Question

Find the maximum value of angle of friction and prove that it is equal to the angle of repose

Answer 1

Angle of friction (φ): Angle made by the resultant of normal reaction and limiting frictional force with the normal reaction is called angle of friction.

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Angle of repose (θ): The minimum angle of the plane at which the body kept on it starts to slide due to its own weight is called angle of repose

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To prove:θ=φ∑Fy=0N−Wcosθ=0N=Wcosθ∑Fx=0−Wsinθ+F=0F=WsinθµN=WsinθµWcosθ=Wsinθµ=tanθbut µ=tanφtanφ=tanθφ=θ−−−proved