Work done as energy transferred by a force, the equation W = F s, and the link between work done and energy.

What this dot point is asking

CCEA wants you to define work done as the energy transferred when a force moves an object, use and rearrange the equation W = F s, and explain that the work done equals the energy transferred. This connects forces (Unit 1 mechanics) to energy.

The answer

What work done means

If no movement happens, no work is done, no matter how large the force. Holding a heavy bag still does no work in the physics sense, even though it feels tiring.

Work and energy

So work done and energy transferred are measured in the same unit, the joule, and are numerically equal.

Force and distance must be in the same direction

The distance used is the distance moved in the direction of the force. If you push a trolley horizontally, only the horizontal distance counts. Lifting an object uses the vertical height moved against gravity.

Worked example: pushing against friction

Examples in context

Example 1. Climbing stairs

Walking up stairs, you do work against gravity equal to your weight times the vertical height climbed. This energy is transferred to your gravitational potential store, which is why climbing is tiring.

Example 2. Pushing a stalled car

The work you do, force times the distance pushed, transfers energy to the car's kinetic store (speeding it up) and to heat through friction in the wheels and road.

Example 3. A weightlifter holding a bar overhead

While raising the bar the lifter does work against gravity, transferring energy to its gravitational potential store. Once the bar is held still overhead, it moves no further, so no further work is done on it in the physics sense, even though the lifter still uses energy keeping their muscles tensed.

It is useful to remember that work done is just another name for energy transferred by a force. So a question that asks for "the energy transferred when a force moves an object" is asking for the same calculation as "the work done", using $W = Fs$. This link lets you switch between the language of forces and the language of energy in the same problem.

Try this

Q1. State the equation for work done and the unit of work. [2 marks]

• Cue. $W = F s$; work is measured in joules (J).

Q2. A force of $150\ \text{N}$ moves a box $4.0\ \text{m}$. Find the work done. [2 marks]

• Cue. $W = 150 \times 4.0 = 600\ \text{J}$.

Q3. Why is no work done when you hold a heavy box still? [1 mark]

• Cue. The box does not move, so no distance is moved and no work is done.