Re: [Phys-l] a conservation equation

["LaMontagne, Bob" <RLAMONT@providence.edu>]

My original musings were really related to the the language we use. We subdivide energy into kinetic (energy of motion) and potential (energy of position)

But even though we can develop from F=ma an equation like

mgt1 j + p1 = mgt2 j + p2  (vector p's)  

that looks a lot like the corresponding energy equation, we don't talk about a kinetic momentum (momentum of motion) or a potential momentum (momentum of "time") - it's just momentum. 

The term mgt is rarely seen explicitly - and I have never seen it refered to as momentum. The closest we come to writing it is when we refer to impulse and change in momentum, and then we see it as mg(delta t). It is the asymetry of approaches that struck me as interesting.

Bob at PC



-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker
Sent: Wednesday, March 17, 2010 2:23 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] a conservation equation

On 03/17/2010 08:25 AM, LaMontagne, Bob wrote:

> mgt1 j + p1 = mgt2 j + p2  (vector p's)         [1]
>
> This is formally similar to the conservation of energy equation,

As the subject line suggests, this is a conservation
equation.  All conservation equations look alike, as
they should.

Equation [1] expresses conservation of momentum.  It
is "formally similar" to conservation of charge, 
conservation of energy, conservation of baryon number,
and so forth.

> the
> difference being that it is a vector equation and that it involves
> momentum and a term mgt analogous to mgy. The energy equation
> conserves the sum of KE and a positional energy. The other equation
> conserves the sum of momentum and a temporal term.

I wouldn't say "momentum and a temporal term".  It
conserves momentum, period.  Force times time is
momentum, and momentum is the subject of equation [1].

> Is anyone aware of an attempt to develop a momentum-time conservation
> approach 

Again:  It's not momentum-time.  It's just momentum.

> to physics similar to the familiar KE-position conservation
> approach -  i.e., an attempt to avoid an impulse-momentum approach by
> using a conservation law involving momentum and a temporal potential
> of sorts similar to an avoidance of a work-KE approach by using
> conservation of KE and positional energies? I would assume that the
> biggest impediment would be finding suitable forces that are
> functions of time instead of position.

Equation [1] is just plain conservation of momentum.

Conservation of momentum is a bedrock principle, used
day in and day out in innumerable ways, throughout all
of physics, engineering, et cetera.

For starters, the so-called third law of motion is most
usefully expressed in terms of conservation of momentum.

In particular, there are many situations such as fluid
dynamics where talking about the force balance at a 
point is hopelessly confusing, but talking about the
momentum content and momentum flow is straightforward
(and is therefore the conventional approach).

On 03/17/2010 09:45 AM, Herbert Schulz wrote:

> > Conservation of Energy (a scalar conservation law) and Conservation
> > of Momentum (a vector conservation law) are true under different
> > conditions. It is possible for either, both or neither to be true
> > depending upon the conditions.

I disagree.

Conservation of energy and conservation of momentum are
bedrock principles of physics, true for all practical
purposes (and other purposes besides) under all conditions.

Do not confuse "conservation" with *constancy*.
  http://www.av8n.com/physics/conservative-flow.htm#sec-conservation+-constancy

On 03/17/2010 10:49 AM, Bob Sciamanda wrote:

> > > Noone in this thread is denegrating the usefulness of the momentum 
> > > conservation theorem for closed systems.

But my point is that conservation applies, and has always
applied, even to non-closed systems.  Do not confuse
conservation with constancy.
  http://www.av8n.com/physics/conservative-flow.htm#sec-conservation+-constancy

> > > We were speculating regarding the possible usefulness of defining a 
> > > "potential momentum function" and turning the impulse/momentum theorem into 
> > > a conservation principle encompassing external forces.  

There is no "speculation" required.  Conservation of momentum
is a bedrock principle of physics, even for non-closed
systems.  Do not confuse conservation with constancy.
  http://www.av8n.com/physics/conservative-flow.htm#sec-conservation+-constancy

A conservation law (as opposed to a constancy law) always
accounts for transfer across the boundary.  External 
forces are the transfer term in the conservation of
momentum equation.  The represent momentum flowing 
across the boundary of the region.  For example, using
conservation of momentum in this form, including the 
flow terms, is central to the derivation of the Euler
equation for fluid flow.
  http://www.av8n.com/physics/euler-flow.htm

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