Coefficient of Static and Kinetic Friction

Coefficient of Static Friction:

The ratio of limiting frictional force to the normal reaction is called coefficient of static friction. It is denoted by μ. Coefficient of static friction depend upon the nature of two surfaces. It is independent of the area of contact when the normal reaction is kept constant.

Determination of coefficient of static friction: Let us consider a body f mass ‘m’ placed over the surface of inclined plane. The inclination of surface S is gently increases until the block begin to slide. Let F be the limiting friction and mg be the weight of the body. When the body begins to slide,

F = mgsinθ

R = mgcosθ

Now, $\mu =  \frac{F}{R} =  \frac{mgsin \theta }{mgcos \theta } = tan  \theta $

Hence, coefficient of friction can be measured by measuring the inclination of the plane.

The table below shows the coefficient of static friction between certain pair of materials.

  Material   μ
Steel and steel 0.58
Wood and Wood 0.35
Ice and Ice 0.10
Glass and glass 1.00
Rubber tyre and concrete 0.70
Wood and metal 0.40
Steel and brass 0.35

Coefficient of Kinetic friction: The coefficient of kinetic friction is defined as the ratio between the frictional force F when the object moves with a uniform velocity to the normal reaction R of the surface on the object. It is generally denoted by μ’ .

$$\mu’ =  \frac{F’}{R}$$

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