Question

derive the expression for co-efficient of friction in terms of angle of repose
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Answer 1

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.

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.

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,

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

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=μNwhere μ is the coefficient of friction and N is the normal reaction.

==>N=mg.cosθ

N=mg.cosθnow,

==>mg.sinθ=μmg.cosθ

==>tanθ=μ

==>θ=tan −¹(μ)

θ=tan −¹(μ)here θ is known as angle of repose.

Hope u understand the concept...