Re: [Phys-L] ? FCI --> momentum flow

[John Denker <jsd@av8n.com>]

On 10/21/2013 03:12 PM, Jeffrey Schnick wrote:

> Now let's talk about what the original question was about, the
> upward flow of downward momentum.

OK.

> Consider the same vertical stack of three books.

OK.

> Downward momentum is flowing upward from the earth.

OK.

> As it gets to the bottom book, some of that momentum turns around
> and starts flowing downward and some of it keeps going up through
> the bottom book to the middle book.  Right here is the problem.
> Downward momentum is flowing upward from the bottom book to the
> middle book, but, it does not correspond to a downward force being
> exerted on the middle book by the bottom book; rather, it is a force
> being exerted on the middle book by the earth.

I reckon that too many different concepts are hiding behind the
proposition "it" in that passage.

The problem goes away if we consider three separate upward flows.
  Flow I)   The flow of downward momentum from the earth to Book I.
  Flow II)  The flow of downward momentum from the earth to Book II.
  Flow III) The flow of downward momentum from the earth to Book III.

The way the books are stacked, Flow III must pass through the space
occupied by Book I and Book II on its way to Book III.  However, it
would be a red herring to say it "flows through the books" because
the books have got nothing to do with it.  Flow III was going to
pass through that space no matter what, with or without Book I
and/or Book II.

Also it might help to use the term "carried by" in contrast to
"passing through".  The return flow -- i.e. the downward flow 
of downard momentum -- is /carried by/ the atoms and chemical 
bonds of the table and other stuff.

We can also label each part of the overall flow according to what 
law of physics is responsible for that part.  The gravitational
part of the flow /never/ turns around.  If and when the overall
flow turns around, it is because some non-gravitational interaction
has come into play.

Newtonian gravity is a /central force/ which guarantees that
each and every gravitational part of the momentum flow always 
flows in a straight line.

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

I should draw a more complicated version of the diagram
  http://www.av8n.com/physics/force-intro.htm#sec-balanced-forces
showing the separate flows in more detail.   Alas, that would take
more of my time than is available at the moment.

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

> One might try to get out of the dilemma by saying that the momentum
> in question is simply disappearing from the earth at the same rate as
> it is appearing in the middle book.  This is flow and it is globally
> conservative.  However, there is a closed surface containing the
> earth and momentum gets from inside that surface to outside that
> surface without ever flowing through that surface.

In the immortal words of Richard Nixon:  We could do that, but it
would be wrong.

> Hence such a flow is not locally conservative.

Which is how you know it is wrong.  All in all, we have a fine
proof by contradiction:  This is how you know that the hypothesis
of momentum "disappearing" and "reappearing" somewhere else is 
not viable.  For more on this, see
  http://www.av8n.com/physics/conservative-flow.htm