Friction

Static and kinetic frictional forces arising at solid contact interfaces.

General idea of the topic

Friction is the tangential force that appears between two surfaces in contact and opposes sliding, or the tendency to slide. It does not have a single value: while the surfaces do not slide, static friction adjusts to whatever is needed up to a maximum; once they slide, kinetic friction takes a practically constant value.

This topic starts from that double behaviour and from a simple empirical model in which the maximum friction is proportional to the normal force through a coefficient that depends on the surfaces. It is a useful but limited model: it does not depend on the apparent contact area and does not describe high velocities or very smooth or lubricated surfaces well.

What the student is expected to understand

By the end, the student should be able to decide whether a body slides or stays at rest by comparing the force that pushes it with the maximum static friction, and to calculate the acceleration when it slides using the kinetic coefficient.

The student should also understand why static friction is not μN in general but an inequality, and why the kinetic coefficient is smaller than the static one.

Recommended learning route

1. Static Friction: studies friction while there is no sliding, its adjustable value and its maximum before the body starts to move.
2. Kinetic Friction: analyses the constant force that opposes the motion once there is sliding and the energy it dissipates.
3. Coefficient of Friction: characterises the surfaces through the static and kinetic coefficients and discusses reference values and their limits.

Physical criterion to acquire

The essential criterion is to find out first which regime the system is in. If it does not slide, friction is an unknown that satisfies the inequality with the maximum; if it slides, it equals μ_k times the normal force and opposes the relative motion. Writing μN from the start, without checking the regime, is a mistake to avoid.

Connection with real problems

• vehicle braking and tyre grip.
• boxes, ramps and conveyor belts.
• footwear, grips and the design of anti-slip surfaces.
• energy loss in mechanisms and wear of parts.

Final goal of the topic

The final goal is to model friction with the correct regime, determine whether there is sliding, and calculate the resulting forces and accelerations together with their validity conditions.