Neutron must travel so that kinetic energy = rest energy

AI Thread Summary
To determine the speed a neutron must travel for its kinetic energy to equal its rest energy, the equation Ek = mc^2 - m0c^2 is relevant. The kinetic energy (Ek) must equal the rest energy (m0c^2), leading to the equation 2m0c^2 = mc^2 when considering relativistic mass. The relativistic mass is defined as m = γm0, where γ is the Lorentz factor. A misunderstanding about the cancellation of terms was clarified, emphasizing the importance of correctly applying the signs in the equations. This discussion highlights the mathematical approach needed to solve the problem of neutron velocity in relation to its energy states.
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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