Physics Problems & Solutions: Special Relativity

A positive kaon (K⁺) has a rest mass of 494 MeV/c² , whereas a proton has a rest mass of 938 MeV/c². If a kaon has a total energy that is equal to the proton rest energy, the speed of the kaon is most nearly

A. 0.25c
B. 0.40c
C. 0.55c
D. 0.70c
E. 0.85c

(GR8677 #20)

Solution:

$\begin{aligned}E_{k(\text{relativistic})}&=E_{p(\text{rest})} \\\gamma m_{0k}c^2&=m_{0p}c^2 \\\gamma&=\frac{m_{0p}}{ m_{0k}}=\frac{938}{494}\approx2 \end{aligned}$

$\begin{aligned} \gamma&=\frac{1}{\sqrt{1-\beta^2}}=2, \hspace{10 mm}(\beta=v/c) \\1&=4\left(1-\beta^2\right) \\4\beta^2&=4-1 \\\beta^2&=\frac{3}{4} \\\beta&=\frac{\sqrt{3}}{2}=0.5\times1.7=0.85 \\v&=0.85c \end{aligned}$

Answer: E

Physics Problems & Solutions

Special Relativity - Speed of Kaon

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