A small block starts slipping down from a point B on an inclined plane A B , which is making an angle θ with the horizontal section B C is smooth and the remaining section C A is rough with a coeffici

Question

A small block starts slipping down from a point $B$ on an inclined plane $A B$ , which is making an angle $θ$ with the horizontal section $B C$ is smooth and the remaining section $C A$ is rough with a coefficient of friction $μ$ . It is found that the block comes to rest as it reaches the bottom (point A) of the inclined plane. If $B C = 2 A C$ , the coefficient of friction is given by $μ = k tanθ$ . The value of $k$ is .......

TestHub · Accepted Answer

Let A C = ℓ ∴ B C = 2 ℓ ∴ A B = 3 ℓ Apply work – Energy theorem W t + W m g = Δ K E mg ( 3 ℓ ) sin θ - μ mg cos θ ( ℓ ) = 0 + 0 μ mgcos θ ℓ = 3 mg / sin θ μ = 3 tan θ = ktan θ k = 3

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