Name: Motion on Rough Inclined Plane
Uploaded: 2019-07-19
Duration: 6 min 27 s
Description: You know that smoothness of the surface influences the friction on the object moves over it. Let us discuss the motion of a block on a rough surface in this...

Question

Explain what is meant by coefficient of friction and angle of friction. Establish relation between them.

Accepted Answer

Co-efficient of friction:

For the given surfaces, the limiting force of friction $f_{S}$ is directly proportional to normal reaction $R$

or $f_{S} \propto R$

$∴ f_{S} = μ_{S} R$

Where $(μ_{s})$ is called the co-efficient of static or limiting friction. In above formula $f_{S}$ has its maximum or limiting value when object is about to move. when the object is in uniform motion the force acting between two surfaces in relative motion is called the kinetic or sliding force of friction $f_{k}$ which is less than the limiting force of friction.

$∴ f_{k} = μ_{k} R_{k}$ where $μ_{k}$ is co-efficient of kinetic friction. $μ_{k}$ is always slightly less then $μ_{S}$ . This is because once the motion actually starts inertia of rest has been overcome.

Angle of friction:

It is the angle which the result but of limiting force of friction and normal reaction makes with normal reaction as shown is fig. $1$ .

Relation between coefficient of friction and angle of friction.

In fig. $1$ .

$f_{S} =$ Force of limiting friction and $R$ normal reaction.

$f_{S} = P \sin θ$

$R = P \cos θ$

$∴ μ_{S} = \frac{f_{S}}{R} = \tan θ_{S}$

where $θ_{S}$ is angle friction.

Explain what is meant by coefficient of friction and angle of friction. Establish relation between them.

Important Questions on Friction

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