Re: transfer of momentum

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 12:13 -0500 11/19/03, John S. Denker wrote:
> In this area and practically every other area, it
> is good to have more than one way to do things.
> Front door and fire escape.  Belt and suspenders.
> If I can solve a problem only one way, I get
> worried.

Right. And I guess I don't need to add (but obviously I am going to
anyway) that for the beginning student, these multiple techniques
should be learned one at a time, and it is not wise to overload the
student with multiple approaches before they have digested the first
one. So it seems to me that this thread is mostly about what order we
should bring in the multiple approaches.

My personal preference is with Chuck's sequence, which starts with
momentum transfer (the well-known moving company), extends that to
impulse, then force, then Newtons' laws, and only then introduces the
formal idea of acceleration. And only after they see acceleration as
a formal concept do they get to the special case of constant
acceleration, and those ubiquitous formulas like at^2/2, and the
like. That way, they already know that these formulas, useful though
they are, are only a special case of something much more general.
Finally, after they have become conversant with all the rest, we give
them the capstone--energy, the really useful way to solve many
problems that they couldn't before.

Some have argued that perhaps energy should come first or perhaps
second, but I rather think there are advantages to putting it last.
Energy is a pretty abstract concept, and introducing it too early can
give the students the impression that it is more than an idea, and
may even make them resistant to approaches that are useful, but may
be a bit harder to apply. I think I want students to understand the
concept of forces before I load them down with energy.

But at the end of this, the students do have several useful ways to
solve most any problem (if, of course, they haven't forgotten the
first ones by the time they get to the last). We emphasize this
repeatedly--if you can't do a problem one way, try another. But we
try to make sure that the first way is absorbed before we add the
next.

Hugh
--

Hugh Haskell
<mailto:haskell@ncssm.edu>
<mailto:hhaskell@mindspring.com>

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