The surface exerts a force equal but opposite to the force due to gravity. This force is called the normal reaction. Because it acts at 90° to the surface, this force has no component acting parallel to the surface.

If equilibrium is to be maintained, the surface must continue to exert a force which is equal but opposite to the force of gravity but now this force has a component which acts parallel to the surface.

It is often useful to resolve the reaction force into two components; one acting at 90° the surface and one acting parallel to the surface.

The component acting at 90° to the surface is the normal reaction.

The component acting parallel to the surface is the force of friction.

Similarly, we can resolve the force of gravity into two perpendicular components.

To maintain equilibrium

Therefore, if the angle between the surface and the horizontal is q, 

The force of friction acting between two surfaces

^* There are, of course, an infinite number of other things that the force of friction does not depend on !

Experiments show that the magnitude of the force of friction acting between two surfaces is directly proportional to the magnitude of the normal reaction, R.

Therefore we can write F_f = a constant × R

the value of the constant depends on the nature of the two surfaces (what materials they are and how "smooth" they are).

The constant is called the coefficient of friction for the two surfaces.
However, there are two coefficients for a given pair of surfaces:

So, for two surfaces which are stationary relative to each other

and for two surfaces which are sliding past each other

For two given surfaces, µ_s > µ_d

If a surface is described as "smooth", we mean that it exerts no force of friction. Therefore, a surface described as smooth can only exert a force at 90° to itself.

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© David Hoult 2008