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I have a physics question for you:
(modified from Young & Freedman, 11th ed., 8.88): A large nucleus
at rest decays into 2 particles the ratio of whose masses is r.
What fraction of the total kinetic energy (after the decay) does
each particle have? (This is a classical, non-relativistic
treatment.)
First, feel free to do the problem before scrolling down to see my
answer below.
I tried a couple different methods and show only the one that I
like the most!
Next, notice what this means about how the fraction of total kinetic
energy which each particle carries off depends on the fraction of
the total mass which each particle got. Interesting, I think!
Seems fundamentally significant to me.
Finally, and the reason I turn to the Forum for Physics Educators,
consider doing the same problem relativistically. I don't get the
same simple, neat answer,
in fact, I get a complicated mess.
Does this still simplify somehow?
Or is the peculiarly simple and appealing result only true in the
classical limit? Maybe a different (and still elegant) result is
always true?
I've tried total energies instead of kinetic energies, still a
mess. Besides, that wouldn't work in the classical limit anyway.
Sigh! I would appreciate any thoughts on this.
Thanks,
Ken