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John,
In trying to make the concepts and ideas of physics clear and unambiguous
to our students, we are all prone to be a tad pleonastic. The onliest good thing
about this is that we're in the minor leagues compared to lawyers.
Paul O. Johnson
Collin County College
----- Original Message -----
Sent: Sunday, December 10, 2000 10:50
PM
Subject: Re: Mass/Energy concepts and
terminology
In this thread there have been a number of odd
statements. I can't figure
out which are facetious and which are
merely befuddled.
In current professional usage, "mass" means "rest
mass". Indeed, saying
"rest mass" is a pleonasm, so I'll stop saying
it. The "m" that appears in
equations like E = m c^2 is this
mass.
Therefore the aforementioned famous formula does not describe the
total
energy. Far from it. The total energy includes
contributions from:
-- the mass
(as described above),
-- the
kinetic energy (which is not included in the
mass),
-- the gravitational
potential energy,
-- the
electrostatic potential energy,
and
-- many other
things.
To say it another way: Mass is not "equivalent to" energy
or "identical
to" energy. It is just one contribution to the
energy.
If you want to deal with particles not at rest, a useful
formula is
E^2 = p^2
c^2 + m^2 c^4
and if the students can only remember one
relativistic formula, IMHO this
is the one you want them to remember.
Draw a graph of E versus p.
This is elegant and has some nice
properties:
a) it reduces nicely to E=mc^2 in the at-rest
case;
b) it reduces nicely to E=pc in the massless case;
and
c) to lowest order it says KE = p^2 / 2m for a
slowly-moving massive
particle.
There is very little professional
use of the quantity "gamma m".
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