A uniform ladder of mass (m = 14.5 kg) and length (L) leans against a frictionless wall, see figure. Find the static friction force between the ladder and the floor if the angle θ = 64.0°?

Answer 1

consider the point where the ladder meets the wall. Sum moments about that point.

mg*1/2 *L*cos64-mu*mg*L sin64=0

solve for mu. Notice the weight of the ladder mg divides out, as does length L.

Answer 2

I did that work got .197 but its wrong