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https://texercises.com/exercise/momentum-of-a-proton/
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Exercise:
Calculate the momentum of a EkO proton. Compare the result to the momentum according to the classical calculation.

Solution:
Solving the relativistic energy-momentum relation E^ pc^ + E_^ for the momentum yields pc sqrtE^-E_^ pcF sqrtEr+Ek^ - Er^ pcS Longrightarrow p resultpP The classical calculation yields p_textrmcl sqrtmsscEkin pclF sqrt times Er times Ek/c pclS approx resultpclP The classical calculation agrees with the relativistic calculation up to four significant figures so in this example three significant figures its prediction is correct. For higher momenta the deviation becomes much more significant.
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Exercise:
Calculate the momentum of a EkO proton. Compare the result to the momentum according to the classical calculation.

Solution:
Solving the relativistic energy-momentum relation E^ pc^ + E_^ for the momentum yields pc sqrtE^-E_^ pcF sqrtEr+Ek^ - Er^ pcS Longrightarrow p resultpP The classical calculation yields p_textrmcl sqrtmsscEkin pclF sqrt times Er times Ek/c pclS approx resultpclP The classical calculation agrees with the relativistic calculation up to four significant figures so in this example three significant figures its prediction is correct. For higher momenta the deviation becomes much more significant.
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special relativity
Tags
kinetic energy, momentum, rest energy
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Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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