Question

derive the expression angle of of repose and angle of inclination inclination​

Answer 1

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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.