[Phys-L] Re: A Third law question

[hhaskell at MINDSPRING.COM (Hugh Haskell)]

At 15:39  -0400 10/13/05, rlamont wrote:
> This is a "straw dog" argument. Momentum conservation comes quite
> naturally from applying Newton's Laws to collisions. N3 gives the
> forces as equal and opposite, the collision times are the same,
> N2 gives the momentum changes of the colliding objects to be
> equal and opposite. Momentum conservation becomes a simple
> consequence of Newton's Laws - not an ad hoc quantity invented
> for the purpose of rationalizing data. Starting from momentum and
> then deriving Newton's Laws is certainly equivalent, but I don't
> see how it is superior. Both approaches require careful study of
> various simple physical interactions, each can then be used to
> produce the other, and they both have the same problem with the
> definition of mass.
You are correct. One can start at either end of the chain and arrive
at the other. My argument is that momentum is something that is more
easily grasped, more visualizable as it were and less abstract, than
is acceleration, which is inherent in Newton's laws. The logic is the
same either way (except that going from momentum to NSL involves
differentiation of the momentum, while going from NTL to momentum
conservation involves integrating the force--I think the former is
easier for introductory students to visualize than the latter,
although they are clearly two sides of the same coin). The only
reason to go one way rather than the other has to do with how well
the students learn.

And it is important to examine the details along the way. What I have
found, however, is that it is easier to get the students to
understand the empirical nature of momentum conservation in
collisions, than it is to get them to understand what they are doing
when they try to measure accelerations under the influence of
different forces.

It is also a very powerful method for solving many problems, which
is, of course, one of the reason why it is so widely used. It also
allows us to look only at the big picture--we don't have to worry
about the nature of the forces or how they are generated or vary with
time--the only thing we need to worry about is the velocity just
before the collision and the velocity just after the collision, and
of course, the mass. But the problem with mass is there no matter
where you start.

Fortunately, most students don't understand that mass is a problem,
and few of them ask the obvious question, "what is mass?" so the
question can usually be introduced at the appropriate time, and the
students can learn that, just like them, we have no idea what mass
(or charge, for that matter) really is, except that it seems to be a
property of matter, and that it can somehow be equated to energy.

But your comments are quite relevant, and the details cannot be
ignored. But which end of the chain you start with is a matter of
pedagogy, not science.

Hugh
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Hugh Haskell
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<mailto:hhaskell@mindspring.com>

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