Physics Technology Update (4th Edition)

Published by Pearson
ISBN 10: 0-32190-308-0
ISBN 13: 978-0-32190-308-2

Chapter 29 - Relativity - Conceptual Questions - Page 1040: 7

Answer

See below.

Work Step by Step

The kinetic energy of an object moving at relativistic speeds is equal to $$K=(\gamma-1)mc^2$$ where $\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$. According to the work-energy theorem, work is equal to change in kinetic energy. If one attempts to make an object go above the speed of light, the value of $\sqrt{1-\frac{v^2}{c^2}}$ will not exist, since the value underneath the radical would be negative. Therefore, there is an infinite amount of energy in an object moving above the speed of light, so an infinite, unattainable work would be needed to move the object beyond the speed of light.
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