Re: Impulse

["John S. Denker" <jsd@MONMOUTH.COM>]

At 09:49 AM 10/31/01 -0500, Justin Parke wrote:
> I understand the concept of impulse as the time integral of a force.  This
> definition remains true regardless of the time interval.

OK.

> In other cases "an impulse" means a force over a vanishingly small time
> interval (like a hammer striking a bowling ball).

Also true.

> These uses of the term impulse are not identical.

They are related but not identical.  The latter can be considered a
limiting case of the former, where a given momentum-transfer is
concentrated into shorter and shorter intervals.

> The first is well defined, the second does not seem as well defined to me,

Yes, the second is somewhat unphysical.  A real hammer and real bowling
ball interact over some clearly nonzero time.

Limits of the type in question are quite dodgy.  They're commonly called
"delta functions" but technically they're not even functions.  (Calling
them "delta distributions" would be more correct.)  They make sense inside
of integrals (where they get multiplied by some infinitesimal dt before
contributing anything to the physics) and in a few other special cases, but
you've got to be careful.  You certainly aren't allowed to multiply two
distributions, for example.

We can discuss this if anybody is interested, but for now it should suffice
to observe that explanations in terms of limits and distributions are going
far in the opposite direction of what Tina was asking for at the beginning
of this thread.

Actually, I'm a bit mystified as to why the subject of "impulse" needs to
be discussed in an introductory course.  Who needs it?  Is there a concept
here, or is it just terminology for the sake of terminology?  Why not just
talk about momentum transfer and leave it at that?