- #26

sophiecentaur

Science Advisor

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2020 Award

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Momentum is always conserved. That statement is always correct for any isolated system. If you want to introduce an outside influence then all bets are off - unless you include the new addition as part of the system.

Two equal masses collide, going in opposite directions (wrt an Earth frame of reference) and with the same intiial speeds. Total momentum was zero and ends up at zero. The KE, wrt the Earth frame , was two times half mvsquared and ends up as zero. The energy lost must go somewhere, of course, but net motion of the masses doesn't contribute.

You cannot introduce Potential Energy (except between the two masses) in your argument or the system is not isolated. Every interaction involves some Potential Energy (even the elastic deformation during collisions). If you hit an infinitely massive object then you cannot consider the Momentum rigorously because, somewhere along the line, you will end up dividing by infinity and be comparing one zero with another zero (very crude maths here, but I won't apologise)

Instead of trying to find loopholes, it might be better if you were to try to spot where your suggestions are flawed. They have to be!

Forget the "Mathematically" bit. Maths is only a tool for working things out and it tends to stick to the model you use (assuming it's the right model).