Disappear into the pockets with one shot. I am assuming that the main reason why all balls do not get pocketed is due to loss of energy due to friction and there is not enough momentum transferred till the last ball is pocketed.
Therefore there must be a maximum force required to be applied so that all balls receive enough energy to remain in motion until it gets pocketed by a series of ricochets etc etc.
Can mathematics give a good answr to what is it that is required to do this almost impossible task.
Lets forget any rules that require balls to go in pocket in a particular sequence, for this thought experiment.
It’s not clear what you’re asking here, so I’ll answer as much as I can.
Formulas don’t make anything do anything. It is possible to pocket all of the balls with the break, as evidenced by the fact that it’s been done. There are formulas that describe the movements and interactions of the balls, but these formulas necessarily contain terms which must be determined empirically by observing actual ball interactions (possibly including the ones where they’re all pocketed). Actually performing the calculations can be very difficult, with so many balls involved, and if you also require performing the calculation for every possible set of initial conditions (to determine which all-sink break requires the least energy), then the problem is going to be, in practice, completely unsolvable.
I think the OP was asking “How hard do you have to hit the cue ball so all the balls have enough energy that the odds of them not eventually sinking just due to random motion are infinitesimally small?” To which the answer probably his “Hard enough that it would shatter into a cloud of dust.”
It sounds like the question is asking whether balls with infinite motion would eventually fall into the pockets. The answer to that is no.
There are paths on a pool table in which infinite movement will not eventually put the ball into a pocket. As an example of that, a ball moving exactly perpendicular to an edge of the table would never enter a pocket, no matter how long it continues moving. It will ricochet along the same back and forth path until friction slows it down.
Also, such a mathematical formula would depend on perfectly spherical pool-balls, a perfectly flat felt table with a perfectly consistent coefficient of friction, no eddies or air-currents, no vibrations through the floor, etc.
Otherwise, you wouldn’t have a “formula” so much as a supercomputer simulation, like a Cray modeling the temperatures inside a hurricane.
is a rational number. But there are a lot more irrational numbers than rational numbers; so if you were to put a pool ball down in a random spot on the table and give it a velocity in a random direction, it will (in the fullness of time) get arbitrarily close to any spot on the table. In particular, if the pockets are regions of the table with finite size, it will eventually enter one of them.
Along these lines, we were shown a movie in junior high science class where they explained the workings of the dots along the side of a pool table and how you could line up shots by simple math involving the numbers of the dots closest to the target and cue balls. My google fu has failed me every time in rediscovering this knowledge. If anyone knows how that works I’d be grateful to hear it.
How many degrees of freedom does a cue stroke have? I count five:
Orientation of cue stick and cue travel direction: horizontal angle, vertical angle.
Point of contact with cue ball: 2 parameters.
Cue momentum: 1 parameter.
This assumes that the cue stick velocity is in the same direction as the cue length, and that any acceleration is irrelevant. (If the acceleration affected the cue ball, wouldn’t it be an illegal double cueing?)
It also ignores shape of cue tip and amount of chalk, but I assume these are fixed and set to maximum chalk respectively. And I’ve combined cue stick speed and mass into a single momentum parameter. Is that OK?
But I’m not a real billiards player. What is the correct answer? How many parameters does it take to model a billiards stroke?
I wonder about that video. You can’t seem much of the player or the others around the table, but I’d expect someone who did that would be jumping up and down in excitement.
Yeah, it’s either a shot set-up in some way or something else is funky going on about it.
Apparently, the record according to this guy, is 8 balls on the break in both 9 ball and 8 ball. ETA: And here’s his story of the 9 ball record he set in 1961. He claims it’s never been tied (as of 2013, at least) and claims it will never be broken, only tied. I’m not sure why he says it can never be broken.
The answer to that question is actually yes. It fact, at most angles, it doesn’t take a lot of bounces for a pool ball to find a pocket, even without infinite motion. On a typical table under normal conditions, it’s difficult to make contact with the cushions more than 6 or 7 times, no matter how hard you hit the ball, but if friction was reduced even by just half, I think most shots (at least, those that are more than a few degrees away from being perpendicular) would probably sink in fewer than a dozen rebounds.
With ZERO friction/infinite motion, the chance that one of the balls would fall into a pattern of bouncing exactly perpendicular to two opposing rails is extremely low. Slight imperfections in the cloth, rubber cushions, and the balls themselves would make that pretty much impossible, even if the ball had initially been hit perfectly straight by some kind of specially calibrated machine.
