(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two particles of equal mass M and equal net energy E are approaching each other at an angle of 90 degrees. Find the net energy of one particle in the rest frame of the other. Do not assume that the velocities are small compared to the speed of light.

2. Relevant equations

The Lorenz transformations and relativistic energy.

3. The attempt at a solution

I don't know. I've been bashing my head against this one for hours. It looks so simple, and yet I just can't make it work. I've been reading pages about invariant mass, relativistic addition formulas, 4-vectors, and so on, but I just can't seem to conceptualize it. This is a sample qualifying problem that I'm supposed to be able to solve in twenty minutes or less, and the exam is now two weeks away. Frustration is riding very high.

My guesses thus far start from the assumption that in the frame of the particle moving along the x axis, the components of the velocity of the particle moving on the y-axis is:

[itex]\left\{-\gamma v, -v, 0\right\}[/itex]

and t' in the particle rest frame is [itex]\gamma t[/itex]

Should I be trying to figure out the relative velocities of the two particles, and using that to compute a new gamma for E = gamma m c^2? If so, how? I've tried just taking the root of sums of the squares of the components, but it doesn't look right. If this isn't the right approach, what am I missing?

Also, please tell me I'm not crazy for trying to reenter this field after 13 years away.

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# Homework Help: Energy of a particle in an orthoganally moving rest frame

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