Frictional force acting between two bodies that are in the state of rest is called static frictional force.It is because of interlocking of irregular surfaces that are in contact.When we apply force to move the body,this interlocking opposes the relative motion and this opposition is called frictional force.So it comes into picture only when we try to move it by applying a force.If no force is applied,there is no frictional force comes into action.
Frictional force is directly proportional to normal reaction.Normal reaction the reaction force applied by a lower body on the upper body as a reaction to the force applied on it and it is normal to the surface of contact.The proportionality can be eliminated with a constant called coefficient of friction.It is a constant with out units and dimensions as it is the ratio of similar physical quantities that is force and normal reaction.The corresponding frictional force is called maximum frictional force and is also called as limiting frictional force.
If we have not applied any force on a body and try to move the body,frictional force also becomes zero.If we start applying force,with the applied force,frictional force also start increasing.This happens until the applied force is less than limiting frictional force.Once if the applied force is equal to maximum static frictional force,frictional force reaches its maximum and is not going to increase further.With in this stage,at any instant frictional force is equal to the applied force.Thus static frictional force adjusts its value to the applied force and keeps the body in the state of rest.That is why static frictional force is called self adjusting force.It is a unique property and the balance given by the nature to sustain.
In the following video,it is demonstrated with mathematical example also.Please go through.
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