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Re: PHYS-L Digest - 1 Feb 2004 to 3 Feb 2004 (#2004-34)

Addendum:
Even if you lift out of the air the conservation of gratuitously defined
energy (K + P) and momentum, how do you arrive at the existence of an
orbital trajectory without (gratuitously) adding the stipulation that the
momentum exchange is central? This is tantamount to introducing the central
force concept.

Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
http://www.velocity.net/~trebor
trebor@velocity.net
----- Original Message -----
From: "Bob Sciamanda" <trebor@VELOCITY.NET>
To: <PHYS-L@lists.nau.edu>
Sent: Tuesday, February 03, 2004 9:40 AM
Subject: Re: PHYS-L Digest - 1 Feb 2004 to 3 Feb 2004 (#2004-34)


I would comment that this is an instance of the weakness (incompleteness?)
of attempts to bypass the force concept and begin with (and be confined
to)
energy/momentum concepts (lifted out of the air). To me, the force
concept
(embodied in all three N laws) is the indispensible root basis of
Newtonian
mechanics.

Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
http://www.velocity.net/~trebor
trebor@velocity.net
----- Original Message -----
From: "Brian Blais" <bblais@BRYANT.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Tuesday, February 03, 2004 9:26 AM
Subject: Re: PHYS-L Digest - 1 Feb 2004 to 3 Feb 2004 (#2004-34)


On Tue, 3 Feb 2004, Automatic digest processor wrote:

Quoting Brian Blais <bblais@BRYANT.EDU>:

I was wondering if anyone knew of a calculation showing that the
kinetic
energy of an object in a circular orbit is equal to half of the
potential
energy, where the calculation does *not* use acceleration or force
at
all.
Is there an argument for this based purely on energy concepts?

0) Be careful, the result as stated only applies to objects
orbiting in a 1/r potential (although generalizations are
possible to other power laws).

I was assuming a gravitational situation, and wasn't clear in my
original
post.

1) Certainly it is possible to derive the viral theorem
without mentioning acceleration. The standard derivations
don't mention it. Indeed you don't need to know the masses
of the particles involved.

Look at
http://math.ucr.edu/home/baez/virial.html
about halfway down, in the section called "the proof".


Actually, this derivation refers to force. Perhaps I should have asked,
in
the simple case of a 1/r potential, one small mass orbitting a much
larger
one, is there a simple way of obtaining the KE=1/2 PE relationship?

3) Why do you care, anyway? If you know the potential,
you implicitly know the force, and conversely if you know
the conservative force you implicitly know the potential,
plus or minus an arbitrary gauge term.

Good question! I teach an algebra-based, 1-semester intro physics
course.
This course has no prerequisites, is not followed by further physics
courses,
and may be (perhaps) the last science class the students will ever take.
As
such, it doesn't fit into the mold that most textbooks use. Because of
limited time, I have to be very selective in the topics that I can
cover.
Others would perhaps disagree with my choices, but I am certainly open
to
considering other options. I found that covering energy and momentum,
pretty
much in 1-D, was a way that I could link classical physics, relativity
and
quantum mechanics without introducing a huge number of new concepts each
time. I found that vectors took too long to cover well, so I don't
cover
force at all: everything is in terms of energy. I do cover
acceleration,
but
I am trying to see if there is any way I can get away without that to.
For
example, I can cover near-surface gravitational potential energy,
usually
denoted U=mgh, without mentioning that "g" is an acceleration by writing
it in
units of J/(m*kg), and describing it as the energy needed to lift 1 kg 1
meter
high. Accleration can also be covered in terms of changes in momentum
over
time, which of course is equivalent to the standard kinematic way of
describing acceleration.

I feel that if there are only a few rules, conservation of
energy/momentum/etc., used in many different circumstances, then the
students
will gain an appreciation for the *simplification* that physics
descriptions
entail.

Kepler's law, which is high on my list of priorities to teach, is
usually
derived from acceleration and force, and not with energy. If I had a
simple
derivation of the KE=1/2 PE relationship, then Kepler's law follows
straightforwardly. Lacking this, I could decide not to teach Kepler's
law,
cover enough of the other concepts (acceleration due to gravity, and
force) to
come up with Kepler's law, or assert the KE = 1/2 PE relation is either
empirical or "has a derivation beyond the scope of the class".

thanks,

Brian Blais

-----------------

bblais@bryant.edu
web.bryant.edu/~bblais