A ladder 10-m long and weighing 50 N rests against a smooth vertical wall. If the ladder is just on the verge of slipping when it makes a 50 degree angle with the ground, find the coefficient of static friction between the ladder and the ground.

Answer 1

The upper wall exerts only a normal force on the ladder -- no friction force. The normal force there (F1) is such that
F1*L sin 50 = W*L/2* cos 50
F1 = (1/2)*W tan 50 = 0.596 W
The normal force at the base equals the weight W, since the other contact point is smooth and frictionless. If it is just about to slip, the maximum static friction force at the base (Ff,max) equals the normal force at the top, which I called F1.

Ff,max = mus*W = F1 = W/2 tan 50

mus = F1/W = (1/2) tan 50 = 0.596
is the static friction coefficient

Answer 2

I want the work to be shown