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I have a sum as follows.

Two small balls of equal mass can move inside a rough endless horizontal tube of length $l$. One ball impinges with velocity $u$ on the other at rest. If the friction of the tube produces a retardation $f$ in either ball, and if after impact the balls just meet up again, prove that $2lf=(u^{2})e$ where $e$ is the co-efficient of restitution.

My problem is how can there be another collision immediately afterwards? In the sum it says if

after impact the balls just meet up again

how can the balls meet again? Have I misunderstood the sum? Any explanation will be appreciated.

harsh
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  • I think this question is better off in the physics stack exchange. – Ron Gordon Jan 24 '13 at 16:11
  • Also, the title is rather vague: most questions posted at math.se are a "problem in math question."! And ironically, this is more a "problem in physics question." – amWhy Jan 24 '13 at 16:13
  • No actually @rlgordonma and @ amWhhy this a Math question.. I want to know if it is possible to have an immediate collision since normally when a collision like the first happens, the velocity of the mass which moves to the same direction which had a zero velocity early would have a higher velocity than the other. Thanks in advance. – harsh Jan 24 '13 at 16:18
  • @harsh: even if that were true, have you thought about the units involved? Is $f$ the mass of the balls? If so, then the LHS has units of (mass)(length), while the RHS has units of (length^2)/(time^2) time whatever the units are of this coefficient (which, in my encounters with such parameters, are typically dimensionless). – Ron Gordon Jan 24 '13 at 16:21
  • Is this the original question, or have you translated it? – Chris Eagle Jan 24 '13 at 16:28
  • @rlgordonma no the f is retardation..so the units are fine in both sides.. @ Chris Eagle I have not modified, this is the original question. – harsh Jan 24 '13 at 16:43
  • Should this say "two small balls of equal mass"? – Trevor Wilson Jan 24 '13 at 17:08
  • I'm not clear on the shape of the tube. Is it cylindrical with width $l$? – Trevor Wilson Jan 24 '13 at 17:09
  • yes @TrevorWilson someone had edited it the other way.sorry. I understood it is of length l. – harsh Jan 24 '13 at 17:33
  • To make this a math question I think you would need to define restitution and retardation for us. I tend to agree with other commentators that this would get a better response at Physics.SE – Trevor Wilson Jan 24 '13 at 17:35
  • "after impact the balls just meet up again" does not mean that the balls meet again "just after the impact". It means that the second time they meet, they just meet, i.e., collision happens at the moment when their relative velocity drops to zero. –  Jan 24 '13 at 17:35
  • @harsh This is a nice question. Mechanics is very much within the sphere of mathematics, so don't let people get you down. (In fact, all three of the Cambridge STEP papers have a mechanics section on them.) Could you supply a link to the question, because some things are unclear. Is your $f$ the coefficient of static friction ($f=\mu$?) or the static frictional force ($f \le \mu R$?). – Fly by Night Jan 24 '13 at 18:00
  • @FlybyNight Thanks. :) This is all given for the problem. No other data was given. I took this from a book, not from a site. – harsh Jan 25 '13 at 11:39

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