Work Done & Friction

Work Done

Work done is a measure of the energy transferred when a force moves an object over a distance. It happens whenever a force causes displacement in the direction of the force.

Formula for work done:

Work done $W = \text{force} \times \text{distance}$

Or written with symbols:

$$W = F \times d$$

• $W$ is work done in joules (J)
• $F$ is force in newtons (N)
• $d$ is distance moved in metres (m)

Work done by a force always causes energy to be transferred from one store to another. For example, pushing a box transfers energy from your muscles to the boxs kinetic energy store.

If the force and displacement are not in the same direction, only the component of the force in the direction of movement does work.

For example, if a force is applied at an angle $\theta$ to the direction of movement, the work done is calculated using the component of the force in the direction of movement: $W = F \cos \theta \times d$.

For instance, if you push a box with a force of 10 N and it moves 3 m along the floor, the work done is:

$$W = 10 \times 3 = 30 \text{ J}$$

Friction

Friction is a force that opposes motion between two surfaces that are in contact. It acts in the opposite direction to the movement or attempted movement.

Friction converts kinetic energy into thermal energy (heat), which is why surfaces get warm when rubbed together.

The amount of friction depends on:

• Surface roughness: Rougher surfaces have more friction because their bumps catch on each other.
• Force pressing the surfaces together: The greater the force pushing the surfaces together, the greater the friction.

Friction causes energy to be dissipated, meaning some useful energy is lost as heat and cannot be used for useful work.

For example, when you slide a book across a table, friction between the book and table slows it down and heats both surfaces slightly.

Energy Transfer by Work

Work done transfers energy to or from an object. When work is done on an object, energy is transferred to it, increasing its energy store.

For example, doing work against friction transfers energy to the thermal energy stores of the surfaces involved, causing heating.

When friction acts, some of the kinetic energy of moving objects is converted into thermal energy, which is often wasted energy because it cannot be used to do useful work.

Energy conservation means that energy is never lost but can be transferred into less useful forms, such as heat due to friction.

Energy transferred by work done moves energy between stores, for example from chemical energy in muscles to kinetic energy or thermal energy.

For example, when cycling uphill, you do work against friction and gravity. Some energy is transferred to the bikes kinetic energy store, but some is lost as heat due to friction between the tyres and road and in the bikes moving parts.