Consider a block resting on some horizontal surface. Let some external force **F _{ext}** be applied on the block. Initially the block does not move. This is possible only if some other force is acting on the block. The force is called the force of

As F_{ext} is increased, f_{s} also increases and remains equal to F_{ext} in magnitude until it reaches a critical value f_{s}^{(max)}. When F_{ext} is increased further, the block starts to slide and is then subject to **kinetic friction**.

It is common experience that the force needed to set an object in motion is larger than the force needed to keep it moving at constant velocity. For this reason, the maximum value of static friction f_{s} between a pair of surfaces in contact will be larger than the force of kinetic friction f_{k} between them.

**Static Friction**

f_{s}^{(max)} ∝ F_{N}

f_{s}^{(max)} = µ_{s} F_{N}

where µ_{s} is called the coefficient of static friction. The normal force F_{N} of the surface on the block can be found by knowing the force with which the block presses the surface.

Since f_{s} = F_{ext} for f_{s} ≤ f_{s}^{(max)}

f_{s} ≤ µ_{s} F_{N}

**Kinetic Friction**

f_{k} = µ_{k} F_{N}

where µ_{k} is the coefficient of kinetic friction.

In general, µ_{s} > µ_{k}

Values of µ_{s} and µ_{k} for a given pair of materials depend on the roughness of surfaces, cleanliness, temperature, humidity, etc.