Name: Kinetic Friction and Its Laws
Uploaded: 2019-07-19
Duration: 2 min 55 s
Description: What happens when a body slides on a surface? Does it experience any frictional force? What are the governing laws? We will explore in this video.

Question

State coefficient of friction, angle of limiting friction and angle of repose. Derive relation between them.

Accepted Answer

Coefficient of friction is value that shows the relationship between the frictional force and the normal reaction force acting between the surfaces.

$f = μ N$ ,
where, $μ$ is coefficient of limiting friction, $f$ is frictional force and $N$ is normal reaction force.

Angle of friction between any two surfaces in contact is defined as the angle which the resultant of the forces of limiting friction and normal reaction makes with the normal reaction force as shown in figure.
It is marked in the figure as $θ$ .

As shown in the figure, for $∆ A O C$ ,
$\tan θ = \frac{A C}{O A} = \frac{O B}{O A} = \frac{F_{l i m}}{N} = μ \Rightarrow μ = \tan θ$

The angle of repose or angle of sliding $α$ (as shown in the figure) is defined as the minimum angle of inclination of a plane with the horizontal such that a body placed on the plane just begins to slide down.

Since, object is just about to slide, forces are balanced along the incline and perpendicular to incline.
From the diagram,

$f = m g \sin α$

$N = m g \cos α$

From the above two equations,
we get, $\frac{f}{N} = \tan α$

So, $μ = \tan α$

Hence, we observe that both angle of limiting friction $(θ)$ and angle of repose $(α)$ are equal to the coefficient of friction $(μ)$ .

State coefficient of friction, angle of limiting friction and angle of repose. Derive relation between them.

Important Questions on Laws of Motion

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