Determining momentum from energy?

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The discussion focuses on calculating the momentum of a proton with 800 MeV of kinetic energy using the equation E^2 = p^2c^2 + m^2c^4. The user initially calculates the rest energy of the proton, resulting in a total energy of 1739.57 MeV. After attempting to solve for momentum, they encounter a discrepancy in their calculations, suspecting an error. Ultimately, the user resolves the issue and successfully finds the correct momentum. The thread highlights the challenges of applying relativistic equations in physics homework.
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Homework Statement



What is the momentum of a proton with 800MeV of kinetic energy?

Homework Equations



E^2=p^2c^2+m^2c^4

The Attempt at a Solution



I know that E should be kinetic energy + rest energy, so I calculate rest energy first.

rest energy = mc^2= (1.67*10^-27)*(3*10^8)^2 = 939.57 MeV. total E=939.57+800=1739.57 MeV

Plug and chug and solve for p. m^2c^4=.1414MeV (this seems wrong)

(1739.57)^2-.1414 = 3026103.644 MeV, divide that by (3*10^8)^2 and take the root to get p, which comes out to be 5.7985*10^-6. My answer needs to be in GeV, so it seems that I'm off by a factor of 40. I've been doing physics homework all day so my brain is fried and I've been beating my head against a wall for the last hour trying to solve this problem. I know that I'm missing something stupid, but I just can't see what it is. Help!
 
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