mattst88
Oct13-08, 09:32 PM
1. The problem statement, all variables and given/known data
What is the speed of a proton when its kinetic energy is equal to its rest energy?
2. Relevant equations
K = mc^2(\gamma - 1)
E_0 = mc^2
\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}
3. The attempt at a solution
K = E_0
mc^2(\gamma - 1) = mc^2
\gamma = 2
\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} = 2
0.5 = \sqrt{1 - \frac{v^2}{c^2}}
0.5^2 = 1 - \frac{v^2}{c^2}
c^2 \sqrt{1 - 0.25} = v^2
v = c \sqrt{0.75} = 0.866 c
Am I right to use relativistic energy? Have I come to the correct answer? Please advise.
What is the speed of a proton when its kinetic energy is equal to its rest energy?
2. Relevant equations
K = mc^2(\gamma - 1)
E_0 = mc^2
\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}
3. The attempt at a solution
K = E_0
mc^2(\gamma - 1) = mc^2
\gamma = 2
\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} = 2
0.5 = \sqrt{1 - \frac{v^2}{c^2}}
0.5^2 = 1 - \frac{v^2}{c^2}
c^2 \sqrt{1 - 0.25} = v^2
v = c \sqrt{0.75} = 0.866 c
Am I right to use relativistic energy? Have I come to the correct answer? Please advise.