Chapter 7, Problem 7.147QP

According to Einstein’s special theory of relativity, the mass of a moving particle, m_moving, is related to its mass at rest, m_rest, by the equation

$m_{\text{moving}}=\frac{m_{\text{rest}}}{\sqrt{1-{\left(\frac{u}{c}\right)}^2}}$

where u and c are the speeds of the particle and light, respectively. (a) In particle accelerators, protons, electrons, and other charged particles are often accelerated to speeds close to the speed of light. Calculate the wavelength (in nm) of a proton moving at 50.0 percent the speed of light. The mass of a proton is 1.673 × 10⁻²⁷ kg. (b) Calculate the mass of a 6.0 × 10⁻² kg tennis ball moving at 63 m/s. Comment on your results.