Question

a uniform ladder weighing 330N is leaning against a wall. the ladder slips when the angle with the floor 50degrees. assuming the coefficient of static friction at the wall and the floor are the same,obtain a value of coefficient of static friction.

Answer 1

The normal force F1 is:
F1 * L * sin 50 = W * L/2 * cos 50
F1 = (1/2) * W
* cot(50) = 0.4195 * 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 = mu * W = F1 = W/2
cot(50)
mu = F1 / W = (1/2) cot(50) = 0.4195