Re: Apparent weight

[phrp@bigcat.fhsu.edu (Roger Pruitt)]

Eugene P. Mosca wrote:
> Roger Pruitt wrote:
>
> *********************
> I think you are making it too hard, Rick. Leigh asked for an operational
> definition. What I offered was such a way of defining weight. I don't care
> to know how the bathroom scale works, nor do I think that is important.
> The number I get when I stand on it is my weight.
>
> I take the scale with me in the shuttle and "stand" on it and get zero.
> Therefore, I'm weightless.
> *********************
>
> It seems to me that the above statements fail to provide an acceptable
> definition of weight.  Consider a reference frame in which Twin A stands
> on a stationary scale (Scale A) resting on a horizontal floor and
> identical Twin B stands on a scale (Scale B) fastened to a platform that
> is accelerating down a frictionless incline, at the bottom of which is a
> loop-the-loop.  The two scales will have different readings even though
> the twins have equal masses.  In addition, Scale B's reading will vary
> dramatically as it and Twin B traverse the loop-the-loop.  Further, if the
> incline is not frictionless the readings of Scale B will be different.
>
> If we agree to accept scale readings as the definition of weight then it
> seems to me that weight is a peculiar animal and one that is not commonly
> accepted anywhere.  I am not ready to pass off this definition to my
> students.  If I am somehow missing the point, please straighten me out.

If we accept the idea that weight is NOT an intrinsic property of the
object, then twin A and Twin B will have different weights. All I am
trying to do is to say that there is a consistency in what we call
weight if we divorce ourselves from calling it the mg force. 

I've used textbooks that talk about a person's weight on the earth and
then say that a person would weigh less on the moon. Later on the text
will talk about a person being weightless in orbit around the earth.
Some people say weight is the mg force and then are forced to invent a
concept called "apparent weight." I don't think this is necessary or
obvious. At least it isn't to me. I agree with Bob Carlson that my
definition of weight is not what is standard. Leigh asked for an
operational definition, and I gave it. The question now is, what are we
measuring with the bathroom scale or the force probe?

I gave a very simple explanation to Leigh's question (ignoring the
latitude effect, the earth's revolution about the center of mass of the
earth-moon system, the revolution of the earth about the sun and the
solar motion about the center of our galaxy, etc.) just to illustrate.
If we operationally define weight as that which is measured when we
stand on our bathroom scales (or a fancier force detector), then what
are we measuring? It certainally isn't the mg force. In fact it is the
normal force. In my very elementary explanation, I wrote N=mg-mv^2/r
where N is the normal force and r is the radius of the earth. (I presume
that all reading this can add the necessary details such as the latitude
effect, specific radius, etc..) The scale pushes up on our feet and by
Newton's third law we are pushing down on the scale with the same force.
The scale is registering this force is it not? If we are in obit around
the earth, then the mv^2/r term is the same magnitude as the mg force (g
being less at that location than when we are on the earth) and N=0. We
are weightless. There is no force excerted on our feet by the bathroom
scale.

> My recommendation is to avoid using the term weight.  It is a difficult
> choice, however, because it permiates most of our textbooks.  The terms
> gravitational force and normal force allow for more clarity.

Weight is such a part of our vocabulary, why avoid it? However, let's
give a reasonable definition of it that is operationally meaningful and
consistant with all of the ways it is used. Let's not invent new phrases
such as "apparent weight" because we have given a woefully poor
definition of weight such as what appears in most (if not all)
textbooks.

This whole business of weight came about, did it not, as a result of
Ludwig's list of textbook misconceptions. My apologies to Bob Carlson,
but I believe, as I've said, that weight as defined in most textbooks is
a disgace.

Roger
> Gene

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|  Roger A. Pruitt, PhD        |
|  Department of Physics       |
|  Fort Hays State University  |
|  Hays, KS  67601             |
|  Ph. (785) 628-5357          |
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