A uniform rope is placed over a triangular wedge whose base angle is 37°. The maximum hanging length in one limiting equilibrium configuration is x₁ and the minimum hanging length in the other is x₂. If x₁/x₂ = 3, find the coefficient of friction between rope and wedge.

Question

G1 Physics · Accepted Answer

Write limiting equilibrium for the two opposite impending motions of the rope. Friction reverses direction in the two cases. Using sin37° = 3/5, cos37° = 4/5 and x₁/x₂ = 3, the two equations give μ = 1/2.