The nature of friction, the coefficient of friction, the limiting friction model with the inequality between friction and the normal reaction, and applying friction to objects on horizontal and inclined surfaces.

What this dot point is asking

AQA wants you to understand friction as a resistive force, use the coefficient of friction, apply the limiting friction model with the inequality between friction and the normal reaction, and solve problems for objects on horizontal and inclined surfaces. Friction sits on top of the forces topic, so every friction problem is a force diagram plus the friction model.

The nature of friction

Friction is a contact force that acts along the surface, opposing relative motion or the tendency to move. It is what allows you to walk, brake and grip. In the A-level model friction is not a fixed force: while a body is stationary, static friction is exactly as large as needed to maintain equilibrium, up to a maximum value. Once the body slides, friction takes that maximum value and acts against the direction of motion.

The friction model

The inequality is the crucial subtlety. To decide whether a body moves, compute the maximum available friction $\mu R$ and compare it with the force that is trying to cause motion. If the driving force is less than or equal to $\mu R$, friction holds the body in equilibrium; if it is greater, the body accelerates and you use $F = ma$ with friction at $\mu R$.

On a horizontal surface

On level ground with no vertical applied force, the normal reaction equals the weight, $R = mg$, so limiting friction is $\mu mg$.

On an inclined plane

When asked whether a body on a slope will slide, compare the down-slope weight component $mg\sin\theta$ with the limiting friction $\mu mg\cos\theta$. If the body is moving up the slope, friction acts down the slope; if down, friction acts up. Getting the friction direction right is essential, because it changes the sign in the equation of motion.

A general method for any friction problem

The same routine handles every friction question, on the level or on a slope. First draw a clear force diagram with weight, normal reaction, friction and any applied force. Second, resolve perpendicular to the surface to find the normal reaction $R$ (this is where $\cos\theta$ enters on a slope, and where an angled applied force changes $R$). Third, compute the maximum available friction $\mu R$. Fourth, compare the driving force with $\mu R$ to decide whether the body is in equilibrium or accelerating. Fifth, apply $F = ma$ along the surface with friction acting in the correct sense, taking $a = 0$ if the body stays still.

A subtle but examinable point is that an applied force at an angle alters the normal reaction. A force pulling partly upward reduces $R$, and so reduces the maximum friction, making the body easier to move; a force pushing partly downward increases $R$ and the friction. This is why you must resolve perpendicular to the surface before quoting $\mu R$, rather than assuming $R = mg$.