A library is using a new ladder to reach books above 6 feet. The normal force on the walls cannot exceed 200 lb or ladder will damage the wall or books. What is the maximum allowable weight, W, on the ladder. (The wall is friction-less and the friction on the floor is large enough to not let the ladder slip.)

Like most static problems, the first step in solving any problem is to construct a free-body diagram. From the free body diagram at the left, there are three unknown forces, W, A_x and A_y. The wall reaction is known since the maximum wall force is 200 lb. The unknown forces can be found by applying the force and moment equilibrium equations,

     ΣF = 0
     ΣM = 0

W can be found by writing the moment equation about the pivot point, A. In this case the moment due to the reaction force of 200 lb must cancel out the moment of W about point A.

Before the moment can be solved, the distance D needs to be found.

The moment equation will give

     ΣM_A = 0
     200 (6) - W (3.464) = 0
     W = 346.4 lb

Is the length of the upper arm important in the design calculations? How?