Two particles collide, COM frame, relativistic velocities.

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SUMMARY

The discussion focuses on a two-body collision in the center of mass (COM) frame, specifically analyzing the relativistic velocities of particles during the collision process. The equation derived, dE/dPf = Vc + Vd, demonstrates that energy change with respect to momentum is consistent in both Newtonian and relativistic frameworks. Participants emphasize replacing Newtonian equations with their relativistic counterparts to validate the results. The conversation highlights the importance of understanding relativistic momentum and energy conservation in particle collisions.

PREREQUISITES
  • Understanding of relativistic momentum and energy equations
  • Familiarity with the center of mass frame in physics
  • Knowledge of basic collision theory in particle physics
  • Proficiency in algebraic manipulation of equations
NEXT STEPS
  • Study the derivation of relativistic momentum equations
  • Learn about energy conservation in relativistic collisions
  • Explore the implications of the Lorentz transformation on particle velocities
  • Investigate the differences between Newtonian and relativistic collision outcomes
USEFUL FOR

Physics students, educators, and researchers interested in particle dynamics, particularly in the context of relativistic physics and collision analysis.

EdgyWaters
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Homework Statement


2-body, COM frame collision
a+b ---> c+d
E = Ea+Eb = Ec+Ed
Show that
dE/dPf = Vc+Vd
Show that the answer is the same when the velocities are relativistic
I don''t know how to work out the relativistic aspect of the question.

Homework Equations

The Attempt at a Solution


E = Pc^2/2Mc - Pd^2/2Md
(Pf^2)/2(I/Mc + I/Md) = (Pf^2)/2(Md+Mc/McMd)
dE/dPf = Pf(1/Mc+I/Md) = Vc + Vd
 
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What is Pf?
How can E depend on anything if it is fully determined by the initial (or final) state?

If you can solve it in the Newtonian case, replace all Newtonian equations with their relativistic versions, and see if it still works.
 

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