Statics 11/12/2019

Since the system is in equilibrium. the normal reaction $N$ from the ramp, the resultant reaction $R$ from the ground and the weight $W$ of the rod must have lines of action that are concurrent (at the point $D$ ).

The rest of the question is geometry/trigonometry. Applying the Sine Rule to triangle $ABF$ tells us that $\sin x^\circ = \tfrac13$ , and hence that $\cos x^\circ = \tfrac23\sqrt{2}$ . Then $DC = CB = AE = \tfrac32\cos x^\circ = \sqrt{2}$ , while $CE = 1$ . Thus the coefficient of friction $\mu$ must satisfy $\mu \ge \tan y^\circ \; = \; \frac{AE}{DE} \; =\; \frac{\sqrt{2}}{\sqrt{2}+1} \; = \; \boxed{2-\sqrt{2}}$