A ladder of length l and mass ms leans on a frictionless wall. The lower end of the ladder stands on a horizontal surface where the coefficient of friction is μ
The ladder forms the angle α with the ground, and the center of mass of the ladder lies in the middle on the ladder. Show that a person of mass mp can stand anywhere on the ladder when μ = (mp + ms/2) / (mp + ms) * 1 / tan α.