Re: Weight and Mass

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 13:11 -0400 9/24/01, Joe Heafner wrote:
> >  From: Tina Fanetti <FanettT@QUEST.WITCC.CC.IA.US>
> >
> >  I thought I had explained clearly what the difference between
> > weight and mass was to my students.  I asked them to write down any
> > questions they had at the end of class and some one wants me to
> > explain the difference again with examples.
> weight = the gravitational force on an object due to Earth
>
> mass = the quantity of material present in a sample; fundamentally
> related to the number of atoms in the sample
I agree that this is the "quick and dirty" definition of weight, but
we often use the word "weight" in the sense of the force we would
exert on a scale place under our bottom. In other words, we refer to
astronauts in orbit as "weightless" even though the force of the
earth's gravity on them is only about 10% less than it is on the
surface of the earth (in order to get around this problem, NASA
invented the execrable term "microgravity" to describe the
circumstance of astronauts in orbit, and a whole genration of
students has grown up to think that there is no gravity in space). An
airplane in a "high g" turn renders the occupants of the airplane
"heavier" in common parlance. And passengers on high speed elevators
feel both heavier and lighter during the course of their trips,
although the changes in the value of "g" during these intervals are
microscopic, and udetectable by the body. Furthermore, even the
common definition you mention is not exact. The thing we call the
force of gravity of the earth, as it is normally used, that is, the
reading of a scale when both scale and user are at rest and firmly
planted on the earth, includes the effects of the earth's rotation on
that reading, which varies with latitude.

Let's try this as an alternative definition of weight: the net value
of all the forces acting on the body *except* gravity. Since we are
incapable of sensing gravity, this seems like an intuitive way to
proceed. It makes weight a variable quantity depending on the
acceleration of the object being weighed. If it is not being
accelerated, the net force, including gravity, is zero. So the net
force excluding gravity would be numerically equal to that of
gravity, and gives the traditional answer. but if the object is being
acclerated, then excluding gravity gives a value different from the
traditional value, but more in keeping with common usage. What
physics texts commonly define as weight, that is mg, we simply call
"the force of gravity," and we can incorporate a modification for the
rotation of the earth depending on the level of sophistication of the
class. We could then go back to calling orbiting objects weightless,
and we could create this condition (not just simulate it) in aircraft
flying ballistic orbits (the "vomit comet"), and approach it in
underwater exercises, or while diving or riding in certain amusement
park rides. And best of all, we could banish the word "microgravity"
to where it belongs: intergalactic space. It would not seem so
paradoxical to talk about weighing more or less, depending on the
state of our acceleration, and we wouldn't have to confuse students
by continually telling them that they only "feel" heavier or lighter,
it isn't "real." It would be real. The force of gravity on us would
be mg, which we cannot sense. The net effect of all the other forces
on us would be weight [m(g-a)--a vector equation], which we can
readily sense. Amidst all of the new concepts that the students are
swimming confusedly through, here at least would be one that they
could understand, because it conforms to their experience.

Hugh
--

Hugh Haskell
<mailto://haskell@ncssm.edu>
<mailto://hhaskell@mindspring.com>

(919) 467-7610

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