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Re: Apparent weight



Date: Tue, 17 Feb 1998 11:37:27 EST
Reply-to: phys-l@mailer.uwf.edu
From: Raacc@aol.com
To: phys-l@atlantis.uwf.edu
Subject: Re: Apparent weight

A. R. Marlow writes:

<<However, exactly as in the case of the centrifuge, we
are psychologically tempted to create a downward force
acting on us and pressing us to the surface of the earth;
it doesn't exist, can do no work and isn't perceived by
our senses, and so it is rightly said to be fictitious.
In the course of Einstein's development of general
relativity (over a period of several years), he realized
this, and expressed it in the form of the observation that
such a "force" could be transformed away by a mere change
of reference frame. (This is never the case with a real
force.) He then went on to work out what gravitation is
-- the effect of traveling through curved spacetime.
These real effects are as present on the space shuttle or
in a freefalling elevator as they are at the surface of
the earth. The main difference in the space shuttle is
that no one is tempted to create a fictitious downward
force since they do not experience any upward push from
the earth.>>

Enlightening, now back to earth. First to quote Johnny
Cash: I hear that train a coming, its coming round the
bend.

I once took a two quarter circuit analysis course. During
the first quarter, we ended studying RLC circuits. In the
second quarter, Fourier and Laplace transforms were
introduced. The author posed the question, and I'm
quoting from memory. Why did we not introduce these
transforms earlier? Then he answered his question.
Because it would be like using a locomotive to crack a
walnut.

If you were teaching a first quarter course in mechanics,
how would you approach the problems below? Remember that
most of your students will not be physicists, but many
will be engineers. Also, they will transfer to
engineering schools that have certain prerequisites and
that are perfectly capable of teaching the physics they
want their students to know.

Now I have an exam to write for an engineering statics
class. While Newton's name permeates the text, I don't
recall seeing Einstein's name once. I wonder how those
bridges stay together?

Choose your model. How do you approach these problems?
If you use a free body diagram, what do you call the
forces acting on the mass?

1. A mass is sitting on the floor of an elevator. The
elevator may be at rest, accelerating up, or accelerating
down.

2. Same as Number 1, except the mass is on a scale in the
elevator.

3. Same as Number 1, except the mass is hanging from a
rope attached to the ceiling of the elevator.

4. Same as Number 1, except the mass is on a chair and
the chair is suspended from ropes attached to the ceiling
of the elevator.

5. The mass is in near earth orbit.


Bob Carlson

Oh, what a tangled web we weave. I suppose the subject
above is a misnomer. What I am really talking about is the
Newtonian idea of forces that appear in rotation. You have
heard about the amusement-park ride in which you stand with
your back to a wall in a rotating cylinder and the bottom
falls out of the cylinder.

My take on all of this is the following: (1) (according to
Newton). The wall of the cylinder exerts a force on us to
keep us going in a circle. Without that force we would fly
off in a straight line. No centrifugal force needed or
wanted according to Newton. (2) (according to the modern
theory of mechanics) Sometimes when making a mathematical
model of this kind of rotation it is useful to treat just
the radial part of the motion. When we do that we find
that we have to deal with the angular momentum of our
bodies about the center of the rotation in order to have a
realistic model. From the Lagrangian or the Hamiltonian
form of the theory a part of the kinetic energy of the body
can be converted into a "centrifugal potential". This
centrifugal potental will result in a centrifugal force
when the equations of motion are written. It is a fiction
in the sense that it appears only because we have separated
out one of the degrees of freedom, but it is not a real
force in the sense that, in the analysis, it actually comes
from the kinetic energy term via the angular momentum. (3)
If now you want to get really "picky" about this you can
pull out "Mach's Principle" and claim that all frames of
reference are equivalent. Then you must deal with these
forces physically. This is a problem the Einstein grappled
with. Opinions differ as to whether he solved the problem!
WBN


Barlow Newbolt
Department of Physics and Engineering
Washington and Lee University
Lexington, VA 24450
Telephone and Phone Mail: 540-463-8881
Fax: 540-463-8884
e-mail: NewboltW@madison.acad.wlu.edu

"Prediction is very difficult, especially about the future."

Neils Bohr