Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 26 - The Special Theory of Relativity - Problems - Page 768: 43

Answer

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Work Step by Step

The initial energy is supplied by the 2 incoming particles. Equation 26–6b tells us the initial energies. Let M be the mass of the final particle; the final energy is the rest energy of this particle since there is no KE. $$2\gamma mc^2=Mc^2$$ $$M=2\gamma m=\frac{2m}{\sqrt{1-v^2/c^2}}$$ Energy is conserved. There was no loss of energy in the collision (though the KE was transformed into mass). There is no final kinetic energy. All of the kinetic energy was lost. $$KE_{lost}=KE_{initial}=2(\gamma-1)mc^2=(\frac{1}{\sqrt{1-v^2/c^2}}-1)2mc^2$$
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