Calculating Relativistic Energy and Momentum of a Proton

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SUMMARY

The discussion focuses on calculating the relativistic energy and momentum of a proton, emphasizing that the classical kinetic energy formula, mv²/2, is only valid at low speeds. For high-speed scenarios, the exact relativistic equations must be applied to accurately determine energy and momentum. The conversation highlights the limitations of approximations in physics and the necessity of using precise formulas for high-velocity particles.

PREREQUISITES
  • Understanding of relativistic physics concepts
  • Familiarity with the equations of motion in special relativity
  • Knowledge of energy and momentum conservation laws
  • Basic proficiency in algebra and calculus
NEXT STEPS
  • Study the relativistic energy equation: E = mc² / √(1 - v²/c²)
  • Learn about relativistic momentum: p = mv / √(1 - v²/c²)
  • Explore the implications of relativistic effects on particle collisions
  • Investigate the differences between classical and relativistic mechanics
USEFUL FOR

Students of physics, educators teaching special relativity, and researchers in particle physics will benefit from this discussion.

cosmos42
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Homework Statement


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Homework Equations


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The Attempt at a Solution


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I see you are aware that mv^2/2 is only an approximation. As a general rule of thumb, any approximation will have some limited domain of usefulness. In this case, it is only an approximation at low speeds. For high speeds you should use the exact expression.
 

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