A block starts from B on an incline. Section BC is smooth and CA is rough. The block comes to rest exactly at A. If BC = 2AC and μ = k tanθ, find k.

Question

G1 Physics · Accepted Answer

Let AC = x, so total vertical fall corresponds to 3x along the incline. Loss of gravitational potential energy is mg(3x sinθ). Friction acts only over AC: friction work = μmg cosθ·x. Equating gives μ = 3tanθ, so k = 3.