Determining dilated lifetime of muons.

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SUMMARY

The discussion focuses on calculating the dilated lifetime of muons using their momentum (3094 MeV/c) and proper lifetime (2.198 microseconds). The key equations involved are time dilation, t = to/((1-u^2/c^2)^1/2), and relativistic momentum, p = (mv)/((1-v^2/c^2)^1/2). Participants emphasize using MeV/c for momentum and MeV/c² for mass to ensure unit consistency. Understanding the relationship between relativistic momentum and the Lorentz factor (γ) is crucial for determining the dilated lifetime.

PREREQUISITES
  • Understanding of special relativity concepts, particularly time dilation.
  • Familiarity with relativistic momentum equations.
  • Knowledge of units in particle physics, specifically MeV/c and MeV/c².
  • Basic grasp of the Lorentz factor (γ) and its application in relativistic calculations.
NEXT STEPS
  • Study the derivation and application of the Lorentz factor (γ) in special relativity.
  • Learn how to convert between different units in particle physics, particularly MeV/c and kg.
  • Explore examples of time dilation calculations involving high-energy particles.
  • Investigate the implications of relativistic effects on particle lifetimes in experimental physics.
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Physics students, particle physicists, and educators looking to deepen their understanding of relativistic effects on particle lifetimes.

amb1989
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The question provides momentum that the muons move with (3094 MeV/c) and proper lifetime (2.198 micro seconds) and asks to find the dilated lifetime.



2. t= to/((1-u^2/c^2)^1/2) and p=(mv)/((1-v^2/c^2)^1/2)



3. I think that I am supposed to use the momentum given to back order velocity then use that with the time dilation equation but I'm not sure what units I should use for the mass of the muon. I saw one with kg and one with MeV/c and I feel like I should use MeV/c but I'm not getting the units to work out and I'm just going no where right now. Any help would be nice. Thanks.
 
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If you know γ, can you find the dilated lifetime? What equation relates relativistic momentum to γ? Since you are given the momentum, you can use that equation to find γ and then the dilated lifetime. Forget kilograms. If you use MeV/c units for the momentum and MeV/c2 units for the rest mass, the equation will work out fine.
 
OK thank you very much I'll work that out and see what I come out with.
 

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