It is common to see a heap of conical shape formed by a large number of similar size hard spherical objects, for example, a heap of pebbles, sand etc. Suppose we want to model this system as a collection of identical hard balls, with dry friction between the balls described by coefficient $\mu_1$ and the friction between the balls and the floor described by coefficient $\mu_2$. Based on a "toy" problem with three cylinders forming a pyramid one can conjecture that there is some threshold condition for $\mu_1$ and $\mu_2$ that guarantees equilibrium for a heap. What are the conditions for a heap of identical hard spheres to be in a static equilibrium?
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