# Its allll relative - E=mc^2

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I just have a quick theory question about Energy-mass Equivalence. Say you have a particle with with 9GeV of energy! using 1/2mv^2 the velocity of this particle would be greater than the speed of light and hence not possible (i remain hopeful this will change one day ). To find out how much mass the particle has gained by using E=mc^2, do i use the total energy of the particle, the 9GeV, or just extra energy the particle has above the energy it has at the speed of light? so to find E to plug into that equation would i take the energy of the same mass particle travelling at the speed of light and minus that from my initial energy of 9GeV and use that energy for the E=mc^2 equation?

Hope that makes sense to people, any help will be appreciated!

Hope that makes sense to people, any help will be appreciated!

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(Original post by

I just have a quick theory question about Energy-mass Equivalence. Say you have a particle with with 9GeV of energy! using 1/2mv^2 the velocity of this particle would be greater than the speed of light and hence not possible (i remain hopeful this will change one day ). To find out how much mass the particle has gained by using E=mc^2, do i use the total energy of the particle, the 9GeV, or just extra energy the particle has above the energy it has at the speed of light? so to find E to plug into that equation would i take the energy of the same mass particle travelling at the speed of light and minus that from my initial energy of 9GeV and use that energy for the E=mc^2 equation?

Hope that makes sense to people, any help will be appreciated!

**TMCkins**)I just have a quick theory question about Energy-mass Equivalence. Say you have a particle with with 9GeV of energy! using 1/2mv^2 the velocity of this particle would be greater than the speed of light and hence not possible (i remain hopeful this will change one day ). To find out how much mass the particle has gained by using E=mc^2, do i use the total energy of the particle, the 9GeV, or just extra energy the particle has above the energy it has at the speed of light? so to find E to plug into that equation would i take the energy of the same mass particle travelling at the speed of light and minus that from my initial energy of 9GeV and use that energy for the E=mc^2 equation?

Hope that makes sense to people, any help will be appreciated!

KE = (gamma - 1)mc

^{2}

where gamma = 1 / sqrt(1 - v

^{2}/c

^{2})

rest energy = mc

^{2}

total energy = rest energy + KE

total energy = mc

^{2}+ (gamma - 1)mc

^{2}

total energy = gamma *mc

^{2}

EDIT: v and c were transposed in the gamma expression, now corrected

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**TMCkins**)

I just have a quick theory question about Energy-mass Equivalence. Say you have a particle with with 9GeV of energy! using 1/2mv^2 the velocity of this particle would be greater than the speed of light and hence not possible (i remain hopeful this will change one day ). To find out how much mass the particle has gained by using E=mc^2, do i use the total energy of the particle, the 9GeV, or just extra energy the particle has above the energy it has at the speed of light? so to find E to plug into that equation would i take the energy of the same mass particle travelling at the speed of light and minus that from my initial energy of 9GeV and use that energy for the E=mc^2 equation?

Hope that makes sense to people, any help will be appreciated!

You need to use the total energy of the particle - from your statement, I'm not sure if 9GeV is the total energy of the particle, or just the energy the experimenter imparted to the particle. (That is, is 9GeV the energy of the particle, or should it be 9GeV + m c^2, to account for the rest mass?)

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