A ladder leans against a smooth wall, as shown in Fig. 5-11. (By a “smooth” wall, we mean that the wall exerts on the ladder only a force that is perpendicular to the wall. There is no friction force.) The ladder weighs 200 N and its center of gravity is 0.40L from the base, where L is the ladder’s length. (a) How large a friction force must exist at the base of the ladder if it is not to slip? (b) What is the necessary coefficient of static friction?