4.5.2Work done
When a force causes an object to move through a distance, work is done on the object. So a force does work on an object when the force causes a displacement of the object.
The work done by a force on an object can be calculated using the equation:
work done = force × distance moved along the line of action of the force W = F s
work done, W, in joules, J; force, F, in newtons, N; distance, s, in metres.
You should be able to recall and apply this equation.
The phrase "along the line of action of the force" is doing real work in that definition. Only movement in the direction the force acts counts. Carrying a bag horizontally does no work against its weight, because the weight acts downwards and the movement is sideways.
Worked example
A force of 250 N pushes a box 6.0 m across a floor in the direction of the force. Calculate the work done.
- Write the equation: W = F s.
- The distance moved is along the line of action of the force, so it can be used directly.
- Substitute: W = 250 × 6.0.
- = 1500.
- Give the unit: joules.
Answer: 1500 J
One joule of work is done when a force of one newton causes a displacement of one metre.
1 joule = 1 newton-metre
You should be able to convert between newton-metres and joules — which, given that equation, means recognising that they are the same size of unit. A value of 350 Nm of work is 350 J.
You should also be able to describe the energy transfer involved when work is done. Doing work on an object transfers energy to it: pushing a box along the floor transfers energy from the chemical store of the person to the thermal store of the box and floor through friction, while lifting it transfers energy to its gravitational potential store.
Common mistake
Newton-metres appear in two different places at GCSE — as a unit of work done, where 1 Nm = 1 J, and as the unit of the moment of a force, where it is not a joule. Read which quantity the question is about.
- Work done
- the energy transferred when a force causes an object to move through a distance, calculated as force × distance moved along the line of action of the force
4.5.2Work done against friction
Work done against the frictional forces acting on an object causes a rise in the temperature of the object.
This is the same conservation argument as for energy transfers in a system, applied to a particular case. Energy is transferred by the force doing work, but if the object ends up moving no faster and no higher, that energy has not gone into its kinetic or gravitational potential store. It has been dissipated to the thermal stores of the object and its surroundings, so the temperature rises.
Worked example
A cyclist brakes and comes to a stop. Describe the energy transfers, and explain why the brakes become hot.
- Before braking, energy is in the kinetic store of the bicycle and rider.
- The brake blocks press against the wheel, so there is a large frictional force.
- The wheel moves against that frictional force, so work is done against friction.
- Work done against frictional forces causes a rise in temperature.
- The energy from the kinetic store is therefore transferred to the thermal store of the brakes, the wheel and the surroundings — which is why the brakes get hot.
Answer: Energy is transferred from the kinetic store of the bicycle to the thermal store of the brakes and surroundings, because work is done against friction — and work done against friction raises the temperature.
Common mistake
Friction does not destroy the kinetic energy. The energy is transferred to thermal stores, which is measurable as a temperature rise — the total energy is unchanged.
Before you practise
- Work is done when a force causes a displacement of an object.
- W = F s must be recalled, where s is the distance moved along the line of action of the force.
- Movement at right angles to a force does no work against that force.
- One joule is one newton-metre — the work done when a force of 1 N causes a displacement of 1 m.
- Doing work on an object transfers energy to it.
- Work done against frictional forces causes a rise in the temperature of the object.
- Newton-metres are also the unit of the moment of a force, where they are not joules — check which quantity is meant.