notes
Static friction

Static friction is the force of friction between two surfaces so long as there is no relative motion between them. It is always equal to the applied force.

Force that resists initiation of motion of one body over another with which it is in contact

Opposes Impending motion

Denoted by f_{s}
Let the ball be at rest initially
Applied force, F_{a} = 0; Static friction, f_{s} = 0
Later, applied force, F_{a} = F, then fs also increases but only up to a certain limit. As soon as F_{a} becomes greater than f_{s}, the ball starts to move.
_{}
F_{s} acts when a body is at rest. Hence called Static friction.

Limiting value of f_{s} depends on Normal reaction, and is independent of the area of contact
f_{s} max ∝ N
f_{s} max = constant × N
f_{s} max = μ_{s} N
where μ_{s} is the coefficient of static friction
This coefficient depends on the nature of surfaces in contact.

According to the Law of Static friction, Static friction is always less than or equal to the limiting value of f_{s}
f_{s} =< f_{s} max
f_{s} max = μ_{s} N
f_{s} =< μ_{s} N
Kinetic friction

Kinetic friction is the force of friction which comes into play between two surfaces when there is some relative motion between them.

Force that resists motion of one body over another with which it is in contact.

Denoted by f_{k}

As motion starts, f_{s} vanishes and f_{k} appears
Kinetic friction is Independent of the area of contact and velocity of the body

It varies with _{Normal} reaction, N
f_{k} ∝ N
f_{k} = constant × N
f_{k} = μ_{k} N; μ_{k} is the coefficient of kinetic friction
Three scenarios can arise in a body’s motion
1. When applied force > f_{k}
F_{a} > f_{k}
(F_{a} – f_{k}) = ma
a = (F_{a} – f_{k})/m
2. When applied force = f_{k } F_{a} = f_{k}
Therefore, a = 0 i.e. the body moves with uniform velocity
3. When applied force = 0
F_{a} = 0
A =  f_{k}/m
No motion occurs, the body stops
Relation between Coefficient of Static & Kinetic friction
f_{k} = μ_{k} N
f_{s} =< μ_{s} N
f_{s} > f_{k} (to keep the body moving)
μ_{s} N > μ_{k} N
Or, μ_{k} < μ_{s}
Coefficient of kinetic friction is smaller than the coefficient of static friction.