Introduction
Whenever two surfaces are in contact, they exert forces on each other. In many real-world problems — a book resting on a table, a ladder leaning against a wall, a box being pushed across a floor — the nature of that contact determines whether an object moves or stays put. Understanding friction is therefore essential for a large class of 9709 Mechanics questions. Examiners regularly test whether candidates can correctly identify the direction of friction, apply the right form of the friction inequality, and recognise what "limiting equilibrium" means in context.
Core Concept
The Contact Force and Its Two Components
When two surfaces touch, the total contact force acting on an object can always be resolved into exactly two perpendicular components:
- Normal reaction — perpendicular to the surface, preventing the object from passing through it.
- Frictional force — parallel (tangential) to the surface, opposing the tendency of motion or actual motion.
These two components together make up the single contact force. On a free-body diagram they are drawn separately, but they are physically two aspects of one interaction.
The Smooth Surface Model
A surface is called smooth when friction is assumed to be zero (). Only the normal reaction acts. This is a mathematical idealisation — real surfaces always have some friction. Its limitation is that it ignores energy losses and can give unrealistic predictions when friction is significant (e.g., it would predict that any horizontal force, however small, will cause sliding on a horizontal smooth surface). The 9709 syllabus requires you to state and appreciate this limitation.
Rough Surfaces: Limiting Friction and Limiting Equilibrium
On a rough surface, friction adjusts itself up to a maximum value to prevent motion. Three situations arise:
| Situation | Friction condition | State |
|---|---|---|
| Object stationary, no tendency to move | Static equilibrium | |
| Object stationary, tendency to move (e.g. a force applied) | Static (non-limiting) equilibrium | |
| Object about to slip (or in limiting equilibrium) | Limiting equilibrium | |
| Object moving (kinetic friction — beyond 9709 scope) | (approximately) | Motion |
The phrase "about to slip" in an exam question is the signal that limiting equilibrium holds and you must use exactly.
Coefficient of Friction
The coefficient of friction (mu) is defined as the ratio of the maximum frictional force to the normal reaction:
It is a dimensionless constant that depends only on the pair of surfaces in contact. Typical values lie between 0 (perfectly smooth) and about 1 (very rough), though values above 1 are possible. For a given contact, is fixed; what varies is how much of the available friction is actually being used.
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