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Ball A is moving with velocity of v, it collides elastically with five stationary balls. All six balls are of equal mass. What happens next?

SOLUTION

I want to find out how many balls move off from those that were stationary and with what velocity they move away.

I apply the elastic collision equation ①, conservation of momentum ② and conservation of kinetic energy ③. After substituting into equation ② from ① and deriving an equation for the outgoing mass (m_{B}) I then think about what possible outcomes there could be. This leads me to the conclusion that m_{B}= m is the only valid solution. Then I feed that solution back into equation ② to give me v_{B}= v.

Please see attached PDF.

I don't actually use equation ③ directly so it is superfluous, though equation ① is derived from it.My main concern is the use of equation ① in the absence of knowing exactly how much mass moves out of the problem - is my use of it correct?If my solution is not valid is there a way of using cons. of momentum and KE to solve this problem?*

Any insight gratefully received.

* I did try thinking about the problem with m_{A}margining into the masses and having an unknown m_{C}and m_{D}moving away either left and right or right or stationary and right and using m_{A}+ m_{B}= m_{C}+ m_{D}, but even with that I couldn't derive enough equations to eliminate unknowns.

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# B Is my solution to this question about a collision valid?

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