(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The positive pion decays into a muon and a neutrino. The pion has rest mass m=140 MeV/c^2, the muon has m=106 MeV/c^2 while the neutrino is about m=0 (assume it is). Assuming the original pion was at rest, use conservation of energy and momentum to show that the speed of the muon is given by

U/c = [(m_{[tex]\pi[/tex]}/m_{[tex]\mu[/tex]})^{2}- 1] / [(m_{[tex]\pi[/tex]}/m_{[tex]\mu[/tex]})^{2}+ 1]

2. Relevant equations

For massless particles, E=pc u=c [tex]\beta[/tex]=1

p=[tex]\gamma[/tex]mu E=[tex]\gamma[/tex]mc^{2}

3. The attempt at a solution(Note [tex]\gamma[/tex] and u are for mu, since it's the only particle using them)

Alright, I know that P_{[tex]\pi[/tex]}=0 and P_{[tex]\mu[/tex]}+P_{[tex]\nu[/tex]}=0. I found that P_{[tex]\nu[/tex]}=-[tex]\gamma[/tex]m_{[tex]\mu[/tex]}u_{[tex]\mu[/tex]}

I replace p in m_{[tex]\pi[/tex]}c^{2}=P_{[tex]\nu[/tex]}c + [tex]\gamma[/tex]m_{[tex]\mu[/tex]}c^{2}and reduced it down and got

m_{[tex]\pi[/tex]}c=[tex]\gamma[/tex]m_{[tex]\mu[/tex]}(c-u)

I then unraveled the gamma, moved some stuff around, and squared both sides and got (m_{[tex]\pi[/tex]}/m_{[tex]\mu[/tex]})^{2}=(c-v)^{2}/(1-v^{2}/c^{2})

I don't know if this is the right path, but I have tried many different methods from this point and nothing seems to get any closer to what I need. Thanks for any help.

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# Homework Help: Massless Particles and the algebra involved

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