Re: [Phys-l] momentum dissipation?

[John Denker <jsd@av8n.com>]

On 04/26/2010 09:47 AM, Scott Orshan wrote:
> Let me first comment on the statement
>
> Momentum should be covered in it's entirety before acceleration comes
> up (except for a fancy word that means 'Slope of a Velocity Graph').

That's one opinion.  IMHO it is somewhat overstated,
but I understand the underlying sentiment.
 
> The way I see it, students should be able to work out any dynamics 
> problem using Newton's 2nd, Newton's 3rd and the definitions of velocity 
> and acceleration before they are ever even exposed to momentum and 
> mechanical energy.

That's another opinion.

There is overwhelming evidence that you can do it
either way:
 -- conservation laws first, or 
 -- force laws first.

De gustibus non disputandum.

My personal preference is for conservation laws first,
but I am not going to argue for either extreme.  I am
going to argue against both extremes.

> Momentum and mechanical energy are convenient ways to integrate changes 
> in position under conditions of varying forces (and sometimes masses) 
> whose profiles may not be entirely known, but they are just that 

No, they are not "just" that.  Not even close.

>  - a 
> tool, rather than the fundamental factors that are involved in the 
> cause-effect relationships that define dynamics. (Forces, masses, 
> delta-positions and delta-times.)

That is diametrically wrong.  There is nothing in physics 
more fundamental than the conservation laws.

Relativity changes the force laws, but not the conservation
principles.  Quantum mechanics changes the force laws, but
not the conservation principles.  The conservation law are
fundamental.

> An object does not change its motion because it knows it has to conserve 
> momentum. It changes its motion because it is being pushed on. That is 
> what students have to realize. Ask the simple question:
>
> When two pool balls collide and bounce, why does one go in one 
> direction, and the other go in another direction?

If the intent is actually to ask literally "why" (as in 
cause and effect) then the question is unphysical and 
should not be answered literally.  Usually when people 
ask "why" they don't mean it literally, and would be 
better off asking "how do you know".
  http://www.av8n.com/physics/causation.htm

Physics needs to say what will happen in this-or-that
situation.  It sometimes -- but not necessarily -- says
/how/ it happens.  It rarely if ever says /why/ it happens.
In particular, the laws of motion have nothing to say about 
cause and effect.  This has been recognized since Day One
of modern science (1638) and indeed this recognition has
been cited as /defining/ what we mean by Day One.  
  Reference:  Stillman Drake.

> If the answer is, "To conserve momentum" then they don't get it. If the 
> answer is "Equal forces were applied to each, in the opposite 
> directions" then they understand a little better.

I vehemently disagree;  see below.
 
> Regarding the airplane moving through the air, if it is moving at a 
> constant velocity in a straight line, then its momentum isn't changing 
> (ignoring fuel being burned and exhausted). So whatever it does to one 
> piece of the air, there has to be an opposite motion to another piece of 
> air.

This is completely wrong physics.  This is not an opinion.
It is provably wrong physics.
 
> Ask your students to brainstorm this:
>
> In order to stay in the air, the wings and the air must exert equal 
> down/up forces on one another. It usually appears that the air is being 
> pushed down. So if there is zero net momentum change on the airplane, 
> and the air is being blown downward, what is moving upward?

Force is not the same as momentum.

It is routine to have momentum /flowing through/ a given
region of space without accumulating in that region.

Water flowing around and around in a circular channel
makes the point that flow does not imply accumulation.

The Newton's cradle apparatus offers an easy, clear
demonstration:  
  -- initial: ball #1 in motion, incoming; 
              balls #2,3,4,5 at rest.
  -- final:   ball #5 in motion, outgoing; 
              balls #1,2,3,4 at rest.

Momentum de-accumulates from ball #1 and accumulates in
ball #5.  Momentum flows through balls #2,3,4 without
accumulating there.

This is profoundly important physics ... yet it is easy
to understand, easier than the force laws.  I have no 
trouble explaining this to third-graders.

Bottom line:  There are some problems that are more easily
handled in terms of force, and other problems that are 
more easily handled in terms of momentum and energy ... 
plus scads of problems that can be handled either way.

In the fields of physics of flight in particular and fluid 
dynamics in general, the momentum-and-energy approach is
by far the easier way to go.  To say the same thing the
other way, trying to draw the free body diagram for the 
forces on the boundary of a fluid element is needlessly
complicated, vastly more complicated than keeping track
of the momentum flow.