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: 45

Answer

$p=\frac{\sqrt{ KE^2+2(KE)(mc^2)}}{c} $

Work Step by Step

Start with equations 26–6a and 26–9. $$E=KE+mc^2$$ $$(pc)^2=E^2-(mc^2)^2$$ Now combine them, substituting E from the first equation into the second equation. $$(pc)^2= (KE+mc^2)^2-(mc^2)^2$$ $$(pc)^2= KE^2+2(KE)(mc^2) $$ $$p=\frac{\sqrt{ KE^2+2(KE)(mc^2)}}{c} $$
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