When work is done
Definition
Work done
Work is done on an object when a force causes it to move through a distance along the line of action of the force.
- A force does work only if it causes a displacement, which is movement from one position to another in a particular direction.
- Work is done when a person lifts a box, when a car’s driving force moves it forwards, or when a bicycle’s brakes exert friction while the bicycle is moving.
- If you push a wall that does not move, no work is done on the wall, because there is no displacement even though a force is applied.
- Work done is measured in joules (J\text{J}J).
Calculating work done
- Work done is calculated with the equation W=FsW = FsW=Fs.
- WWW is the work done in joules (J\text{J}J).
- FFF is the force in newtons (N\text{N}N).
- sss is the distance moved along the line of action of the force in metres (m\text{m}m).
- The line of action is an imaginary straight line in the direction the force acts, and the distance must be measured along this line.
- The equation rearranges to F=WsF = \dfrac{W}{s}F=sW and s=WFs = \dfrac{W}{F}s=FW.
Example
A worker pushes a crate with a force of 75 N75\ \text{N}75 N. The crate moves 4.0 m4.0\ \text{m}4.0 m in the direction of the force. Calculate the work done on the crate.
- Write the equation: W=FsW = FsW=Fs.
- Substitute the values: W=75 N×4.0 mW = 75\ \text{N} \times 4.0\ \text{m}W=75 N×4.0 m.
- Calculate the work done: W=300 JW = 300\ \text{J}W=300 J.
Joules and newton-metres
- One joule of work is done when a force of one newton causes a displacement of one metre along the line of action of the force.
- So 1 J=1 N m1\ \text{J} = 1\ \text{N m}1 J=1 N m: joules and newton-metres are equivalent units for work done.
- Because the values are equal, converting needs no calculation: 50 N m=50 J50\ \text{N m} = 50\ \text{J}50 N m=50 J and 120 J=120 N m120\ \text{J} = 120\ \text{N m}120 J=120 N m.
Work done and energy transfer
- When work is done, energy is transferred mechanically, and the work done equals the energy transferred (both measured in joules).
- Lifting an object transfers energy to its gravitational potential energy store.
- Accelerating an object transfers energy to its kinetic energy store.
- Friction slowing an object transfers energy from its kinetic store to thermal energy stores.
- So if 300 J300\ \text{J}300 J of work is done on an object, 300 J300\ \text{J}300 J of energy is transferred.
Work done against friction
- Friction acts against the motion of an object, so a force must do work against friction to keep it moving.
- Work done against friction transfers energy to thermal energy stores, raising the object’s temperature.
- For example, bicycle brakes get warmer in use because friction does work as the brake pads rub against the wheel.
Common Mistake
- Applying a force does not always mean work is done; the force must cause a displacement.
- Use only the distance moved along the line of action of the force, not the total distance travelled.
- Work done is measured in joules, not newtons; newtons measure force.
Exam technique
- For a calculation, write W=FsW = FsW=Fs, substitute the force in newtons and the distance in metres, and give the answer in joules.
- For an energy-transfer question, state that work is done and name the energy store that increases.
- For friction, say energy is transferred to a thermal energy store, causing a rise in temperature.
Self review
- When does a force do work on an object?
- State the equation linking work done, force and distance.
- What are the units of work done, force and distance?
- How much energy is transferred when 200 J200\ \text{J}200 J of work is done?
- Why does work done against friction raise an object’s temperature?
