Question

A uniform 7.1 m tall aluminum ladder is leaning against a frictionless vertical wall. The ladder has a weight of 272 N. The ladder slips when it makes a 57.0degrees angle with the horizontal floor.
Determine the coefficient of static friction between the ladder and the floor.

Answer 1

The frictional torque is barely able to keep it from slipping at 57 degrees from horizontal. Set the net torque about the point of contact with the vertical wall equal to zero.

Wladder*(L/2)*cos57 = Wladder*mus*Lsin57

0.5 cot57 = mus = 0.325

"mus" is the static friction coefficient