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Its allll relative - E=mc^2

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 :wink: ). 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! :biggrin:
Original post by 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 :wink: ). 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! :biggrin:


You need to use the relativistic expression for KE to solve this paradox:

KE = (gamma - 1)mc2

where gamma = 1 / sqrt(1 - v2/c2)

rest energy = mc2

total energy = rest energy + KE

total energy = mc2 + (gamma - 1)mc2

total energy = gamma *mc2



EDIT: v and c were transposed in the gamma expression, now corrected
(edited 9 years ago)
Original post by 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 :wink: ). 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! :biggrin:

The equation "kinetic energy = 1/2 m v^2" is true in general (I think), but only if by "m" you mean "the relativistic mass". As the velocity of the particle increases, the relativistic mass goes up (by a factor of 11+v2c2\frac{1}{\sqrt{1+\frac{v^2}{c^2}}}) [EDIT: I actually can't remember whether that should be a plus or a minus :/ ]; this balances out the energy increase, so that v never has to be greater than c.

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?)
(edited 9 years ago)

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