Small Conceptual Relativistic Energy Question

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SUMMARY

The discussion centers on the relativistic energy of two masses, each of mass m, moving in opposite directions at speed v, as observed from a frame moving west at speed u. The key conclusion is that the total energy is greater in the moving frame compared to the rest frame. This is due to the relativistic velocity addition, which results in a smaller relative velocity between the two masses in the moving frame, thus affecting the total energy calculation. The participant confirms that the total energy is indeed larger in the frame moving with speed u.

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  • Understanding of special relativity concepts, particularly relativistic energy.
  • Familiarity with velocity addition formulas in special relativity.
  • Basic knowledge of kinetic energy and its relativistic formulation.
  • Ability to manipulate equations involving Lorentz transformations.
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  • Study the derivation of the relativistic energy formula E = γmc².
  • Learn about Lorentz transformations and their implications on energy and momentum.
  • Explore examples of relativistic velocity addition in different reference frames.
  • Investigate the implications of relativistic effects on particle collisions.
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Hi, I have an assignment due in the morning, and it is complete, there is just one tiny thing I am unsure of: In a rest frame, a mass m moves west at speed v, and another mass also m moves east at speed v. Now consider the setup as viewed by an observer going west at speed u.

I had to find the total energy in each of these frames, and I did, and now I have to say in which frame the total energy is bigger...that's the problem, the equations are not simple and I can't tell by looking at them!
Conceptually I would probably assume it is bigger in the rest frame, because the relative velocity of the two masses in the rest frame is 2v, and I think this relative velocity is smaller in the moving frame, because that's how velocity addition works, or at least in this case, where they are moving in the same direction with respect to u. But someone else told me it is bigger in the moving frame.

Who is right?
 
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Never mind, it appears it is bigger in the moving frame.
 

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