Re: Galileo's Freefall Experiment

["Tom McCarthy" <tmccarthy@steds.org>]

When I look at these arguments, I try to place myself in their shoes.  What
were the concetual frameworks of the day and how were various people
knocking them down.  I think Aristotle was looking at falling objects in
terms of a natural tendency.  I don't think he had a good idea what a force
was but that nature had a way of acting upon objects.  If the object was
placed in water, they behaved the same way but scaled down.  When Galileo
proposed his argument, I don't think he had this dual nature in mind-gravity
and mass.  He just had mass.  So he proposed this argument, based upon his
conceptual framework, to expose the ridiculousness of Aristotle's claim.
Shouldn't he have concluded, though, from your statement of connectedness
that the accel. should increase as the mass increased?
    I know that surface area and so on makes a big difference but if the
mass got larger and the face of the object looking downward stayed the same,
wouldn't Galileo have to conclude the accel increases as mass increases?  He
used cannon balls as his objects, so he couldn't measure a difference.  He
should have used coffee filters!  It seems like he didn't quite understand
things either!
    Again, thanks for the insights.

Tom

-----Original Message-----
From: Bob Sciamanda <trebor@velocity.net>
To: phys-l@atlantis.uwf.edu <phys-l@atlantis.uwf.edu>
Date: Monday, September 14, 1998 11:25 AM
Subject: Re: Galileo's Freefall Experiment


> 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