Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 36 - Relativity - Exercises and Problems - Page 1099: 38

Answer

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Work Step by Step

We know that the relativistic kinetic energy is given by $$K=(\gamma_p-1 )mc^2$$ where $v=0.8c$ is the speed of the particle, and $\gamma_p=\left[1-\frac{v^2}{c^2}\right]^{-1/2}=\left[1-\frac{0.8^2\color{red}{\bf\not}c^2}{\color{red}{\bf\not}c^2}\right]^{-1/2}=\bf \frac{5}{3}$ Thus, $$K=\left( \dfrac{5}{3}-1 \right)mc^2= \frac{2}{3} mc^2$$ Plug the known; $$K= \frac{2}{3} (1\times 10^{-3})(3\times 10^8)^2 $$ $$K= \color{red}{\bf 6.0\times 10^{13}}\;\rm J$$ Recalling that the rest energy is given by $$E_0=mc^2=(1\times 10^{-3})(3\times 10^8)^2$$ $$E_0= \color{red}{\bf 9.0\times 10^{13}}\;\rm J$$ The total energy is given by $$E=\gamma_pmc^2=E_0+K$$ Plug from above; $$E= (9.0\times 10^{13})+(6.0\times 10^{13})$$ $$E= \color{red}{\bf 1.5\times 10^{14}}\;\rm J$$
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