Hi, I am trying to quickly resolve a fairly basic question that cropped when considering relativity. Classically, the total energy of a system is often described in term of 3 components:(adsbygoogle = window.adsbygoogle || []).push({});

Total Energy = Rest Mass + Kinetic + Potential

If I ignore potential energy, i.e. a particle moving in space far from any gravitational mass, then I assume the general form above can be reduced to:

[1] [tex]E_T = m_o c^2 + 1/2mv^2[/tex]

Now [tex]m_o[/tex] is the rest mass, while I assume [m] has to be described as the relative mass as a function of its velocity [v], i.e.

[2] [tex]m = \frac {m_o}{\sqrt{(1-v^2/c^2)}}[/tex]

However, relativity also introduces the idea of relativistic momentum:

[4] [tex] p = mv = \frac {m_o v}{\sqrt{(1-v^2/c^2)}}[/tex]

However, the following link show the definition of `Relativistic Energy in Terms of Momentum’: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html#c4 which I have expanded to the following form:

[5] [tex]E_X^2 = m_o^2 c^4 + p^2c^2 = m_o^2 c^4 + m^2v^2c^2[/tex]

Now my initial assumption was that [tex][E_X \equiv E_T][/tex], but examination of equations [1] and [5] suggests that this cannot be the case. Could somebody explain my error or the difference in the implied energy of these 2 equations?

As a side issue, energy is a scalar quantity, while momentum is a vector quantity. I see how multiplying [p] by [c] gets us back to the units of energy, but was slightly unsure about the maths of mixing these quantities. Would appreciate any clarification of the issues raised. Thanks

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# Basic Energy-Momentum Issue

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