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how can we relate momentum, energy and mass?

The famous Einstein relationship for energy


can be blended with the relativistic momentum expression

to give an alternative expression for energy.
The combination pc shows up often in relativistic mechanics. It can be manipulated as follows:

and by adding and subtracting a term it can be put in the form:

which may be rearranged to give the expression for energy:

Note that the m with the zero subscript is the rest mass, and that m without a subscript is the effective relativistic mass.


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