Friction

This lesson covers friction as required by the Edexcel 9MA0 A-Level Mathematics specification. You need to understand the friction model, the coefficient of friction μ, and how to apply friction in equilibrium and motion problems.

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The Friction Model

Friction is a force that opposes the motion (or attempted motion) of an object along a surface. It acts along the surface at the point of contact.

Key Properties

1. Friction always acts in the opposite direction to the motion (or to the direction in which the object would move if friction were absent).
2. The magnitude of friction depends on the normal reaction R and the coefficient of friction μ.
3. Friction is self-adjusting up to a maximum value.

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The Laws of Friction

When the object is stationary or on the point of moving (limiting equilibrium):

F ≤ μR

where F is the frictional force, R is the normal reaction, and μ is the coefficient of friction.

When friction is at its maximum (limiting friction):

F = μR

This occurs when the object is on the point of sliding (limiting equilibrium) or when the object is already sliding.

When the object is in motion: