one other value are given.

Common mistakes and how to put them right

• Using the total distance travelled rather than the distance moved along the line of the force.

  Put it right by resolving the force or using only the component in the direction of motion.

• Forgetting to convert centimetres to metres before multiplying.

  Put it right by dividing by 100 so the distance is in metres.

• Writing the unit of work as newtons or newton metres per second.

  Put it right by using joules (J), since 1 J = 1 N m.

Exam tips

• Write the equation, substitute the values with units, then give the answer with the correct unit; this makes method clear even if the arithmetic slips.
• Check whether the force and distance are in the same direction before using W = F s; if not, state that only the component along the motion does work.
• Link the numerical answer back to energy transfer, for example '60 J of energy is transferred mechanically to the box'.