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Sitaram
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Joined: 14 Sep 2005
Posts: 1079
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 Posted: Fri Mar 31, 2006 6:44 am Post subject: A Question on weight, mass, accuracy and precision |
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I would like some feedback from physics students on the following
argument:
Here's the question which someone posted:
| Quote: |
What is the exact weight of the earth, in pounds, with everything in it and
on it included?
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It is a trick question, since their answer is that "the earth weights
EXACTLY zero, since it is weightless in space."
Here are my objections to their reasoning, together with their replies.
Their first answer:
| Quote: |
The answer is 0.000...0
Mass is a measure of the quantity of matter in an object.
Weight is the gravitational attraction between an object and the Earth, and
also, the Earth and that object.
So, with the Earth as a frame of reference, the weight of the Earth is 0.
You would be weightless in space, and so is the Earth. Your mass would
not change though.
The question, what is the MASS of the earth, in METRIC TONS is a very
different question.
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My objection:
| Quote: |
At the risk of provoking even more thinking, or worse yet, provoking
Libre, consider the following hypothetical scenario:
I place a chunk of dry ice (frozen Carbon Dioxide) upon a scale, and it
happens to register 1 pound (pardon me for not saying a kilo, but I am a
true blue North American).
Now, CO2 does not melt in the conventional sense, as frozen water (aka
ice) does, but rather sublimates (ouuu that sounds ever so sexual), and
passes directly from the solid phase to the gaseous phase (and
remember, plasma is the fourth state of matter).
So we may observe as our chunk of dry ices, evanescently as the
Cheshire Cat's smile, approaches as close as we please to a weight of
zero. But it is not meaningful to say that it ever reaches zero, for when it
disappears, then there is nothing remaining to which we might predicate
the qualia of weight.
In Structured Query Language (SQL) there is something called NULL,
which is often mistakenly identified as zero. But NULL has a very different
meaning. When a field contains null, the null signifies that the value is
either unknown, or possibly meaningless. NULL is a big question mark.
When we say that something is weightless in space, what we mean is that
some astronaught is flailing about with his hands and legs, and must be
very cautious about peeing.
It all depends upon how you choose to define weight.
So it may be misleading to say that the Earth has a weight of zero. It may
be more meaningful to fill in our weight field with the NULL. Furthermore,
the Earth is in a certain orbit precisely because of the gravitational
attracting between the Earth, sun, moon, planets, and virtually all the
mass in the universe.
All these matters had quickly passed through my mind when I first saw
Libres post. But I felt that if I were to cavil about such things, and Libre
was actually unaware of the subtle distinction between mass and weight,
then I would be perceived as an insensitive, pedantic putz, and Libre
would feel even more hurt, and would do something hasty in desperation.
It is not that the object in space becomes weightless, but rather that the
concept of weight in space becomes meaningless, or at very least, vague
and illusive.
Were we to place the Earth on the surface of Jupiter, it would take up a
percentage of Jupiter surface area comparable to New York State's
occupation of the earth's surface, or perhaps even New York City's
occupation, to hazard a guess. And the earth would definitely have weight
on the surface of Jupiter.
And speaking of Jupiter (the name of a deity), if a deity is the source of
existence, then one cannot speak of that deity existing, or not existing,
just as it is difficult to speak of the weight of the Earth, and yet Earth's
mass is the source of our notion of weight.
When anthropoligist Margaret Mead asked some natives where babies
come from, they were perfectly conscious of the correct answer, but felt
embarrassment and compassion Ms. Mead, as the thought perhaps SHE
did not know the answer. So, to be politically correct, they gave the
answer which they give to small children, namely, that babies are found
under cabbage leaves (or something similar). And Doctor Mead promply
published the astounding fact that there exist natives so primitive that
they are ignorant of the facts of human reproduction.
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Their response:
| Quote: |
True, NULL is very different from ZERO. I'm a database programmer,
among other things, and I certainly appreciate the difference between
NULL and ZERO.
Now, as far as the dry ice, you're wrong about that. When an object
changes state - as in sublimation - no mass whatsoever is lost in the
process. That is a principal known as Conservation of Mass and was
proved by Lavoirsier (sp?) shortly before the French Revolution. To get
right to the point, if you captured the CO2 that had sublimated off the dry
ice and weighed it, along with any remaining dry ice, the weight would be
identical to the original dry ice weight. The only reason the CO2 gas floats
in the air is because it is bouyant in air, but it has mass.
Now, as far as the Earth having weight with respect to the sun, that is
correct. It also has (a different) weight with respect to every other object
in the universe. Mass is different - that is an intrinsic property of the
object and it is not relative to other objects, but WEIGHT is only
meaningful as a measure of the attraction between 2 objects. When we
speak about WEIGHT, our frame of reference is the Earth itself. Almost
always is. So the Earth, with respect to itself as a frame of reference,
weighs zero.
If you were in an elevator that was in free fall because let's say the cable
broke (God forbid) you would be weightless with respect to the elevator
cab but you would have your normal weight with respect to the Earth.
True the Earth is in orbit about the Sun, and has weight with respect to the
Sun, but has no weight with respect to itself. Since, as I said, weight is
almost always - unless otherwise stated - in respect to the Earth, the
Earth cannot have any weight with respect to itself. If you were able to
measure the weight with a giant scale, and put it in space, and put the
earth on it, it would register 0.
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My rebuttal:
| Quote: |
You have the better makings of a lawyer than a friend, perhaps, in part,
because you are so passionately concerned with being right, rather than
rightly concerned with being compassionate.
You cavil in your argument between the concept of weight and mass.
Were some of the carbon dioxide molecules to escape earth's
atmosphere, then, by your argument, their weight would be zero, even
though their mass would be constant. In your next breath, you concede
that the earth does have some weight with respect to the sun, which
conflicts with your earlier statement that the earth weighs exactly zero.
Nothing can be measured exactly. Anything measured through
instrumentation, whether weight on a scale, or temperature on a
thermometer, or volume or velocity, etc., can never be exact since all
instruments are limited in accuracy to a plus or minus range of precision.
So, when you said that the earth weighs exactly zero, then you are in
error.
My example was about the weight on a scale of a block of dry ice, and
you know perfectly well that as the dry ice sublimates, the scale will
register less and less weight, until finally, when the block is gone, it will
register zero.
You twist my words by changing the premise of the example from the
weight of the block into the mass of all the molecules collected.
Many confuse argument, dispute and contention with discourse and
dialectical inquiry. Socrates was concerned with being right for the sake of
truth while the sophists, his opponents, were concerned with truth for the
sake of being right and gaining attention.
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His final response:
| Quote: |
Thought about in a certain context - the context I am suggesting - then
the earth has zero weight. In other contexts, it does have weight. I
believe I covered all that somewhere above.
I'm not cavilling(?) at all. There is a fundamental difference between the
two. Weight is a force and mass is a quantity of matter. I don't see them
as the same at all - that's the key to my "thought provoking question".
It's true that nothing can be measured exactly. I'm not measuring
anything, I'm using logic to arrive at an answer.
The sum of all the forces acting on a body in static equillibrium is precisely
zero. If I tried taking measurements I'd get some fluctuation because of
measurement error - as you suggested. That error is noise, contaminating
the true answer of zero.
The dry ice weighs exactly the same, whether in a solid phase or a
gasseous phase. A super accurate scale, in a vaccuum (removing air from
the experiment) would prove it. Of course if you let the molecules of CO2
escape, the specimen on the scale will weigh less - nothing remarkable
about that. LavWAHsiYAY proved almost the exact same thing - but he
used specimens of iron rusting away.
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MY CLOSING COMMENTS to this e-mail:
For me, it is a matter of equivocating on mass versus weight. I also see a
problem with the use of the word EXACT in any measurement, which
raises an issue of precision versus accuracy in instrumentation.
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