Question

difference between angle of friction and angle of reference

Answer 1

Angle of friction and angle of repose are two angles that come up in mechanical engineering. The angle of repose also has a use in soil mechanics. The main difference between angle of friction and angle of repose is that the angle of friction is defined as the angle between the normal reaction force and the resultant force of normal reaction force and frictionwhen an object just begins to move, whereas the angle of repose is defined as the minimum angle of an inclined plane which causes an object to slide down the plane. 

Answer 2

Suppose angle of friction = alpha and angle of repose = theta

Let us suppose a body is placed on an inclined plane as in the above figure.

Various forces involved are:-

1. weight,mg 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, mg can be resolved in two components:-

mgcos theta opposite to R

and mgsin theta opposite to F

In equilibrium,

F = mgsin theta -------- eq.1

R = mgcos theta ---------eq.2

On dividing eq.1 by eq.2 we get,

F/R = mgsin theta/mgcos theta

mu = tan theta