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

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

Informative response - but I'm still a little fuzzy about a couple of items. 

I should have been a little more precise and said "momentum flow". I do agree that the momentum requires an integration and some history. However, I find I can't contrive of a situation where it is not "upward" (opposite to the rest of the stack)at a particular moment in the free fall frame. 

Also, what can be said about the momentum flow? Can that be anything but upward (upward flow of upward momentum)?

I am only asking these questions because some of the posters seemed to imply that the distinction between "upward flow of downward momentum" and the other three variants was obvious. It seems that it is frame dependent - and in this case dependent on your view of the role of gravity.

On the other hand, I do like the fact that in the traditional lab frame that most of us would be using, the great thing about the momentum flow approach is that the gravitational force is supplying the same momentum flow to the book whether it is allowed to fall or not. That seems clearer to me than the use of mg for "weight" even if the object is not falling with acceleration g.

Bob at PC

> -----Original Message-----
> From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of John Denker
> Sent: Friday, November 01, 2013 1:40 PM
> To: Phys-L@Phys-L.org
> Subject: Re: [Phys-L] ? FCI --> momentum flow
>
> On 11/01/2013 08:38 AM, LaMontagne, Bob wrote:
>
> > Isn't the momentum of the top book upward?         [***]
>
> 1) In the lab frame, the book is at rest.  It has no momentum,  upward or
> otherwise.
>
> 2) In any freely-falling inertial frame, there is no g-vector and  hence no
> natural definition of "down".  However, in an attempt  to capture the spirit of
> the question and not get unduly nit-picky,  let's switch temporarily to the lab
> frame, paint big arrow on the  wall labelled "This Way Down" and then switch
> back to the freely  falling frame.  This arrow is somewhat unnatural and
> potentially  misleading, so we will have to use it carfully, but for now I
> assume is the intended definition of "down".
>
> 3) Even then, we cannot say that the momentum of the book is  upward.
> The momentum is changing according to
>
>          (d/dt) p = F                 [1]
>
>  where F is the force exerted by the supports.  This force is  in the "upward"
> direction.  However we cannot conclude that  the momentum is upward.  We
> can find the momentum by integrating  the equation of motion [1], but there
> will be a constant of  integration.  Different freely-falling frames will have
> different  constants of integration.  In some frames, the book will start  out
> with an enormous momentum in the "downward" direction, which  gradually
> over time becomes less downward.
>
> > Due to the rigid nature of
> > the earth and the books further down in the stack, the top book is
> > being pushed radially outward relative to the surrounding flow of
> > space-time.
>
> That's all true in the freely-falling frame.
>
> >  Where is the downward force?
>
> We agree that the freely-falling frame, the only relevant /force/ is "upward",
> using the somewhat-unnatural definition of "upward".
>
> Note that upward force is not the same as upward momentum.  I mention
> this because the top-line topic sentence [***] asked about momentum,
> where as the last sentence asked about force.  There is a constant of
> integration.  Different freely-falling frames will have different constants of
> integration.
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