Typically, a ladder stands on a horizontal surface (the floor) and leans against a vertical surface (the wall). Suppose a ladder of length l = 3.04m, with mass m1 = 13.3kg, rests against a smooth wall at an angle of ! = 24.8! (between the wall and the ladder). Assume the mass of the ladder is uniformly distributed. A student, who has a mass of m2 = 62.0kg, stands on the ladder. The student is standing on a rung that is r = 1.43m along the ladder, measured from where the ladder touches the ground.
(a) What friction force must act on the bottom of the ladder to keep it from slipping? Neglect the (small) friction force between the smooth wall and the ladder.
(b) Suppose the coefficient of static friction between the ladder and the floor is 0.31. Will the ladder slip?