Re: [Phys-L] Systems

[John Denker <jsd@av8n.com>]

On 02/11/2014 03:35 PM, Jeffrey Schnick wrote:
> When we were talking about a beaker of water on a pan balance, with
> a steel ball having been lowered intoit,  I considered the beaker of
>  water as the system, hence my system was what the engineers call a 
> control mass.  Because the steel ball was in contact with the
> system, momentum was flowing from the steel ball into the system.
> You insisted on considering a control volume to be the system.  To
> my mind, by doing so, you complicated the problem in that you then
> had to concern yourself with momentum flow in the string that was 
> supporting the steel ball.  Why the insistence on a control volume
> in this case?  To me, your introduction of the equation dE=PdV+TdS 
> indicates that you are comfortable with using a control mass as your 
> system.

Let me say a few words that may or may not answer the question:
My outlook is colored by experience with fluid dynamics.  The 
foundation stone for a big part of fluid dynamics is Euler's
equation.  Deriving that -- and understanding it -- is little
more than an exercise in switching from the control-mass point 
of view to the control-volume point of view.
  http://www.av8n.com/physics/euler-flow.htm

I can switch back and forth from one viewpoint to the other ten
times in a single minute without noticing.  If somebody wants me
to /explain/ why I chose this-or-that viewpoint, that's more of
a challenge.

  Corny analogy:  When I'm riding my bike, I can switch gears
  ten times in a mile without noticing.  If somebody wants me
  to /explain/ what's going on, for instance if I'm teaching
  some kid how to ride, I /can/ explain it, but it might take
  me ten minutes to explain all the factors that go into a single
  shift.

  Sometimes the answer is based on 20/20 hindsight:  I've been
  down this road before, and I'm shifting in anticipation of
  something that's around the corner where the kid can't yet
  see it.

> [.....] rotating bullet [.....]
> I can see considering the bullet to consist of two parts, a nose part
> and a tail part for instance, and each of those parts can be a
> subsystem, but I'm not familiar with the way you used the term
> subsystem as a subset of the degrees of freedom.  Is that a common
> use of the expression?

That's quite a different question, but oddly enough, the answer
is almost the same.

Believe it or not, I'm trying to keep things simple, to get the
job done with the minimum of ideas.   There's a saying among
fishermen that you can catch a big fish with a small hook but
not vice versa ... but if you're using a small hook, make sure
it is reeeeally strong.

Here's the deal:  The idea of multiple subsystems aka multiple 
parcels is simple but really powerful.  It is a small but ultra-
strong hook.  It can handle hard problems and easy problems, 
all without much fuss.  Note the contrast:
 -- The multi-subsystem idea is natural for fluid dynamics, but 
  it can also cover the idea of some degrees of freedom out of
  equilibrium with others.
 -- The converse does not hold:  The "thermal" / "non-thermal" 
  distinction is natural for the cold, rapidly-moving bullet,
  but it cannot be extended to cover ordinary fluid dynamics.

I have a lousy memory, but I have learned to compensate.  That
is, if I'm going to go to the trouble of learning something, I
need to make sure it is simple, powerful, and versatile.

==========================

Note that Newtonian mechanics is essentially all based on the
control-mass approach.

In contrast, the conservation laws are most conveniently stated 
using the control-volume approach.

BTW, to forestall any unnecessary "QED before Newton" remarks,
let me point out that according to my observations, and also
some guy named Piaget, conservation is something that people
pick up fairly early.  I see not the slightest evidence that
it is more difficult or more esoteric than Newtonian mechanics.