In cases where there is no relative motion between the surfaces in contact, friction is known as static friction. (abbreviated as `f_s` ). Static friction is an adjustable force which may have any value from zero to certain maximum value, under a given case. The maximum possible value of this static friction is known as limiting static friction.

`=>0 le f_s le ` Limiting static friction.

(Liming static friction) (Normal reaction between the surfaces in contact)

`f_(s Lim)=mu _2 N`

where `mu_2` is a constant, (characteristic of the surfaces in contact) known as coefficient of static friction. Thus `0 le f_s le mu_2 N`

Let us consider a case to understand it. A block of mass `2` kg lies over a rough horizontal surface. The coefficient of static friction between the block and surface is `0.5`

`N=Mg`
` 0 le f_s, le N= 10 N`

Now a horizontal force say `F` is applied on block. `F` is gradually increased from zero

Friction
for `F = 0` `f = 0`

for `F = 5 N` `f = 5 N`

for `F = 9.99 N` `f = 9.99 N`

for `F = 1 0 N` `f = 1 0 N` when `F > 1 0 N`

Now when force is increased beyond `1 0 N` relative motion starts and friction becomes kinetic