Halliday, Resnick & Walker — Equilibrium and Elasticity: Problem 38

38 In Fig. 12-41, a uniform plank, with a length $L$ of 10.5 m and a weight of 445 N, rests on the ground and against a frictionless roller at the top of a wall of height $h = 3.05$ m. The plank remains in equilibrium for any value of $\theta \ge 70^\circ$ but slips if $\theta < 70^\circ$. Find the coefficient of static friction between the plank and the ground.