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Friction

Friction is important in engineering, here we will look at the simplified friction between an object and a surface which it is being pulled across. Firstly we must discuss the normal force.

Normal Force

The normal force is a force that acts against gravity. Generally speaking, as gravity pushes an object down, the surface the object is on exerts a normal force to counter the force of gravity (newtons third law). So the force of gravity and the normal force keep the object on the surface.

This force does not always oppose gravity directly, it acts in a direction perpendicular to the contact of the surface and the object, so if the surface is flat and not inclined, the Normal Force directly opposes gravity and has a magnitude of
N = mg

However, if the surface is an incline plane of angle $\theta$, the normal force becomes:
N = mg$\cos(\theta)$

The coefficients of friction

The coefficient friction (represented $\mu$) is the ratio of the frictional force between two objects and the force keeping them together (normal force) so:
$\mu = \frac{F}{N}$, where: N = normal force, F = frictional force
Depending on the situation, the coefficient of friction can be defined in different ways.
here we will look at the static and kinetic coefficients of friction.

Static coefficient of friction
The static coefficient of friction ($\mu_s$) is the coefficient of friction between two objects where there is no relative movement meaning that they are stationary compared to each other.

Kinetic coefficient of friction
The kinetic coefficient of friction ($\mu_k$) is the coefficient of friction between two objects with relative movement between them.

The static coefficient of friction is generally larger than the dynamic coefficient of friction, however in some circumstances they can be equal to each other ie
$\mu_k \leq \mu_s$

Some tips for calculating frictional force

1)The frictional force can never be greater than the force being applied in a static scenario, if you are getting this result, the object will not move and the frictional force will balance out the applied force.
2)In a dynamic scenario, if the frictional force is greater than the applied force, the object will be decelerating.
3)Be careful to work out the normal force correctly, it is not always simply N = mg