Answer
See answers.
Work Step by Step
a. Kinetic energy is 5.00 times greater than the rest energy. Use equation 26–5b to find the speed.
$$KE=(\gamma-1)mc^2=5.00mc^2$$
$$\frac{1}{\sqrt{1-v^2/c^2}}=6.00$$
$$v=c\sqrt{1-\frac{1}{(6.00)^2}}=0.986c$$
b. Kinetic energy is 999 times greater than the rest energy. Use equation 26–5b to find the speed.
$$KE=(\gamma-1)mc^2=999mc^2$$
$$\frac{1}{\sqrt{1-v^2/c^2}}=1000$$
$$v=c\sqrt{1-\frac{1}{(1000)^2}}$$
Use the binomial theorem.
$$v\approx c(1-\frac{1}{2}(\frac{1}{1000})^2)=c(1-5.0\times10^{-7}) $$
