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Unformatted text preview: of the astronaut as measured by Earth can increase arbitrarily due to time dilation. 2a Since E = mc 2 / 1-v 2 c 2 1 / 2 , if E is to remain nite as m 0, then v must approach c . Thus, a massless particle must travel at the speed of light. E | p | = c 2 | u | | u | = c E = pc 2b K E-E K = ( -1) mc 2 = 1-u 2 c 2 -1 / 2 1 + 1 2 u 2 c 2 + K 1 + 1 2 u 2 c 2-1 mc 2 K = 1 2 mu 2 2c 1 dx = ( dx-vdt ) dt = dt-v c 2 dx u x dx dt u x dx dt u x = u x-v 1-u x v c 2 if v c this reduces to u x = u x-v 3 Use conservation of energy. The energy of the initial particle is Mc 2 . The energy of each of the 2 photons is pc From conservation of momentum, the photons must be traveling in opposite directions. Mc 2 = 2 pc p = 1 2 Mc 2...
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- Spring '10