Question

Define coefficient of static friction and
coefficient of kinetic friction. What is angle
of friction? Find its relation with coefficient
of friction
​

Answer 1

Answer:

according to first law of friction

f= uR

where u is constant of proportionality .

coefficient of static friction

u=f/R

where f is force of static friction

R is normal reaction

N=mgcosθ_1

f= mgsinθ_2

2÷1

=> f/N= sinθ/cosθ

=> uN/N=tanθ

=> u=tanθ

Answer 2

Answer:

Angle of friction is given by $tan\theta=\mu$

Explanation:

• The coefficient of friction is the ratio of the force of friction between two bodies and the normal force force pressing them together.  

        Mathematically given by, $\mu =\frac{frictional ~force(F)}{Normal~ force(N)}$

• In static friction, the frictional force resists the force applied on an object.
• The coefficient of static friction is the ratio of the maximum static friction  between the surfaces in contact to the normal force.
• In kinetic friction, the frictional force resists the motion of an object.
• The coefficient of kinetic friction is the ratio of the kinetic friction  between the surfaces in contact to the normal force.  
• Angle of friction is defined is the angle between the normal force and frictional force.

       The normal force is given by $N=mgcos\theta$

       The frictional force is given by $F=\mu ~mgsin\theta$

       Dividing both equations,

       $\frac{F}{N} = \frac{~mgsin\theta }{mgcos\theta}$

        $\implies \frac{\mu N}{N} = tan\theta$

        $\implies tan\theta=\mu$

      Therefore, the angle of friction is given by $tan\theta=\mu$