Relativistic speed of a particle

AI Thread Summary
To find the speed of a particle whose total energy is twice its rest energy, the equation E² = p²c² + m²c⁴ is utilized. The attempt led to the conclusion that momentum p equals SQRT(3)mc, but this approach mistakenly equated momentum with mv, which is incorrect in relativistic physics. In relativity, momentum is defined as p = gamma*mv, where gamma is the Lorentz factor. The correct method involves applying the relativistic energy-momentum relationship to derive the particle's speed. Understanding the distinction between classical and relativistic momentum is crucial for solving such problems.
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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