Question

Define angle of repose. Deduce its relation with coefficient of limiting friction.

Answer 1

The 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.

let any inclined plane inclined with $\theta$ angle with horizontal and a body which mass is m just begins to slide down.

then,

$mg.\sin \theta =\mu N$

where $\mu$ is the coefficient of friction and $N$ is the normal reaction.

$N=mg.\cos \theta$

now,

$mg.\sin \theta =\mu mg.\cos \theta$

$\tan \theta =\mu$

$\theta =ta{n}^{-}1\left(\mu \right)$

here $\theta$ is known as angle of repose.