How Does Special Relativity Affect the Mass of Colliding Particles?

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SUMMARY

The discussion focuses on calculating the mass of a resulting particle after two identical masses, initially at rest, collide under the influence of a constant force F. The relevant equations include the force equation F = gamma^3mv and the energy-momentum relation E^2 = p^2c^2 + (2m)^2c^2. Participants emphasize the importance of conservation of energy and momentum in solving the problem, particularly in determining the energy and momentum of the mass before impact. The complexity of the calculations is acknowledged, especially when applying relativistic equations.

PREREQUISITES
  • Understanding of special relativity concepts, including mass-energy equivalence.
  • Familiarity with the equations of motion in relativistic physics.
  • Knowledge of conservation laws: conservation of energy and conservation of momentum.
  • Proficiency in manipulating equations involving gamma factors in relativistic contexts.
NEXT STEPS
  • Study the derivation and application of the Lorentz factor (gamma) in relativistic physics.
  • Learn how to apply conservation of momentum in relativistic collisions.
  • Explore the implications of mass-energy equivalence in particle physics.
  • Investigate examples of relativistic collisions and their outcomes in various scenarios.
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Students of physics, particularly those studying special relativity, as well as educators and anyone interested in understanding the dynamics of colliding particles in relativistic contexts.

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Homework Statement



Two identical masses m are initially at rest, separated by a distance x. A constant force F
accelerates one particle until it collides and combines with the other. What is the mass of
the resulting particle?

Homework Equations



F = gamma3mv

The Attempt at a Solution



Presumably you must calculate conservation of energy (which is whatever the energy is of the single mass moving must equal that of them combined).

Then I guess you need to calculate conservation of momentum, which should also be easy especially since it's in one direction after all.

Lastly you could just plug it into the equation E2 = p2c2 + (2m)2c2

The thing I don't understand is what energy/momentum the mass has pre-impact. We've never done a problem with the equation I gave before so I'm not sure if it's needed, but in any case I attempted solving with that equation for F and then multiplying by t to get the momentum and got c3*m*a*t/(c2 - (at)2)3/2 which seemed way too complicated for so early. I would also just do energy of the big mass = gamma*m*c^2+mc^2 and that would give me the part for E^2 and i w ould have all necessary parts... But I don't know if my original thing is right at all :/
 
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