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Take a line which goes through the centroid and is far from being an area bisector. You can deform C infinitesimally so that the intersection of L with the boundary is now a vertex. Now the line connecting the new vertex with the centroid is still far from being an area bisector.
"Of the models listed here, I think the initial, linear model is probably the most accurate." Hertz's theory of non-adhesive elastic contact (en.wikipedia.org/wiki/Contact_mechanics) gives $F\sim(2-d)^{3/2}$.
@GlenTheUdderboat: the "reasonable" solution is the one I gave, since the impact on the top rack ball is divided between the next two as given by the cosine, but the impact on those balls cannot be balanced by the inside balls, only by the next ball down along the edge.
At the moment of impact, force balance would imply that the forces propagate only along the sides of the triangle. Therefore, after the impact the corner balls and the cue ball would be moving. Solving for energy and momentum conservation we get that the cue ball moves back at 1/5 its original speed and the corner balls move at $2\sqrt{3}/5$ that speed.
Isn't it the case that a generic 3-line arrangement can be extended to a simplicial arrangement by adding at each intersection of two lines the parallel to the third line?
@YuriBakhtin: I mean that I have a probability measure $\mu$ on the space of point configurations $(x_1, x_2, \ldots)$, and the measure is invariant under the operation $\pi_{ij}: (x_1, x_2, \ldots x_i, \ldots x_j, \ldots) \mapsto (x_1, x_2, \ldots x_j, \ldots x_i, \ldots)$. That is, if $A$ is a measurable set of configurations, then $\mu(A) = \mu(\pi_{ij}(A))$.
