Name: Work Done on a Block
Uploaded: 2019-07-19
Duration: 3 min 57 s
Description: Check out this solved illustration based on calculating work done on an object by forces acting at different angles. Just click this video to explore!

Question

Define angle of repose and angle of friction. Establish relation between them.

Accepted Answer

Angle of friction ( $ϕ$ ): Angle made by the resultant of normal reaction and limiting frictional force with the normal reaction is called angle of friction.

Angle of repose ( $θ$ ): The minimum angle of the plane at which the body kept on it starts to slide due to its own weight is called angle of repose

Suppose angle of friction = $α$ and angle of repose = $θ$
Let us suppose a body is placed on an inclined plane as in the above figure.
Various forces involved are:-
1) Weight( $m g$ ) of the body, acting vertically downwards.
2) Normal reaction( $R$ ), acting perpendicular to inclined plane.
3) Force of friction( $F$ ), acting up the plane.
Now, $m g$ can be resolved in two components:-
$m g \cos θ$ opposite to $R$
and $m g \sin θ$ opposite to $F$
In equilibrium,
$F = m g \sin θ . . . . . . . . . . . . . . . . . (1) R = m g \cos θ . . . . . . . . . . . . . . . (2)$
On dividing $(1)$ by $(2)$ we get,
$\frac{F}{R} = \frac{m g \sin θ}{m g \cos θ} = \tan θ μ = \tan θ$
Where $μ$ = coefficient of limiting friction.This is equal to the tangent of the angle of repose between two surfaces in contact.
Now, since $μ = \tan ϕ$
i.e coefficient of limiting friction between any two surfaces in contact is equal to tangent of the angle of friction between them.
Thus,
$θ = ϕ$
i.e angle of friction is equal to angle of repose.

Define angle of repose and angle of friction. Establish relation between them.

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