From: edprochak@gmail.com   
      
   On Thursday, April 5, 2018 at 3:20:11 AM UTC-4, John Heath wrote:   
   > On Tuesday, April 3, 2018 at 8:05:29 AM UTC-4, Gary Harnagel wrote:   
   > > On Tuesday, April 3, 2018 at 4:50:28 AM UTC-6, John Heath wrote:   
   > > >   
   > > > Now that we are back on subject I would enjoy hearing thoughts on   
   > > > this. Is it momentum or the center of mass that is being conserved?   
   > >   
   > > It seems they are the same thing.  If you assume center of mass is   
   > > conserved, you can prove that momentum is conserved and vice versa.   
   >   
   > Yes I hear you. It is not absolutely momentum conservation or absolutely   
   > center of mass conservation. They both work so why draw a line between   
   > the two.   
      
   Center of mass is just a reference point because real bodies   
   are actually collections of many particles. Our means of measurements   
   begin at the macro level so we simplify the calculations using   
   center of mass. That you confuse them is troubling. It is like   
   confusing the rocket for the fuel.   
   >   
   > On another note what about one of the masses radioactively decaying   
   > losing mass but not violating the conservation of momentum as stated   
   > before. It is a tricky problem with no easy answers that I can think   
   > of. Ears open if you have a fix.   
      
   I started to prepare a long presentation about this but let   
   me just present a short description. First the problem has   
   nothing to do with the nonradioactive object. Its momentum   
   is obviously conserved.   
      
   So consider the radioactive object let us simplify it by   
   first giving it initial momentum of zero. IOW, it is sitting   
   at rest. P=mv = m*0 = 0   
      
   Now let's make the object itself even simpler. Assume it is   
   a single radioactive atom. Such cases have been studied in detail.   
   It turns out, you must apply both the conservation of momentum   
   and the conservation of energy. When you do, it has always been   
   found that both equations balance.   
      
   The atom emits a particle. The particle travels off in one direction   
   and the remaining nucleus moves opposite. The momentum balances, but   
   the total mass does not seem to balance initially. The difference   
   in the total mass turns out to balance as the source of the   
   kinetic energy comes from a small amount of mass that is converted   
   to energy  according to Einstein's famous E=mc^2   
   When the measurements and calculations for both momentum and energy   
   are completed, it has always been found that both equations balance.   
      
   If you would like a specific example, this is how the neutrino   
   particle was initially proposed. It was because certain decay   
   events did not balance. The leftover momentum and energy was   
   carried by a another particle. Later this other particle   
   was detected independently of the decay experiments aand named   
   the neutrino.  You should read about the discovery of the neutrino.   
   I cannot do the story justice here. But it is a demonstration of   
   how momentum and energy conservation laws always work out.   
      
   But again, to truly understand these two conservation laws, you   
   really should sit down and learn how to do the calculations.   
   The problems can be fascinating puzzles that are very satisfying   
   to solve.   
      
   HTH,   
     Ed   
      
   [[Mod. note -- The history of the neutrino's hypthesizing and later   
   discovery, and then of the solar neutrino problem and its resolution   
   with the realisation that (at least some) neutrinos have nonzero mass,   
   is indeed fascinating.  The Wikipedia history   
     https://en.wikipedia.org/wiki/Neutrino#History   
   looks like a decent starting point.   
   -- jt]]   
      
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