Question

Write the relation between angle of friction and angle of repose ​

Answer 1

Answer:

Angle of friction:-)

lt is the angle made by resultant of of limiting friction and the normal reaction with the the normal reaction.

OR

lt is the angle made by net reaction offered by the surface with the normal reaction when the body is just about to move .

[representation of angle of friction is shown in attachment].

Angle of repose:-)

lt is the angle made by inclined plane with the horizontal at which body begins to slide down the plane . When the body is just about to slide down .

$Friction = \mu sn$

[representation of angle of repose is shown in attachment .]

Relation b/w friction and angle of repose :-)

Angle of repose is always equal to angle of friction .

Answer 2

Answer:

Note: Diagram of Angle of Friction and Angle of repose.

Angle of Friction:

=> The angle of Friction between any two surface is contact is defined as angle between reaction force (R) and resultant of reaction force and frictional force (OB).

In OAB,

$\sf{\implies \tan \theta = \dfrac{AB}{OA}}$

$\sf{\implies \tan \theta = \mu}$

$\sf{\implies \theta = \tan^{-1}\;(\mu)}$

$\sf{\implies \tan \theta = \dfrac{Fr}{R}=\dfrac{\mu Re}{R} = \mu}$

The tangent of angle of friction is equal to coefficient of friction.

Angle of Repose:

=> The angle of repose is defined as the maximum angle of inclined of a plane with the horizontal such that a body placed on the plan just began to slide down on the inclined.

Balanced condition,

=> mg sinФ = F           ...........(1)

=> mg cosФ = R          ...........(2)

Divide eq (1) by eq (2),

$\sf{\implies \dfrac{mg \sin \theta}{mg\cos \theta} = \dfrac{F}{R}}$

$\sf{\implies \tan \theta = \mu}$

$\sf{\implies \theta = \tan^{-1}\;(\mu)}$