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Derive relation between angle of friction and angle of repose

Derive relation between angle of friction and angle of repose 

Grade:11

1 Answers

Arun
25758 Points
3 years ago
Dear Mahesh
 
213-1012_MASS.JPG
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
 
Where mu = coefficient of limiting friction.
This is equal to the tangent of the angle of repose between two surfaces in contact.
 
Now, since mu = tan alpha i.e coefficient of limiting friction between any two surfaces in contact is equal to tangent of the angle of friction between them.
Thus, Theta = alpha i.e angle of friction is equal to angle of repose.

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