Determining momentum from energy?

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SUMMARY

The momentum of a proton with 800 MeV of kinetic energy is calculated using the equation E^2 = p^2c^2 + m^2c^4. The rest energy of the proton is determined to be 939.57 MeV, leading to a total energy of 1739.57 MeV. The momentum is then calculated to be approximately 5.7985 x 10^-6 GeV/c after correcting for unit conversion. The initial confusion stemmed from a miscalculation involving the rest mass energy.

PREREQUISITES
  • Understanding of relativistic energy-momentum relations
  • Familiarity with the concept of rest mass energy (E=mc^2)
  • Basic knowledge of unit conversions between MeV and GeV
  • Proficiency in algebraic manipulation of equations
NEXT STEPS
  • Study the derivation of the energy-momentum relation E^2 = p^2c^2 + m^2c^4
  • Learn about relativistic momentum and its applications in particle physics
  • Explore the implications of kinetic energy on momentum in high-energy physics
  • Review unit conversion techniques between different energy scales, specifically MeV and GeV
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Students in physics, particularly those studying particle physics or relativity, as well as educators looking for examples of energy-momentum calculations.

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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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