Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Perfectly centered break of a perfectly aligned pool ball rack

mathoverflow.net

Post reply on HN
Print view View original

51–60 of 69 posts

Re: Perfectly centered break of a perfectly aligned pool ball rack

#51

Post by eru »

zodiac wrote: post #43
Someone wrote: post #32

Earlier quoted context omitted.

Not necessarily; it might be possible to have some balls collide in such a way that at least one comes to a stop. At least one ball will keep moving though, and it isn't clear to me whether it is possible to prevent that moving ball from, eventually, hitting that stopped ball again. I think that would require at least three balls (ignoring pockets)

> it might be possible to have some balls collide in such a way that at least one comes to a stop. can you give an example?

If you just have two identical balls.

Re: Perfectly centered break of a perfectly aligned pool ball rack

#52

Post by ballstothewalls »

prakashk wrote: post #48
ballstothewalls wrote: post #31

Earlier quoted context omitted.

I think he is confused. Wolfram's site only has Mathematica 9 listed

> I think he is confused. You don't mean that the GP (taliesinb) is confused, do you?. He works for Wolfram Research, developing Mathematica.

That is what I meant, but I guess I look like the fool now. I still don't see that Mathematica 10 has been released, but I guess it is close.

Re: Perfectly centered break of a perfectly aligned pool ball rack

#53

Post by [deleted] »

zodiac wrote: post #43
Someone wrote: post #32

Earlier quoted context omitted.

Not necessarily; it might be possible to have some balls collide in such a way that at least one comes to a stop. At least one ball will keep moving though, and it isn't clear to me whether it is possible to prevent that moving ball from, eventually, hitting that stopped ball again. I think that would require at least three balls (ignoring pockets)

> it might be possible to have some balls collide in such a way that at least one comes to a stop. can you give an example?

[deleted]

Re: Perfectly centered break of a perfectly aligned pool ball rack

#54

Post by rcthompson »

waqf wrote: post #19
rcthompson wrote: post #12

Can anyone explain the "rules" for a 3-way simultaneous colision? Freshman physics only covered collisions between 2 objects, and I've never figured out how to generalize it.

Right, with 3 balls you can't just do an impulse calculation like you can with 2 (too many unknowns, too few equations). The author is simulating the collision as an event which happens gradually over an (admittedly short) period of time, using a differential equation, instead of something that happens all at once. That's why he has to talk about the elasticity model he's using, F ∝ (2-d)^1.5, and how the results var…

Hmm. How does the elasticity model provide the additional constraint needed to give an unique solution?

Re: Perfectly centered break of a perfectly aligned pool ball rack

#55

Post by roel_v »

IgorPartola wrote: post #49
IgorPartola wrote: post #24

Somewhat meta, but at what point does Stack Overflow transition from being a useful, time-saving tool and become a waste of everyone's time? The top answer author clearly put a ton of time on the answer. We are all now reading this. Is anyone able to apply any of the knowledge they gained from this Q&A to anything productive?

Going to reply to my own post since I cannot edit it anymore to clarify. First, I am not saying that this is strictly a waste of time. In fact, I do love learning from things like this. Second, I am not saying we must always be working instead of stopping to try something different. I personally find switching focus very important and I think it's a great tool for a great many people. I find that when people learn so…

"What I wanted to know is who are these experts, why are they giving their expertise away for Internet Points (tm) and is this detracting from their actual work."

While I don't know about this exact post, for most academics, such theoretical exercises are their work. 'Projects' like this are nice and small and contained. They also give you the opportunity to get 'real' questions from people who aren't as close to the material as you are, almost like 'customers', so if you use a question like this in a lecture, it's almost sure to capture the interest of students better than other textbook examples. While I don't teach many courses, I've used examples derived from hybrid 'real world' / theoretical questions as examples to explain our products.

That said, I've surely spend time on questions that will never pay themselves back in such a way. You never know up front which ones will, so it's like playing the VC game - you 'invest' in 10 questions, with the knowledge that 7 will be duds, 2 will break even and the last one will (hopefully) be a home run.

Re: Perfectly centered break of a perfectly aligned pool ball rack

#56

Post by hmsimha »

Someone wrote: post #32
hmsimha wrote: post #20

Earlier quoted context omitted.

I'm no physics expert, but I can account for the second one -- if there's no friction, the balls just keep rolling

Not necessarily; it might be possible to have some balls collide in such a way that at least one comes to a stop. At least one ball will keep moving though, and it isn't clear to me whether it is possible to prevent that moving ball from, eventually, hitting that stopped ball again. I think that would require at least three balls (ignoring pockets)

I can't see how friction is factoring into the directions the balls initially scatter, as it's not taking the rotation of the balls into account. With that being said, wouldn't the balls all go in the same initial direction as they do in the linked example? Aka, the ones that are moving would move in that direction. Theoretically they could eventually bounce off walls and collide into each other in such a way that they eventually stop (though then there's the possibility of other balls that are still moving colliding into them later).

Re: Perfectly centered break of a perfectly aligned pool ball rack

#57

Post by ctdonath »

IgorPartola wrote: post #24

Somewhat meta, but at what point does Stack Overflow transition from being a useful, time-saving tool and become a waste of everyone's time? The top answer author clearly put a ton of time on the answer. We are all now reading this. Is anyone able to apply any of the knowledge they gained from this Q&A to anything productive?

"Strange how much human progress and accomplishment comes from contemplation of the irrelevant." - Scott Kim

Re: Perfectly centered break of a perfectly aligned pool ball rack

#58

Post by kaivi »

7483263789 wrote: post #17
joosters wrote: post #14

Earlier quoted context omitted.

Yes! We demand to know whether the pool table was in the northern or southern hemisphere :)

Tut tut! You're forgetting that the earth is an oblate spheroid, and gravity exerts greater downward force at the poles, than near the equator. We also need to know the precise latitude of the pool table!

One might as well consider the gravitational gradient exerted by the surrounding terrain and significant celestial bodies, as well as the balls themselves. Should we collaborate on assembling such simulation, taking in account all known physical laws? Or has it been done already? Imagine how cool it would be to toggle different forces or constants and see the result change.

Re: Perfectly centered break of a perfectly aligned pool ball rack

#59

Post by a-priori »

Someone wrote: post #32
hmsimha wrote: post #20

Earlier quoted context omitted.

I'm no physics expert, but I can account for the second one -- if there's no friction, the balls just keep rolling

Not necessarily; it might be possible to have some balls collide in such a way that at least one comes to a stop. At least one ball will keep moving though, and it isn't clear to me whether it is possible to prevent that moving ball from, eventually, hitting that stopped ball again. I think that would require at least three balls (ignoring pockets)

This is a problem of energy conservation: the cue ball starts with E = 1/2 mv^2 kinetic energy and, no matter what, that same amount of energy has to exist afterwards in some form.

But where will it go? In an elastic collision, a negligible amount of energy gets converted to heat (through inelastic deformation), and only a small amount will be converted to sound.

The only other place the energy can go is kinetic energy distributed between the balls. This means that there's no way to cause the balls to collide such that they're stationary afterwards.

Hypothetically, you might be able to completely convert the linear motion into rotational motion and have the balls spinning on the spot afterwards... but that's about it.

Re: Perfectly centered break of a perfectly aligned pool ball rack

#60

Post by waqf »

rcthompson wrote: post #54
waqf wrote: post #19

Earlier quoted context omitted.

Right, with 3 balls you can't just do an impulse calculation like you can with 2 (too many unknowns, too few equations). The author is simulating the collision as an event which happens gradually over an (admittedly short) period of time, using a differential equation, instead of something that happens all at once. That's why he has to talk about the elasticity model he's using, F ∝ (2-d)^1.5, and how the results var…

Hmm. How does the elasticity model provide the additional constraint needed to give an unique solution?

It provides a way to apportion the impulse between the two simultaneous collisions. It behaves as a differential equation because the instantaneous force in each collision depends (via the elasticity model) on the instantaneous velocities of the balls, which in turn depend on how much momentum has already been transferred.
Post reply on HN