I was just wondering why what I've done in a spec rel question is wrong.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

A particle of massmis travelling at 0.8c with respect to the lab frame towards an identical particle that is stationary with respect to the lab frame. If the particles undergo an inelastic collision and coalesce, what is the fractional change in the system's kinetic energy as measured from the lab frame?

http://img85.imageshack.us/img85/6922/croppercapture1io7.png [Broken]

2. Relevant equations

[tex]p=\gamma m v[/tex]

[tex]E^2 = (mc^2)^2 + (pc)^2[/tex]

3. The attempt at a solution

http://img183.imageshack.us/img183/6559/croppercapture3vr8.png [Broken]

My lecturer marked the first line here as being wrong; he said that for the momentum term in the denominator I should have put 2mrather than justm. However, my thinking here was that since the momentum of a system is conserved within any given frame, the momentum prior to the collision should be the same as following the collision, which is why I used [tex]\gamma m v c[/tex] rather than [tex]\gamma m_1 v_1 c[/tex]. This makes things vastly simpler as we know the velocity of the moving particle prior to the collision, but we don't know the velocity of two particles after the collision.

Has my lecturer just misunderstood what I was doing, or am I doing something wrong?

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# Homework Help: [Special Relativity] Energy-momentum invariant question

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