Question

A uniform ladder of length (L) and weight 100 N rests against a smooth vertical wall. The coefficient of static friction between the bottom of the ladder and the floor is 0.5. Find the minimum angle theta , which the ladder can make with the floor so the ladder will not slip.

Answer 1

Set the moment about the wall contact point be zero. Since the wall is smooth, the vertical force floor component at the floor equals the weight, W = 100 N.

W*(L/2)costheta + mus*W*L*sintheta = W*L*costheta

(1/2)costheta = mus*sintheta
tantheta = 1/(2*mus)