Re: [Phys-l] interaction

[John Denker <jsd@av8n.com>]

On 08/04/2007 07:32 PM, I wrote:

>      Energy is primary and fundamental.    Energy is conserved.
>      Momentum is primary and fundamental.  Momentum is conserved.

There exist nice pedagogical ways to illustrate an indirect interaction 
of the type that we have been discussing recently.  The interaction is 
easily handled in terms of momentum.

One place to start is with a hands-on demo using Newton's Cradle:
  http://www.zerotoys.com/newsite/products/images/NewtonsCradleLarge1.jpg

Label the balls (left to right) #1 through #5.  Pull back ball #1 
as shown in the figure, then let go. 

Observations:  Ball #1 hits ball #2 and comes to rest.  Balls
#2, #3, and #4 remain nearly at rest, nearly at their original
positions.  Ball #5 goes flying.

Analysis:  To a good approximation:
 -- All of the rightward momentum initially in ball #1 is transferred 
  out of ball #1, which is a big net loss of rightward momentum for 
  that ball.
 -- Rightward momentum flows /through/ balls #2, #3, and #4 with no 
  net gain or loss of momentum for those balls.
 -- Rightward momentum flows into ball #5, which is a big net gain of
  rightward momentum for that ball.

  Note that the direction of flow is distinct from the direction of
  momentum.  A /push/ is a rightward flow of rightward momentum, or
  (equivalently) a leftward flow of leftward momentum.  In contrast,
  a /pull/ would be a rightward flow of leftward momentum, or a
  leftward flow of rightward momentum.  

    And you can go on from there.  A certain type of /shear/ is +X
    transport of +Y momentum.  This might be observed in a block
    sliding with friction, or in connection with viscous flow.  

    Also, a certain type of torque can be described as a +Z flow of 
    XY angular momentum.  That's an example of positive helicity.  

    Et cetera.

The Subject: line asks about "interactions".  Does ball #1 have an 
interaction with ball #5?  Not directly, but indirectly.  The indirect 
interaction is /mediated/ by balls #2, #3, and #4.  

  ++ This indirect interaction is nicely analogous to the interaction 
   between two electrons, /mediated/ by the field.

  ++ It is also nicely analogous to an airplane in flight, which
   very indirectly interacts with the ground.  The airplane 
   interacts directly with some air, which interacts with some
   other air ... etc. ... which eventually interacts with the 
   ground, thereby supporting the weight of the airplane.

I've seen more situations than I can count where keeping track of 
"equal and opposite forces" was a losing proposition, while keeping 
track of the momentum solved the problem nicely.

*) Diagramming the force-pairs is notoriously difficult,  especially for 
 novices.  It's a real dilemma:
 -- Sometimes you want to show only the forces acting on one chosen body
  (or parcel of fluid).  This requires breaking all the force pairs.
 -- If you show all the force pairs, readability may suffer, and/or you
  may be tempted to distort the depiction of the points of application
  of the forces.  See 
     http://www.av8n.com/how/htm/motion.html#fig-momentum-budget
  for an example of such a distortion.
 -- Diagramming shear forces is particularly vexatious.

*) The alternative is to diagram the momentum flow.  
 -- Making good diagrams is still not easy.
 -- There is risk of double-counting if you diagram the rightward flow
  of rightward momentum /and/ the leftward flow of leftward momentum.
  This is not a big problem.  I wish all my problems were this small.
 ++ In any case, diagramming the momentum flow is often easier than 
  diagramming the force-pairs, especially when the situation is complicated.


 Here's one way to do it.  The black ----> arrows show the direction of 
 flow, while the associated >> symbols show /what/ is flowing.
   http://www.av8n.com/physics/img48/momentum-flow.png
 Within each row, all three diagrams depict the same force i.e. the same
 momentum flow.
 The top row depicts the contact force as the block sits on the table.
 The second row depicts the frictional shear force as the block slides
 toward the left with velocity V.