Re: Apparent weight

[Leigh Palmer <palmer@sfu.ca>]

Bob Carlson wrote:

> In a message dated 98-02-14 13:35:36 EST, you write:
>
> << Once our students get this separation of weight from the mg force, then
> they are far more successful with solving dynamics and statics problems. >>
>
> This is surprising since most texts I've used define weight as mg.  I've just
> looked through these texts that all define W = mg.

Well, drop the other shoe. Presumably the books had already defined mass,
inertially I hope. If W = mg is a definition, what is it a definition of?
There are two new quantities in there, W and g. How was g defined?

I think this textbook practice (which seems to be quite common) is sloppy.

> What texts define it differently and therefore make statics and dynamics
> problem solving easier?

Mine would. But then it would also talk about "centrifugal force", and
the term "centripetal force" would never appear at all! If you don't
think that would make solving problems easier then you have not been
properly introduced to the topic of so-called "frame forces". I won't
write my textbook, however. It would also introduce mechanical
impedance and have some radical departures in other areas as well. I
won't write it because there is no market for it. No one wants to
believe that a textbook that doesn't include every topic in Halliday
and Resnick, in the order given in Halliday and Resnick, with the same
symbols and definitions used in Halliday and Resnick, etc., can be any
good. Other* quite well-conceived textbooks have failed because they
were unlike Halliday and Resnick. Who would be so foolish as to attempt
a replication of an experiment which has given consistent results so
many times?

It doesn't make the problem solving easier, but David Hestenes's fine
textbook "New Foundations for Classical Mechanics" does not define
weight at all. In order to avoid the problem he says on p. 318:

                          _    _
  The gravitational force f = mG exerted by the Earth on an object

  is called the *true weight* of the object. The object's apparent
         _
  weight W is

      _    _     _   _    _   _
      W = mg = m(G - w x (w x r)).

  This is the resultant of the gravitational and centrifugal forces

  (Figure 6.1), which are difficult to separate near the surface of

  the Earth, because they are slowly varying functions of position.


(I have tried to compensate for the typographical handicaps of ASCII
in the quote above, but I may not have succeeded in doing so.) In any
event, if you will obtain a copy of this text you will see the topic
treated rigorously and correctly. The book is unsuitable for use as an
introductory textbook for reasons of level and mathematics, but if you
take the considerable trouble to master those it is a wonderful book
for the adventurously inclined physicist. Of course it has suffered
the inevitable fate of revolutionary textbooks and is now out of print.

Hestenes defines W as mg also, but he has previously defined m, G, w,
and r, and in this paragraph he defines g. All are done properly and
with appropriate rigor. (His father was a very distinguished professor
of mathematics at UCLA.)

Leigh

* e.g. Albert Baez's "Physics: a Spiral Approach"