Answer to Question #112880 in Mechanics | Relativity for DEEPAK SINGH

Question #112880
Prove the relation E^2-P^2C^2=m•^2C^4 where P is the momentum.
1
Expert's answer
2020-05-03T17:19:10-0400
"E=\\frac{mc^2}{\\sqrt{1-\\frac{v^2}{c^2}}}\\\\E^2=\\frac{m^2c^4}{1-\\frac{v^2}{c^2}}=m^2c^4\\left(1+\\frac{\\frac{v^2}{c^2}}{1-\\frac{v^2}{c^2}}\\right)\\\\=m^2c^4\\left(1+\\frac{v^2}{c^2}\\gamma^2\\right)"

"E^2=m^2c^4+m^2c^2\\gamma^2v^2=m^2c^4+p^2c^2"


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