Re: Newton's second law

[Robert Cohen <Robert.Cohen@PO-BOX.ESU.EDU>]

I've been following this thread with interest as I've been bothered by
the same things as Justin.

It seems to me that there are three important points to consider:

1. Newton's second law relates the force *on the system* with the change
in momentum *of the system*.  What does it mean to say that the mass of
the system changes?  Consider, for example, if I was sitting on the
train.  I have a certain momentum.  Then, all of a sudden, I look at my
hand.  My hand has a different momentum.  Oh no...vdm/dt is not zero!
But v hasn't changed!

2. In the context of F_net = dp/dt, mass "disappearing" is more akin to
*momentum* disappearing.  In other words, the mass doesn't really leave
the system.  Rather, the momentum of the "lost" mass changes to zero.
In terms of Newton's second law, we can apply the law twice, once to the
train and once to the sand, then (along with Newton's third law) and
show (using dm for the mass of the sand) that

0 = m_train dv_train/dt + v_train dm/dt

is true only if the mass of the sand goes from v_train to zero.

3. In Justin's original example (of sand being thrown perpendicular to
the tracks), we have to keep in mind that Newton's second law is a
vector equation.  The system, in this case, includes the earth and the
earth/train gains a momentum opposite to the momentum imparted to the
sand.  The momentum of the system in the forward does not change.

Am I on the "right track" here? (sorry - couldn't resist)
____________________________________________________
Robert Cohen; 570-422-3428; www.esu.edu/~bbq
East Stroudsburg University; E. Stroudsburg, PA 18301


> -----Original Message-----
> From: Forum for Physics Educators 
> [mailto:PHYS-L@lists.nau.edu] On Behalf Of Justin Parke
> Sent: Thursday, November 06, 2003 7:33 PM
> To: PHYS-L@lists.nau.edu
> Subject: Re: Newton's second law
>
>
> Conceptually I understand quite clearly the difference 
> between sand with no initial horizontal component of velocity 
> falling *into* a rolling train car and sand leaking *out* of 
> a train car.  My question has to do with my apparent 
> misunderstanding of the statement of NII and what "vdm/dt" means.
>
> John Mallinckrodt has provided me with the most satisfying 
> answer so far, but I welcome further input.
>
> Basically, I do not want to tell my students something like, 
> "this term is equal to zero just because you know it must 
> be."  This perpetuates the idea of physics as a mysterious