Why relativistic momentum equals the following?

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Homework Help Overview

The discussion revolves around the concept of relativistic momentum, specifically how it relates to energy and mass in the context of a positron with a given energy. Participants are exploring the derivation of the momentum formula in relativistic physics.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are examining the relationship between momentum and energy, questioning the derivation of the momentum formula P=√(γ²-1)mc. Some suggest eliminating velocity from the equations relating momentum and Lorentz factor, while others propose using the energy-momentum relation for a more straightforward approach.

Discussion Status

The discussion is active, with various approaches being explored. Some participants have provided alternative methods for deriving the momentum, while others are clarifying the relationships between the variables involved. There is no explicit consensus on a single method, but multiple lines of reasoning are being considered.

Contextual Notes

Participants are working within the constraints of a homework problem, which may limit the information available for discussion. The focus is on understanding the derivation rather than arriving at a final answer.

Foruer
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In a solution to a problem we were given, it is written that a positron momentum with energy of 2mc2
(where γ=2) is √(γ2-1)*mc = √(4-1)*mc = √3*mc

How did they get that P=√(γ2-1)*mc?
 
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You are familiar with p = ϒmv right?
And also with ϒ = 1/√(1-(v/c)2) right?

Eliminate v from the two equations and what do you get?
 
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What I get is the answer ?:) thank you :wink:
 
While it gives you the right answer, it is much simpler to use the energy-momentum relation ##E^2 - p^2 c^2 = m^2 c^4## and just solve for ##p##.
 
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