- #1

alba

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The formula usually givento find the relativistic energy of a particle is :## E^2 = p^2c^2 + m^2c^4 ## which is derived from the original Lorentz formula for mass: ##m=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}} ## which gives the value of the total mass including the rest mass and, subtracting the latter, we get the kinetic energy (net increase of total energy):

##E_k=m_0c^2*\left[\frac{1}{\sqrt{1-\frac{v^2}{c^2}}} -1\right]##

If this is correct we know that when v = 0.866c the total energy/mass is twice the rest mass and the Ek is equivalent to one rest mass, in the case of an electron : 0.511 MeV.

My question is:

since E=M, why is it not suggested to find the increased energy (the kinetic energy) in such a simple way? Do you know of any case in which this simple method is not exact, or inconsistent with theory or experiment?

If we accelerate an electron by a kinetic energy of .511MeV we know that it will have energy/mass of 2 electrons, and if we (at LHC) give 7 TeV (7 000 GeV) to a proton of .938 GeV we easily find that the energy/mass has increased by 7000/.938 = 7461 times and the speed is sqrt(1-1/7461^2) =.999999991 c.

Why can't be as easy as that?

##E_k=m_0c^2*\left[\frac{1}{\sqrt{1-\frac{v^2}{c^2}}} -1\right]##

If this is correct we know that when v = 0.866c the total energy/mass is twice the rest mass and the Ek is equivalent to one rest mass, in the case of an electron : 0.511 MeV.

My question is:

since E=M, why is it not suggested to find the increased energy (the kinetic energy) in such a simple way? Do you know of any case in which this simple method is not exact, or inconsistent with theory or experiment?

If we accelerate an electron by a kinetic energy of .511MeV we know that it will have energy/mass of 2 electrons, and if we (at LHC) give 7 TeV (7 000 GeV) to a proton of .938 GeV we easily find that the energy/mass has increased by 7000/.938 = 7461 times and the speed is sqrt(1-1/7461^2) =.999999991 c.

Why can't be as easy as that?

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