What is the total kinetic energy of two protons in different reference frames?

AI Thread Summary
The discussion focuses on calculating the total kinetic energy of two protons moving at 0.5c in different reference frames. In frame S', the calculated kinetic energy is 290 MeV, but the initial attempt yielded 270 MeV using the classical formula 1/2 mv^2, which is incorrect for relativistic speeds. Participants emphasize the necessity of using the relativistic kinetic energy formula instead. The conversation highlights the confusion surrounding the application of classical mechanics in relativistic contexts. Accurate calculations require understanding relativistic effects on mass and energy.
PsychonautQQ
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Homework Statement


In the reference frame S', two protons, each moving at .5c, approach each other head on. Calculate the total kinetic energy of the two protons in frame S', and calculate the total kinetic energy of the two protons as seen in reference frame S which is moving with one of the protons.






The Attempt at a Solution


So for the first part apparently the answer I'm looking for is 290MeV

v = .5c so γ = 1.1547

using 1/2 mv^2
m = 1.6726E-27
v = .5(3E8)

and then multiplying this times two for two protons and 1.15 from gamma, then converting that to eV by 1J = 6.24E18 eV I get 270MeV.. back of the book says 290 MeV.. what am I doing wrong ;-(?
 
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PsychonautQQ said:
using 1/2 mv^2

You'll need to use the relativistic formula for kinetic energy.
 
However we will not provide it. lol
 
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