Calculate Mass at Rest After Relativistic Particle Collision

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SUMMARY

The discussion focuses on calculating the mass at rest of new particles resulting from a perfectly inelastic collision between a relativistic particle with rest mass M0 and velocity v, and another particle with rest mass M1. The solution utilizes the principles of conservation of momentum and total energy, specifically employing 4-momentum, defined as p_\mu=(E/c, \vec{p}). It is established that 4-momentum is conserved, and the invariant mass condition p^\mu p_\mu=-m^2 c^2 is crucial for determining the mass at rest after the collision.

PREREQUISITES
  • Understanding of relativistic physics concepts, particularly mass-energy equivalence.
  • Familiarity with the principles of conservation of momentum and energy.
  • Knowledge of 4-momentum and its application in particle physics.
  • Basic grasp of invariant mass calculations in relativistic contexts.
NEXT STEPS
  • Study the derivation and applications of 4-momentum in particle collisions.
  • Learn about invariant mass calculations in relativistic systems.
  • Explore conservation laws in relativistic mechanics, focusing on energy and momentum.
  • Investigate perfectly inelastic collisions and their implications in particle physics.
USEFUL FOR

Physics students, particle physicists, and anyone interested in understanding relativistic collisions and their outcomes.

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Homework Statement



A relativistic particle with mass at rest M0 and velocity v hits another particle with mass at rest M1. the collision is perfectly inelastic. How can I calculate the mass at rest of the new particles after the collision?



Homework Equations





The Attempt at a Solution

 
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Conservation of momentum and total energy.
 
Easiest way to do this is using 4-momentum, p_\mu=(\frac{E}{c},\vec{p}). Note that 4-momentum is conserved and p^\mu p_\mu=-m^2 c^2 is invariant.
 
Last edited:

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