Question

discuss the law of friction derive the expression for coefficient in terms of angle of repose​

Answer 1

Answer:

An easy way to measure the coefficient of static friction is to place two objects together and then tilt them until the top one slides. The angle at which one object starts to slip on the other is directly related to the coefficient.

When the two objects are horizontal there is no frictional force. As the objects are slowly tilted, the force of static friction must increase from zero to counteract the component of the force of gravity that acts along the interface.

Eventually, as the angle increases, that component of the force of gravity exceeds the maximum value of the force of static friction, and the top object slides off.

How does the angle at which this occurs relate to the coefficient of static friction?

Take the limiting case, the angle reached just before the block begins to slide, and draw the free-body diagram.

Answer 2

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 θ angle with horizontal and a body which mass is m just begins to slide down.

then,

mg.sinθ=μN

where μ is the coefficient of friction and N is the normal reaction.

N=mg.cosθ

now,

mg.sinθ=μmg.cosθ

tanθ=μ

θ=tan

−

1(μ)

here θ is known as angle of repose