Problem source

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Two thin horizontal bars are parallel and fixed at a distance $d$
apart, and the plane containing them is at an angle $\alpha$ to the
horizontal. A thin uniform rod rests in equilibrium in contact with
the bars under one and above the other and perpendicular to both.
The diagram shows the bards (in cross section and exaggerated in size)
with the rod over one bar at $Y$ and under the other at $Z$. (Thus
$YZ$ has length $d$.) The centre of the rod is at $X$ and $XZ$
has length $l.$ The coefficient of friction between the rod and each
bar is $\mu.$ Explain why we must have $l\leqslant d.$ 

Find, in terms of $d,l$ and $\alpha,$ the least possible value of
$\mu.$ Verify that, when $l=2d,$ your result shows that 
\[
\mu\geqslant\tfrac{1}{3}\tan\alpha.
\]