Speed of proton as fraction of c

AI Thread Summary
To find the speed of a proton with a kinetic energy of 1000 MeV, the correct approach involves using the relationship between kinetic energy and total energy, specifically K = E - E0, where E0 is the rest energy. The confusion arises from misapplying the kinetic energy formula, as the standard equation KE = (1/2)mv² is not suitable for relativistic speeds. Instead, the relativistic kinetic energy is given by K = (\gamma - 1)mc², where \gamma is the Lorentz factor. Solving for \gamma and then for speed v as a fraction of c leads to the correct value of approximately 0.875c. Understanding the distinction between total energy and kinetic energy is crucial for accurate calculations in relativistic physics.
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Homework Statement



Find the speed (as a decimal fraction of c) and momentum of a proton that has a kinetic energy of 1000MeV. The proton mass is 1.673x10-27kg, or 938 MeV/c2.

Homework Equations



KE= (1/2)mv2
KE= \gammamc2
p=mv
\gamma=1/(sqrt(1-(v2/c2)))

The Attempt at a Solution



I'm not too sure about the KE, it's supposed to be 0.875c but I can't get that value...
I've been solving for gamma and then solving for u, but I get outrageous values.
 
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Your formula for the kinetic energy is wrong. That's probably why you're getting non-sensical results.
 
Really? It's what our book gives us :/ Mind telling me what I should be using?
 
I doubt that's what your book says. It's more likely you're just confusing the total energy with the kinetic energy. The total energy of an object of rest mass m is given by E=\gamma mc^2. Note when the object isn't moving and therefore has no kinetic energy, you still have \gamma=1 and E_0=mc^2. This energy E0 is called the rest energy; it's the energy an object has just because it has mass. The kinetic energy of an object is the amount of energy in excess of the rest energy. Since the total energy is equal to E=\gamma mc^2 and the rest energy is E_0=mc^2, the kinetic energy is equal to K=E-E_0=(\gamma-1)mc^2.
 
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