Re: Galileo's Freefall Experiment

["Bob Sciamanda" <trebor@velocity.net>]

On third thought, there is a valid re-wording of Galileo's argument which
is valid and has useful content:
If different objects accelerate at different rates in a given force
field, then a "weird" conceptual model would be required to describe the
acceleration produced on an object by this field as a universal monotonic
function of only a single extensive (additive) property (eg. mass) of the
object .

a1 = f (m1);    a2 = f(m2);   then it is required that if 1 and 2 are
combined => a12 = f(m1+m2)

For simplicity, take all quantities as only positive and let f(x) be a
decreasing function of x.

Now let  m1 >m2  (without loss of generality); then we have: a1 < a2 <
a12.

There is nothing wrong with this (nature can do what it likes) but
CONCEPTUALLY, we would like to describe the combined situation as body 1
slowing down body 2 and body 2 speeding up body 1, so that we would
expect: a1 < a12 < a2.

So the model is weird conceptually. Newton's model by-passes the original
restriction by allowing a (in a given force field) to be a function of
two parameters: charge (electric, gravitational, etc) and mass.  It is
then the  RATIO of these two parameters which controls the acceleration.

So, Galileo is saying that only a weird model can account for different
objects having different accelerations (in a given field on the basis of
the difference in MASS ALONE.

-Bob

Bob Sciamanda
Physics, Edinboro Univ of PA (ret)
trebor@velocity.net
http://www.velocity.net/~trebor
-----Original Message-----
From: Bob Sciamanda <trebor@velocity.net>
To: phys-l@atlantis.uwf.edu <phys-l@atlantis.uwf.edu>
Date: Sunday, September 13, 1998 1:01 AM
Subject: Re: Galileo's Freefall Experiment


> Hi Tom,
>    I don't think there is any record of Galileo actually doing the
> experiment, but - if memory serves me - he did offer the argument that
> different objects must fall at the same rate simply because they surely
> must do so if fastened together!  This is a specious argument (it could
> just as "logically"  be applied to electric fields).
> I think this is in his "Two New Sciences".
>
> Bob Sciamanda
> Physics, Edinboro Univ of PA (ret)
> trebor@velocity.net
> http://www.velocity.net/~trebor
>
> -----Original Message-----
> From: Tom McCarthy <TMccarthy@steds.org>
> To: phys-l@atlantis.uwf.edu <phys-l@atlantis.uwf.edu>
> Date: Saturday, September 12, 1998 11:03 PM
> Subject: Galileo's Freefall Experiment
>
>
> > Hello,
> >    I have a question.  Supposedly, Galileo performed a freefall
> experiment
> > where he dropped a composite object of two pieces and the dropped them
> > separately.  Does anyone know the gist of this experiment or where
there
> is
> > a good read on the subject.
> >    Thanks a lot in advance.
> > Tom McCarthy
> > Saint Edward's School
> > 1895 St. Edward's Drive
> > Vero Beach, FL  32963
> > 561-231-4136
> > Physics and Astronomy