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Question

# The coefficient of static friction between a block of mass m and an incline is μs = 0.3. What can be the maximum angle θ of the incline with the horizontal so that the block does not slip on the plane? (Also called angle of repose)

A

θ = tan1 (0.3)

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B

θ = cot1 (0.3)

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C

θ = sin1 (0.3)

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D

θ = cos1 (0.3)

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Solution

## The correct option is A θ = tan−1 (0.3) The situation is shown in figure The forces on the block are (i) (1) the weight mg downward by the earth, (ii) the normal contact force N by the incline, and (iii) the friction f parallel to the incline up the plane, by the incline Taking components perpendicular to the incline, N - mg cos θ = 0 or, N = mg cosθ. .....(i) Taking components parallel to the incline, f - mg sinθ = 0 or, f = mg sinθ or, μsN = mg sinθ. .....(ii) Dividing (ii) by (i) μs = tanθ or, θ= tan−1 μs= tan−1 (0.3)

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