This month's Challenge Question: Specs & Techs from
GlobalSpec:
A group of n particles are
moving freely and randomly. If you consider this group to be a closed system,
is the mass of the system equal to the sum of the masses of the individual
particles? You may consider the speed of the particles to be relativistic.
And the answer is:
Mass is not an additive measure like energy and momentum. Mass is
really the measure of the magnitude of the energymomentum 4vector. If we know
the total energy (E) and the total momentum (P) of a system we can determine
the mass (M) of the system by mean of this wellknown equation:
with
where mi, pi, and I are the individual masses and momentum of each
particle, and the speed of light, respectively.
Therefore, replacing these quantities in the first equation, we
have
Or,
It is clear from this equation that the sum of the individual
masses of the system (Σmi) is not equal to the system mass (M).
If, however, the system momentum is zero, then both masses are
equal. The system momentum is zero when the particles are moving all with the
same velocity (same speed and direction, including zero speed).

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