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Re: Mass



Gravitational mass is a concept associated with an object; gravitational
field is a concept associated with the space surrounding one or more
objects. These two concepts are closely related, but distinct. Because
these two concepts are so closely related, it is convenient (necessary?)
to keep one factor constant when defining the other.

I define gravitational mass operationally by measuring the gravitational
force on several objects, one at a time, in the same gravitational
field. The constancy of this gravitational field is important;
therefore, the constancy of the constitution (and configuration) of the
objects generating the constant gravitational field is important. That
is why I first discussed (with a lame attempt at humor ;-) factors that
change the constitution of objects.

I define gravitational field operationally by measuring the
gravitational force on one object (the test object) at several different
times, during each of which the test object is surrounded by a different
configuration of objects, possibly even different objects. It is
important that the constitution of the test object is the same for all
of these measurements.

Daniel Crowe
Oklahoma School of Science and Mathematics
Ardmore Regional Center
dcrowe@sotc.org
-----Original Message-----
From: Forum for Physics Educators [mailto:PHYS-L@list1.ucc.nau.edu] On
Behalf Of Jack Uretsky
Sent: Wednesday, October 20, 2004 1:03 PM
To: PHYS-L@LISTS.NAU.EDU
Subject: Re: [PHYS-L] Mass

On Tue, 19 Oct 2004, Dan Crowe wrote:

I defined gravitational mass as the ratio of the gravitational force
acting on an object to the local strength of the gravitational field.

I believe that this definition of gravitational mass is correct, but I
did not clearly define "gravitational field".

I agree that if you could define gf independently of gm, your
definition of gm would be correct. You are now giving us a definition
of
gf that does not use the concept gm.


I assume that the gravitational mass of an object is constant. If I
cut
off a piece of an object to fix a hole in my roof, it is no longer the
same object, and its gravitational mass is no longer the same. If I
spill spaghetti sauce on an object, it is no longer the same object,
and
its gravitational mass is no longer the same. (I'm sure the reader
can
imagine many other processes, some of them much more subtle, that
would
change the constitution of an object. ;-)

irrelevant; you are defining gf.

I also assume that the gravitational field due to one or more objects
depends only on their configuration.

You are defining gf as something independent of "one ore more
object." If by "objects" you mean "sources" and you are asserting that
a
"field" is independent of the configuration of its sources, then you are
using a mighty unusual definition of "field".


Begin by placing an object in the gravitational field due to one or
more
other objects.
You are supposedly defining "gf". You may not use the concept
"gf" in your definition. That's part of what "circularity" means.

END OF MY COMMENT
Initially, other effects, such as electromagnetic
interactions, should be minimized to isolate gravitational effects.
Use
the elongation or compression of a coiled spring, or the deformation
of
some other constraint to measure the force acting on the object.

Next move the object to another position (perhaps very far from the
previous position, near very different objects) and repeat the force
measurement. If the deformation of the constraint (e.g., elongation
or
compression of a coiled spring) is different, then the strength of the
gravitational field is different.

After many such measurements, a standard unit of gravitational field
strength can be defined.

The concept of gravitational field can be extended to more complicated
physical situations by analogy.

The validity of these approximations and the usefulness of the concept
gravitational field are determined by the agreement between
calculations
made using the concept of gravitational field and experimental
measurements.

Daniel Crowe
Oklahoma School of Science and Mathematics
Ardmore Regional Center
dcrowe@sotc.org

regards,
Jack

-----Original Message-----
From: Forum for Physics Educators [mailto:PHYS-L@list1.ucc.nau.edu] On
Behalf Of Jack Uretsky
Sent: Tuesday, October 19, 2004 2:39 PM
To: PHYS-L@LISTS.NAU.EDU
Subject: Re: [PHYS-L] Mass

<snip>

2. I object to Dan Crowe's definition of "gravitation mass" because
it
is
circular. "Force" and "field" are not independent concepts. The
circle
closes when I recall that the gravitational field is the force per
unit
mass.

<snip>



--
"Trust me. I have a lot of experience at this."
General Custer's unremembered message to his men,
just before leading them into the Little Big Horn Valley