Neutron must travel so that kinetic energy = rest energy

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SUMMARY

A neutron must travel at a velocity such that its kinetic energy (Ek) equals its rest energy (m0c²). The equation Ek = mc² - m0c² leads to the conclusion that 2m0c² = mc² when considering relativistic mass, where m = γm0. This highlights the importance of correctly applying the concept of relativistic mass and the significance of the negative sign in the energy equation. The discussion emphasizes the need for clarity in mathematical manipulation when dealing with relativistic physics.

PREREQUISITES
  • Understanding of Einstein's mass-energy equivalence (E=mc²)
  • Familiarity with relativistic mass and the Lorentz factor (γ)
  • Basic knowledge of kinetic energy equations
  • Mathematical skills for manipulating algebraic equations
NEXT STEPS
  • Study the derivation of the Lorentz factor (γ) in special relativity
  • Explore the implications of relativistic mass on particle physics
  • Learn about the relationship between kinetic energy and relativistic effects
  • Investigate practical applications of mass-energy equivalence in modern physics
USEFUL FOR

Physics students, educators, and anyone interested in understanding the principles of special relativity and kinetic energy in particle dynamics.

aeromat
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Problem statement
How fast must a neutron be traveling relative to a detector in order to have a measured kinetic energy that is equal to its rest energy?

An "attempt"
I know
Ek = mc^2 - m0c^2

But if Ek = m0c^2, wouldn't the two terms cancel out from this equation? I am having trouble going about with it mathematically, and could use a few pointers if you guys don't mind helping out.

Where m0 is the rest mass.
m is the relativistic mass
 
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No, why would they cancel? You would get

2m_0 c^2 = mc^2

where I assume you're using the concept of relativistic mass m = \gamma m_0.
 
Honestly, I have to say I overlooked that "-" sign. Thank you Pengwuino.
 

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