Work Done Against Friction

When an object moves against a friction force, work is done against friction. This work is transferred to thermal energy, heating the surfaces in contact.

Calculating work against friction

$W_{\text{friction}} = F_{\text{friction}} \times d$

where $F_{\text{friction}}$ is the friction force (N) and $d$ is the distance moved (m).

Example: A box is pushed 5 m across a floor against a friction force of 40 N.

$W = 40 \times 5 = 200 \text{ J}$

This 200 J is converted to thermal energy in the box and floor.

Braking distance

When a car brakes, the brakes exert a friction force that does work against the car’s kinetic energy:

$F_{\text{brake}} \times d = \frac{1}{2}mv^2$

Doubling the speed quadruples the KE, so the braking distance quadruples (at constant braking force).

Friction on slopes

On a slope, friction acts along the surface. The work done against friction equals $F_{\text{friction}} \times d_{\text{along slope}}$, not the vertical height.

Total energy input = useful work (GPE gained) + work done against friction:

$Fd_{\text{applied}} = mgh + F_{\text{friction}} d$

Common errors and how to correct them

• Confusing the applied force with the friction force. The work done against friction uses the friction force, not the pushing force.
• Forgetting that work done against friction = energy dissipated as thermal energy.

How to apply this in an exam

Identify the friction force and the distance. Multiply to find the work done. State that this energy is transferred to thermal energy stores.