Work Done & Energy Transfer

Definition of Work Done

Work done occurs when a force causes an object to move in the direction of the force. It is a measure of the energy transferred by that force.

Work done (W) is calculated using the formula:

$$W = F \times d$$

• F = force applied (in newtons, N)
• d = distance moved in the direction of the force (in metres, m)

The unit of work done is the joule (J). One joule is done when a force of one newton moves an object one metre.

For example, if a force of 10 N moves an object 2 m in the same direction, the work done is $W = 10 \times 2 = 20 \text{ J}$.

Work done always causes an energy transfer from one store to another. For example, when you lift a book, work done by your muscles transfers energy to the book’s gravitational potential energy store.

Calculating Work Done

To calculate work done, multiply the force applied by the distance moved in the direction of the force. It is important that the distance is measured along the line of action of the force.

If the force is not constant or the direction changes, more advanced methods are needed, but for GCSE, we focus on constant forces in a straight line.

For instance, if a person pushes a box with a force of 20 N across a floor for 3 m, the work done is:

$$W = 20 \times 3 = 60 \text{ J}$$

Energy Transfer by Work

Work done transfers energy between different energy stores. The total energy in a closed system remains constant (conservation of energy), but energy can move from one store to another.

Examples:

• Lifting an object: Work done by muscles transfers energy to the object’s gravitational potential energy store.
• Friction: Work done against friction transfers energy from kinetic energy to thermal energy (heating surfaces).

This energy transfer explains why machines and moving objects can heat up when they are used.

Work Done Against Friction

Friction is a force that opposes motion. When you do work against friction, energy is transferred from useful mechanical energy to thermal energy, which is often wasted.

For example, when you rub your hands together, work done against friction transfers energy to thermal energy, making your hands warm.

This conversion reduces the efficiency of machines because some energy is lost as heat rather than doing useful work.

Example: A person pushes a shopping trolley with a force of 50 N for 5 m along the supermarket aisle. Calculate the work done.

Using $W = F \times d$:

$$W = 50 \times 5 = 250 \text{ J}$$

So, 250 joules of energy are transferred by the person pushing the trolley.