Coulomb’s Model for Friction

Introduction

This is a simple, and in some circumstances limited, model for friction. The whole concept is that friction, between an object and surface (for example), matches the applied on the object up until a maximum friction value. Then the object will inevitably begin to accelerate with that maximum frictional force as a resistive force.

Coulomb’s Model

Coulomb stated that the maximum frictional force, called the limiting friction, between two objects is proportional to the normal reaction on one of the objects exerted by the other:
In the case shown above the normal reaction would be equal to the weight of the yellow block, but this won't always be the case. So we have established that the limiting friction is proportional to the normal reaction, so we need a constant of proportionality. This ends up depending on the nature of the surfaces in question and is imaginatively named the coefficient of friction (μ).

  • μ will always be between 0 and 1
  • Depends on surfaces
  • Friction will always act to oppose motion
The forumla:

  • Where R is the normal reaction, and μ is the coefficient of friction.
The frictional force will get bigger to match a force trying to accelerate our object- only up until limiting friction! Then a force applied greater than the limiting friction will cause acceleration.

Inclines and Angled forces

The normal reaction won't always be as eacy as R=mg. Sometimes factors such as the situation being placed on an incline, or having another force acting at an angle cant affect the normal reaction and hence the frictional force!
In this case the normal reaction isn't equal to the weight, but is equal to the component of the weight perpendicular to the surface! This is important as the limiting friction will be smaller.

Solutions

Discuss on Forum!
Topic Checklist
More Maths