The limiting (or maximum) force of friction is proportional to the normal force that keeps the two surfaces in contact with each other, and is independent of the area of contact between the two surfaces. Mathematically,
fmax = µN
If the body does not move, then the static frictional force fs and the external force F parallel to the surface are equal in magnitude; and fs is directed opposite to F. If the external force F increases fs increases.
(a) The friction force on a stationary block is zero.
(b) As long as the external force is less than the maximum friction force, fs = F.
(c) At the limiting case fs max = F. The block is about to slide.
(d) As the value of F slightly increases beyond fs max , the block “breaks away” accelerating suddenly to the right.
(e) If the block is to move with a constant velocity, the applied force must be reduced, because mk < ms.
Whenever two bodies interact by direct contact of their surfaces, there are two contact forces acting on each body
Since these two forces are perpendicular to each other hence the net contact force is and the angle of friction is .
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