🚀 go-pugleaf

On Wed, 17 May 1995, Guntbert Reiter wrote:

> "Donald E. Simanek" <dsimanek@EAGLE.LHUP.EDU> wrote:
> >
> > When you said
> >"Forces cause acceleration (not necessarily movement)" that seemed to me
> >contradictory, for how can you have acceleration without movement?
>
> Of course you can: imagine two "identical" cars with identical
> velocity heading towards each other (velocities aligned) an
> crashing "totally" inelastic (I hope the term is correct). The
> result would be: _first_ a rather big amount of acceleration for
> both objects and _second_  a bunch of torn metal lying there and
> no trace of "movement" left. (This sure is drastic..).

Two interesting issues are raised here. One is the fact that from the
instant just before the cars make contact to the time when they lie at
rest, a twisted mess, there *is* motion, lots of it, during the
deformation process. In fact, if colliding bodies were perfectly rigid,
the velocity would have an infinite discontinuity at collision, and the
acceleration of each body would be infinite. Conclusion: there must be
some deformation of the bodies, and perfectly rigid bodies are impossible,
unless you are willing to deal with infinite accelerations, and the
accompanying infinite forces.

The other is the definition of acceleration:

a = lim (t2 --> t1) [v(t2)-v(t1)]/(t2-t1)

This cannot give a nonzero result unless there is some change of velocity
in the neighborhood of the time at which the acceleration is calculated.
That is, there must be some motion in the vicinity of that point.

I'll offer this for discussion: "You cannot have nonzero accelertion of a
body without movement of that body." I'm assuming here that the
measurements are made in an inertial frame. By movement I mean that the
body changes position over a *finite* time interval, which is what we
usually mean by movement. (You can hardly define movement at a
single infinitesimal instant, or you'd get into some Xeno-like
paradoxes.) This reminds us of the dangers of using terms like
'movement' which haven't been definied carefully in the course, but which
everyone has a colloquial understanding of. This is what causes student
difficulties in accepting that at the top of the trajectory of a ball
thrown straight up, its velocity is instantaneously zero, though its
acceleration is still g (nonzero). "Isn't it *moving* there?" they say.
Who can blame them? I venture the opinion that even those who have had a
calculus course can still fall into traps like this, for they haven't
mastered calculus concepts either.

I've tried to choose words with care here, but see below.

And a correction:

When I said,

> >> >The torque due to a couple is obviously Fd where F is the size of
> >> >either one of the forces and d is the perpendicular displacement between
> >> >them.

I was unforgivably careless in use of language, as Guntbert noted. The
phrase 'due to' should have been 'of'. (10 points deducted!) I got it
right later on in another message of the same thread:

> > "The torque of a couple is the same wherever it is applied..."

which Guntbert liked a lot better.

> *Thats it: The torque of a couple...*

This is another example of how subtleties of language, and imprecise use
of words, can lead us astray in physics teaching. As the old poem goes:

        I try to choose my words with care
        And strive to keep them sweet.
        For they may be the words that I
        Shall later have to eat.

Or something like that.

        -- Donald