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Message: 6
Date: Fri, 22 Feb 2008 15:33:47 -0600 (CST)
From: Jack Uretsky <jlu@hep.anl.gov>
Subject: Re: [Phys-l] non-conservative --> non-grady ???
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Message-ID: <Pine.LNX.4.64.0802221527400.2131@theory.hep.anl.gov>
Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed
1. That the work done around a closed path is zero;
2. That the force is time independent and derivable from a potential.
Reggards,
Jack
On Thu, 21 Feb 2008, Alfredo Louro wrote:
> On Thu, Feb 21, 2008 at 10:04 PM, Jack Uretsky <jlu@hep.anl.gov> wrote:
>> Hi all-
>> Since the two statements are mathematically equivalent, as far as
>> I can see, why is either one to be preferred?
>> Regards,
>> Jack
>>
>
> Well, I thought earlier I would conclude my correspondence on this
> particular thread, but I can't help asking which two statements you
> find mathematically equivalent?
>
> Alfredo
>
>
>> On Thu, 21 Feb 2008, John Denker wrote:
>>
>> > On 02/20/2008 09:57 AM, Alfredo Louro wrote:
>> >> "Piecewise time-independent" is not time-independent at all. And
>> >> whether a force is conservative cannot depend on what the particle is
>> >> doing. One way of defining a conservative force is to say the work
>> >> done by it around a closed path is zero. For any closed path. At all
>> >> times.
>> >
>> >
>> > Do we really want to define "conservative force" that way?
>> >
>> > I called attention to a situation
>> > http://www.av8n.com/physics/img48/accelerator.png
>> > where it was uniformly true that the field /applied to/ the
>> > system was
>> > a) independent of time, and
>> > b) the gradient of some potential.
>> >
>> > This is a statement about the field /applied to the system/
>> > at the time and place where the system happens to be.
>> >
>> >
>> > Do we really want to insist that the field be unchanging at
>> > all other times and all other places as well? That seems
>> > kinda strict. Forsooth, it guarantees that the suggested
>> > definition is vacuous. That is, there cannot be any field
>> > that satisfies the terms of this definition, because surely
>> > there is a non-constant field somewhere in the universe.
>> >
>> >
>> > This example seems to reinforce the point I was making at the
>> > beginning of this thread: The whole business of "non-conservative"
>> > force field is just begging to be misunderstood.
>> >
>> > To summarize:
>> > -- If you mean grady, say grady. Calling a non-grady field
>> > "non-conservative" is asking for trouble.
>> > -- Both grady and ungrady force-fields uphold conservation of
>> > energy. No exceptions have ever been observed.
>> > -- Conservation is not the same as constancy. Local conservation
>> > of XX means that XX is constant /except/ insofar as it flows
>> > across the boundary.
>> > -- For an isolated system, conservation would be the same as
>> > constancy, but that's an almost trivial subset of physics.
>> > Physics relies on /local/ conservation laws that can be
>> > applied to non-isolated systems and subsystems.
>> >
>> >
>> > http://www.av8n.com/physics/conservative-flow.htm
>> > http://www.av8n.com/physics/non-grady.htm