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https://texercises.com/exercise/colliding-protons/
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Exercise:
A particle accelerator produces two beams of protons with beO of the speed of light and moving in opposite directions. Calculate the speed at which one proton approaches in the rest frame of the other proton.

Solution:
The velocity of the first proton relative to the lab frame is v_p while that of the second proton is -v_p. The lab frame O' is thus moving with -v_p relative to the rest frame of the first proton O. With the conventional symbols in the formula for the addition of relativistic velocities we have v -v_p u' -v_p Relative to the first proton the second proton moves with u fracv+u'+fracvu'c^ frac-v_p-v_p+fracv_p^c^ uF -fractimes be c+be^ resultuP
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Exercise:
A particle accelerator produces two beams of protons with beO of the speed of light and moving in opposite directions. Calculate the speed at which one proton approaches in the rest frame of the other proton.

Solution:
The velocity of the first proton relative to the lab frame is v_p while that of the second proton is -v_p. The lab frame O' is thus moving with -v_p relative to the rest frame of the first proton O. With the conventional symbols in the formula for the addition of relativistic velocities we have v -v_p u' -v_p Relative to the first proton the second proton moves with u fracv+u'+fracvu'c^ frac-v_p-v_p+fracv_p^c^ uF -fractimes be c+be^ resultuP
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special relativity
Tags
proton, velocity addition
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(2, default)
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Language
ENG (English)
Type
Calculative / Quantity
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