What is friction ? Explain static frictional force.

Whenever there is relative motion between two surface. The force due to which relative motion is retarded is called frictional force.

As shown in figure, an object is placed on horizontal surface.

Weight (gravitational force) and normal force balance each other. Let horizontal force $\mathrm{F}$ is applied to object.

If $\mathrm{F}$ is the only force acting on body may be of very small value, then also acceleration $a=\frac{\mathrm{F}}{\mathrm{m}}$ and object will move with acceleration $a$ in direction of force.

But, here object does not move hence, there should be a force which act in opposite direction and make resultant force to zero.

Force which act parallel to contact surface is called frictional force $\left(f_{s}\right)$. Frictional force comes to action when external force is applied to object.

When external force $ (F)$ is increased then static friction force also increase upto certain limit and keep object stationary.

Frictional force opposes impending motion.

Impending motion is motion may have occurred if friction force was not present.
As magnitude of external force increase, frictional force also adjust its value hence frictional force is called self adjusting force.
When object (block) start moving in direction of external force, frictional force is called maximum static friction force $\left(f_{s m a x}\right)$.
Law of static friction :
 $(1)$ Maximum static friction force do not depend on area of contact between surfaces.
$(2)$ Maximum static frictional force is proportional to normal force.
$\therefore \mathrm{f}_{s(\max )} \propto \mathrm{N}$
$\therefore \mathrm{f}_{\mathrm{s}(\max )}=\mu_{\mathrm{s}} \mathrm{N}$
$\mu_{\mathrm{s}}=$ coefficient of static friction value of $\mu_{\mathrm{s}}$ depend on nature of surface in contact, material of surface and temperature.
$\mu_{\mathrm{s}}=\frac{\mathrm{f}_{\mathrm{s}}}{\mathrm{N}}$
$\mu_{\mathrm{s}}$ is unitless and dimensionless. Ratio of maximum static friction and normal force is called coefficient of static frcition.
Its value is in range of $0.01$ to $1.5$.
If object does not move than $\mathrm{f}_{\mathrm{s}} \leq \mu_{\mathrm{s}} \mathrm{N}$.