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From: matt@oddjob.UUCP (Matt Crawford)
Newsgroups: net.physics
Subject: Re: Potential Energy (could someone expand on the 'yes' answer?)
Message-ID: <1035@oddjob.UUCP>
Date: Tue, 5-Nov-85 13:03:21 EST
Article-I.D.: oddjob.1035
Posted: Tue Nov  5 13:03:21 1985
Date-Received: Thu, 7-Nov-85 04:42:34 EST
References: <175@tulane.UUCP> <471@iham1.UUCP> <536@talcott.UUCP> <1514@teddy.UUCP> <1076@jhunix.UUCP> <1235@mhuxt.UUCP>
Reply-To: matt@oddjob.UUCP (Matt Crawford)
Organization: U. Chicago, Astronomy & Astrophysics
Lines: 30
Summary: 

The following digresses somewhat from the original question, but
it is all relevant.

The predominant meaning of the word "mass" among physicists is
"rest mass", not mass times some velocity-dependent factor.  For
a single particle with energy E and momentum P (consider all P's
to be vectors in this article), the mass is the square root of
E^2 - P^2.  This does not depend on the frame in which E and P
are measured.

Often physicists will talk about the mass of a pair of particles.
this is just the square root of (E1 + E2)^2 - (P1 + P2)^2.  If
the two particle are the sole decay products of some other
particle, then this is the mass of that original particle.  (Side
note: the combined mass of the decay products will be distributed
about the mean with a standard deviation inversely proportional
to the half-life of the particle that decayed to produce them.
Thus one hears phrases like "the width of the Z-0".)

If you compress a spring with a rock at each end, its mass will
be greater than the separate masses of the rocks and uncompressed
spring.  The extra mass will equal the kinetic energy which the
spring can give to the rocks (divided by c^2, if you like).  If
you separately square the total energy and total momentum of the
spring and rocks, then subtract, you will get the same answer
both while the system is tied together and after the rocks are
sent flying.
_____________________________________________________
Matt		University	crawford@anl-mcs.arpa
Crawford	of Chicago	ihnp4!oddjob!matt