Asked by Emilea
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.
Answers
Answered by
drwls
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)
W*(L/2)costheta + mus*W*L*sintheta = W*L*costheta
(1/2)costheta = mus*sintheta
tantheta = 1/(2*mus)