# Why doesn't the 9th ball move in the break in the nine-ball pool game?

In the game of nine-ball pool, we break the rack like shown below:

In the break, we hit the 1st ball with the cue ball. Many people familiar with pool games say that if the rack is constructed properly (i.e. there're no gaps between adjacent balls), the 9th ball won't move a bit.

As far as I've seen, this folklore is very true. Usually, the 9th ball moves little.

The non-linearity referenced above is due to the Hertz ($\alpha x^{\frac{3}{2}}$) stress-strain relationship for solid spheres. The pool problem, unlike Newton's cradle, also has friction between the balls and the table. The soliton pulses, nevertheless, are due to the elastic deformations of the balls and pass before the balls begin to roll. Friction does play a role in permitting the change of direction of the soliton pulse at balls 4 and 5 (effectively yielding a reflection). Once the balls are moving due to their unbalanced momenta, friction will cause rolling rather than sliding.