Re: F=ma

["Miguel A. Santos" <msantos@ETSE.URV.ES>]

On Tue, 9 Nov 1999, Leigh Palmer wrote:

> I recognize that what I've said above applies also to Newton's
> second law when it is applied to forces of contact. There is a
> possibility of a causal element when Newton's law is applied to
> forces that act at a distance, however.

But not within Newtonian mechanichs, isn't it?
Could you explain a bit more what you mean in this last sentence?
I suppose you're thinking in terms of an interaction which travels with
finite velocity. But for Newton, altough he admitted no to be comfortable
with it, the forces acted intstantly. It would seem that not even for
forces acting at a distance could you mantain then your 'causal element'.


> Anyway, this discussion has reminded me that F=ma is not Newton's
> second law of motion; it is only part of that law, which Newton
> stated in words explicitly recognizing the causal nature of the
> interaction. I think now that the direction of the equation
> probably doesn't matter as much as I had thought it did, since
> several people in this group parse it actively while I parse it
> passively. Perhaps the best teaching strategy is to note the
> diversity in interpretation which is possible and to show the
> students both ways, permitting each to choose the version which
> is more comfortable.
 Now I feel more confortable with the status of this thread. After all,
I started to understand something about F=ma only after having made quite
enough exercises, and having seen with them enough different manners in
which to thing about this law. But I still remember coming across the
question of 'who is first, F or a?' (this is how I remember it now).

 Personally, I prefer 'F=ma', because (1) it seems to me easier to
remember a relation where there is only multiplications and no quotients,
(2) it can always be discused as it is done for the lever or crossbar:
        -willing to get the same 'a', the greater the 'm' is so is 'F'
        -etc.(similar for the two other combinations).

 I thing that many times the 'causality' in a relation is artificially
introduced by our language and the way we use it: we have the custom to
read things from left to right, which results in giving the lhs. of an
equation a privileged place, altough, from an algebraic or logical point
of view, the equal sign is a relation of equivalence.

 Whenever I present some material in which I have to give say
quatity A in terms of B (which had been previously defined/given), but
*that is not meant to be the definition of A*, I put A on the lhs.
of the equal sign. So, "when one connects a dry cell V to a resistor R
a current I is stablished which is given by I=V/R", and you have
introduced the causal relation.

 Later one tries to teach the students that this is just a relation
between three magnitudes which can also be put like V=IR, and that the key
point is the functional relationship.

 Well, I'm a physicist and I got time to learn this point, but what about
the three-years ingeneers studies? Here in Spain, they all have an almost
common physics course during his first semester. Should one also care
about how to state things like F=ma? Is it worth enough, I mean, does this
care improves really their understanding?
 What about at High School? Is this refinement really effective or can it
be subtituted by letting them do enough exercises, discussion,...?

 Just curious about what your (you all) longer experience in implementing
new methodolgies tells you.

 Have a nice day.
 Regards,
        Miguel A. Santos
        msantos@etse.urv.es