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*From*: Bob Sciamanda <trebor@VELOCITY.NET>*Date*: Tue, 3 Feb 2004 10:00:11 -0500

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?)to)

of attempts to bypass the force concept and begin with (and be confined

energy/momentum concepts (lifted out of the air). To me, the forceconcept

(embodied in all three N laws) is the indispensible root basis ofNewtonian

mechanics.at

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:kinetic

Quoting Brian Blais <bblais@BRYANT.EDU>:

I was wondering if anyone knew of a calculation showing that the

potentialenergy of an object in a circular orbit is equal to half of the

energy, where the calculation does *not* use acceleration or force

all.original

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

largerpost.in

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,

the simple case of a 1/r potential, one small mass orbitting a much

course.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

cover.This course has no prerequisites, is not followed by further physicscourses,

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

toOthers would perhaps disagree with my choices, but I am certainly open

andconsidering other options. I found that covering energy and momentum,pretty

much in 1-D, was a way that I could link classical physics, relativity

coverquantum 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

acceleration,force at all: everything is in terms of energy. I do cover

butusually

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,

usuallydenoted U=mgh, without mentioning that "g" is an acceleration by writingit in

units of J/(m*kg), and describing it as the energy needed to lift 1 kg 1meter

high. Accleration can also be covered in terms of changes in momentumover

time, which of course is equivalent to the standard kinematic way ofstudents

describing acceleration.

I feel that if there are only a few rules, conservation of

energy/momentum/etc., used in many different circumstances, then the

will gain an appreciation for the *simplification* that physicsdescriptions

entail.

Kepler's law, which is high on my list of priorities to teach, is

derived from acceleration and force, and not with energy. If I had asimple

derivation of the KE=1/2 PE relationship, then Kepler's law followslaw,

straightforwardly. Lacking this, I could decide not to teach Kepler's

cover enough of the other concepts (acceleration due to gravity, andforce) 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

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