inevitable collisions

If two perfectly elastic balls were placed inside of a large sphere and given initial velocities which caused them to strike eachother, then would they necessarily or not necessarily make contact with eachother again during their infinite travels around the inside of the sphere? assume no friction

 

Log in or Sign up to hide all adverts.

The two bodies, after the impact, could get into a repetitive orbital rythm wich excludes any contact in the future, couldn't they?

 

Log in or Sign up to hide all adverts.

The gravity of the balls would allow them to orbit, depending upon the speed of impact and size of balls.

 

Log in or Sign up to hide all adverts.

I would think that the momentum of each of the balls and the angle of initial contact would effect their collision/non collision outcome.

 

well, you have an attraction point at the center of the sphere, given that the wals of the sphere *always* point towards the center.

would it be possible to forma a sustained reflection pattern of one ball such that it never passes through the center of the sphere? If so, then I would say yes, it's possible. if not, then I would say most likely not.

If the balls first collide in the center of the sphere, then they will always bouce back to the center, and re-hit. We are, of course, assume 0 friction, so the spin of the balls will have no effect on the direction that the balls bounce.

If the two balls first hit off to one side of the sphere, there is a much better chance that they could end up following each other- this woul be the best method to avoid collision, have one ball trace the path of the other, at about the same speed. This would be difficult to acheive, however, as the balls are connecting with each other first. the initial angles and velocities would have to be tightly controlled. And this would still only work in certain cases, and is wholy dependant on if a pattern could be set up to avoid the center of the shpere.

Aslo, the diameter of the two balls in relation to the diameter of the sphere itself would make a huge difference. a 1 meter diameter sphere w/ 2 .45 meter diameter balls would most certainly touch after ever bounce. 2 .00000005m balls int he same sphere would very possibly not.

 

I had in mind the balls traveling upon the inside surface of the sphere, where with enough velocity for each, the centrifugal force would adhere them to that surface throughout their infinite traves (assuming no friction)

 

cant the balls be deflected at an angle to eachother, and not necessarily opposite? we can also assume they have different masses and therefore different velocities after impact; how would this affect things.

 

do you mean opposite directions or different directions? obviously when a cue ball strikes another ball at an angle they do not necessarily travel in opposite directionsl couldnt the deflected angle be any angle less than 180?

 

I believe I have solved my problem. Assume that instead of elastic balls, they were two points assuming the trajectory of the impacted balls; their trajectories would intersect at two locations along their respective paths. the points would collide if the relative velocities of of the points were a rational-number multiple of eachother; but would not if their respective velocities were not. I berlieve this is the answer.

 

Are you familiar with the game POOL? I think the answer could lie in that game. Its all about math.