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Re: [Phys-l] Weight vs mass



I still think it is a mistake to look for "the" date when the
distinction between weight and mass first appeared. It seems
clear that a /partial/ understanding existed very early, and
additional understanding accumulated gradually.

Inertia (as distinct from weight) is observable whenever you have
something massive moving horizontally with not too much friction.
Surely inertia was understood by Themistocles (580 BC) when he
chose to fight in the narrow waters off Salamis, exploiting the
maneuverability (or lack thereof) of the various ships.

It takes 30 seconds of furious rowing to get a trireme up to full
speed. This has to do with inertia, and nothing to do with weight
per se, in the sense that we're not trying to /lift/ the ship.
Top speed is dictated by friction, but the _time_ to get to top
speed depends on inertia; without inertia top speed would be
reached instantly. If you stop rowing, the trireme will coast
for a long, long ways, exhibiting inertia in its most obvious
form.

Inertia (as distinct from weight) may also be observable when you
have something moving in response to a force that is not simply
proportional to its mass. This does *not* include the systems
that Galileo is most famous for studying, such as inclined planes
and pendulums, because the mass drops out of the equation of
motion for such systems.

It does however include buoyant forces. Galileo (1638) discussed
this at some length, e.g. page 106 (National Edition). His
terminology is a bit messy, but he does make clear that weight
[gravità] is not the whole story, and that other considerations
including corpulence, crassitude, and density must be considered.
On page 111 he says:
"For instance, a marble egg will fall through water a hundred
times as fast as a hen's egg, but through air it will not get
four inches ahead in a distance of twenty braccia."
He also points out that a wooden ball doesn't fall at all in water,
but rises ... whereas in air a wooden ball and a stone ball behave
very similarly.

The idea of weightlessness relative to a freely-falling observer,
which we now know as the "Einstein elevator" argument, is given
by Galileo on page 108.

AFAICT Galileo doesn't quantify the general relationship between
force and acceleration, or force and terminal velocity. Instead
he makes a number of important qualitative points, and proves that
his contemporaries' conventional wisdom (handed down from Aristotle)
was quite wrong.

Speaking of ancient Greeks, and of buoyancy, the guy who was
*not* wrong was Archimedes. Schoolbooks commonly give him
credit for "Archimedes's princple" of simple buoyancy ... but
he also discovered and explained (ca 250 BC) the principles
of *stability* for boats and the like, which is orders of
magnitude more sophisticated. I'm not sure this speaks
directly to the question of mass versus weight but it surely
speaks to mass versus /size/, which is a super-important
piece of the overall puzzle.

========================

All this serves to reinforce my already-very-low opinion of
the "historical" approach to teaching introductory science.
History is complicated. It is so complicated that nobody
has ever used /real/ history to organize or motivate an
introductory science course. It can't be done. What we
see instead is something I call the "twistorical" approach,
i.e. something that depends on a grossly twisted pseudo-history.

Kuhn had something to say about this.

I support teaching the history of science. All I ask is that
it be the true history of science, not some hokey just-so story.

In introductory courses, we should present the best available
evidence, which is usually very different from the most ancient
evidence.

There is no law that says pedagogy must recapitulate phylogeny.