Finding speed of particle after collision

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SUMMARY

The discussion focuses on a special relativity problem involving the collision of an object with energy E and momentum p with a mass m at rest. The key conclusion is that the speed of the composite body formed after the collision is given by the formula v = p/(m + E/c²). Participants suggest using conservation of momentum and energy principles to derive this result, emphasizing the importance of these concepts in solving relativistic collision problems.

PREREQUISITES
  • Understanding of special relativity principles
  • Familiarity with momentum and energy conservation laws
  • Knowledge of mass-energy equivalence (E=mc²)
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation of relativistic momentum and energy equations
  • Learn about the mass-energy invariant in special relativity
  • Explore examples of relativistic collisions in physics
  • Investigate applications of conservation laws in particle physics
USEFUL FOR

Physics students, educators, and anyone interested in understanding relativistic collisions and the application of conservation laws in special relativity.

StaryNight
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I'm having problem with the following special relativity question:

An object with energy E and momentum p collides with a mass m at rest and coalesces with it to form a single body without loss of energy. Show that the speed of the composite body is p/(m+E/c^2).

I've tried using the mass-energy invariant but can't seem to derive the above. Any help would be much appreciated.
 
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Have you tried momentum and energy conservation?
 

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