Relativistic speed of a particle

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SUMMARY

The discussion centers on calculating the speed of a particle whose total energy is twice its rest energy using relativistic physics principles. The equation E² = p²c² + m²c⁴ is utilized, leading to the conclusion that the particle's speed v is equal to SQRT(3)c. A critical error identified in the participant's approach is the assumption that momentum p equals mv, which is incorrect in the context of relativity; the correct relationship is p = gamma*mv.

PREREQUISITES
  • Understanding of relativistic energy equations, specifically E² = p²c² + m²c⁴
  • Familiarity with the concept of momentum in relativity, p = gamma*mv
  • Knowledge of the Lorentz factor (gamma) and its application
  • Basic grasp of the relationship between rest energy and total energy
NEXT STEPS
  • Study the derivation and implications of the Lorentz factor (gamma)
  • Learn about the relationship between energy, mass, and momentum in special relativity
  • Explore examples of relativistic particle collisions and energy calculations
  • Investigate the effects of relativistic speeds on time dilation and length contraction
USEFUL FOR

Students of physics, particularly those studying special relativity, as well as educators and anyone interested in understanding the principles of relativistic motion and energy calculations.

harpf
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Homework Statement


Find the speed of a particle whose total energy is twice its rest energy.

Homework Equations


E2 = p2c2 +m2c4

The Attempt at a Solution


4m2c4 = p2c2 +m2c4
3m2c4 = p2c2
SQRT(3)mc2 = pc
SQRT(3)mc = p
SQRT(3)mc = mv
SQRT(3)c = v
I know I can use E = gamma*mc2 to get the answer, but what have I done wrong in my approach? Thank you.
 
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harpf said:
SQRT(3)mc = p
SQRT(3)mc = mv
Your mistake was thinking that momentum equals mv. That's not true in relativity. In relativity, p = gamma*mv.
 
Thank you. I appreciate the help.
 

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