Re: a relativity question

[John Mallinckrodt <ajm@CSUPOMONA.EDU>]

> A question in Giancolli asks: Is a compressed spring more massive than the
> relaxed version of the spring.
>
> I understand that Work has been done and there is no change of KE.
> Classically we say there is now PE stored. But it seems that to conserve
> energy in the relativistic sense that there would be added mass ...

Yes

> ... measured.

Unlikely!

> If so, I wonder if the same would be said of an elevated mass?

No; an elevated mass does not "have" more energy despite the
implications of standard textbooks (and not to mention the usefulness
of that gentle subterfuge in many common situations.)  Gravitational
potential energy is a property of a *system* of interacting masses.

For instance, consider the system consisting of the Earth and all of
its immediate neighboring objects including my car, Martha Stewart,
and the ionosphere.  If you reach in from outer space, lift my car
some distance, and then remove your (lengthy!) arm safely back into
the cosmos, the rest energy of the system--and, therefore, its
mass--has been increased.  My car's mass may also have changed (as a
result, perhaps, of heat conducted to or from your hand while
lifting), but not because of the energy of interaction between it and
the Earth.

--
John Mallinckrodt        mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.