Laws of Frction
The limiting (or maximum) force of friction is proportional to the normal force that keeps the 2 forces in contact with each other, and is independent of the area of contact between the 2 surfaces. Mathematically
fmax = μN
Properties of friction
- If the body does not move, then the static frictional fore fs and the external force F parallel to the surface are equal in magnitude and fs is directed to the opposite to F. If the external force F increases then fs also increases.
- The maximum value of static friction is given by
fs(max) = μsN Here, μs is the static coefficient of friction and N is the magnitude of the normal reaction. If the external force F exceeds fs(max) then the body slides on the surface.
- If the body begins to slide along the surface then, the magnitude of the frictional force rapidly decreases to a constant value of fk given by
fk = μkN Here, μk is the coefficient of kinetic friction.
Angle of Friction
It is the angle which the resultant of the limiting friction and the normal reaction makes with the normal reaction i.e μs = tan θ, where θ is the angle of friction.
Angle of Repose
It is the minimum angle that an inclined plane makes with the horizontal when a body placed on it just begins to slide down. If φ is the angle of repose, then tan φ = μs. Angle of repose (φ) = Angle of friction (θ)