Which expression for Relativistic Kinetic Energy is correct?

[rhz_prog]

I saw that the Relativistic Kinetic Energy calculation for these two sources, seems to be different :

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html
see : Conservation of Energy
EK = gamma*m*c^2

While here :
http://en.wikipedia.org/wiki/Kinetic_energy
see : Relativistic kinetic energy of rigid bodies
EK = gamma*m*c^2 - m*c^2

Which one is right ? Or did I misunderstand something ?

 

[TeTeC]

I haven't read the first link, but from what I know I'd say that the second definition is the right one. E = \gamma mc^{2} is the total energy, not the kinetic energy. You can Taylor expand the first expression E = \gamma mc^{2} - mc^{2} with respect to the variable v/c. The first term in the expression, \frac{1}{2}mv^{2} represents the Newtonian kinetic energy, which will be the dominant term if v/c is small.

 

[yenchin]

Where does the first link say that? All I can see under "conservation of energy" is:

E_final = γmc^2 + E_L

?

 

[jtbell]

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html
see : Conservation of Energy
EK = gamma*m*c^2

That page does not refer to \gamma m c^2 as kinetic energy, but rather, simply as "energy". In fact, the word "kinetic" does not appear on that page at all!

 

[yuiop]

I saw that the Relativistic Kinetic Energy calculation for these two sources, seems to be different :

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html
see : Conservation of Energy
EK = gamma*m*c^2

While here :
http://en.wikipedia.org/wiki/Kinetic_energy
see : Relativistic kinetic energy of rigid bodies
EK = gamma*m*c^2 - m*c^2

Which one is right ? Or did I misunderstand something ?

Your expressions are better written as:

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html
see : Conservation of Energy
TE = gamma*m*c^2

While here :
http://en.wikipedia.org/wiki/Kinetic_energy
see : Relativistic kinetic energy of rigid bodies
KE = gamma*m*c^2 - m*c^2

where TE is Total Energy and KE is Kinetic Energy.
The second expression can also be written as:

KE = TE - RE

where RE is Rest Energy or rest mass energy.

Total Energy can can also be found from this relationship:

TE = \sqrt{(gamma*m*v*c)^2+(m*c^2)^2} = \sqrt{(pc)^2+(mc^2)^2}

which can be written as:

TE = \sqrt{ME^2+RE^2}

where ME is Momentum Energy.

By rearranging this becomes :

RE = \sqrt{TE^2-ME^2}

Since rest energy is usually an invariant, the quantity \sqrt{TE^2-ME^2} is the same when switching from one reference frame to another. In fact, in a perfectly elastic collision, the quantity \sqrt{TE^2-ME^2} is the same for a given particle before and after the collision.

Hope that helps.