Question

A uniform 5.0 m long ladder of mass 25 kg leans against a frictionless wall at an angle of 62 degrees with the floor. Determine the minimum coefficient of static friction needed on the floor for the ladder not to slide.

Answer 1

$$N_F=mg, N_W=F_{friction}=\mu N_F=\mu mg$$

$$N_wL\sin{\phi}=mg(0.5L)\cos{\phi}$$

So,

$$\mu mgL\sin{\phi}=mg(0.5L)\cos{\phi}$$

$$\tan{\phi}=\frac{1}{2\mu}$$

$$\tan{62}=\frac{1}{2\mu}$$

$$\mu=0.27$$