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Re: Galileo's Freefall Experiment



On Sun, 13 Sep 1998, Bob Sciamanda wrote:

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


It is in "Two New Sciences" right around section 108. The argument is
specious, as many of Galileo's arguments were, when he argued "in the
style of Aristotle".

I've given students Galileo's argument and asked them to expose its
errors. Generally this exercise is a distaster. I get naive comments like
"Well, Galileo's conclusion is right, isn't it? So his argument *must* be
right." Or, some students are still in the Aristotelian mode of thought
and can't imagine any flaw in a "logical-sounding" argument so long as
its conclusion doesn't challenge their preconceptions. It shows how
little critical thinking is developed in education.

Note (from reading "Two New Sciences") that Galileo was clearly making his
argument assuming (as did Aristotle) that the body was falling in a fluid
medium, and that the medium affected the body by varying amounts,
depending on the medium's "density". We can do an experiment on this. Get
some muffin cups (paper) or coffee filters. They fall in air as Aristotle
said, with nearly constant speed (reaching terminal velocity very
quickly). The heavy one will fall 1.4 meters while the light one falls one
meter. Easily tested without a stopwatch by starting them at these heights
and listening for the simultaneous "plop" when they land. Glue two cups
together (or use the heavier foil cup of the same size). A heavy cup and a
light one fall at different speeds. Now fasten the heavy and light one
together and drop them together, as Galileo proposed. Three cups will fall
1.76 meters while one falls one meter. See the law: 1, square root of 2,
square root of 3, etc.? Nice, inexpensive lab experiment.

There's no record of Galileo ever perfroming any experiment of dropping
anything from a high tower, and only the later account of Vivani (one of
Galileo's pupils) says he did. In "Two New Sciences" , section 107, he
puts these words into the mouth of his character Sagredo: "But I,
simplicio, who have made the test can assure you that a cannon ball
weighing one or two hundred pounds or even more, will not reach the ground
by as much as a span ahead of a musket ball weighing only half a pound,
provided both are dropped from a height of 200 cubits."

Note that he doesn't say that they will reaxch the ground at the same
time, but will not be separated by more than a span as one reaches the
ground first.

I'll excerpt a section of my "Science History Quiz" from my website. The
Quiz exposes the known facts about some 20 other fables of science
history. Textbooks too often present these without bothering to check the
historical facts. I welcome additional information about these blunders,
for I will soon have the time and inclination to improve and extend this
document.

-- Donald

......................................................................
Dr. Donald E. Simanek Office: 717-893-2079
Professor of Physics FAX: 717-893-2048
Lock Haven University of Pennsylvania, Lock Haven, PA. 17745
dsimanek@eagle.lhup.edu http://www.lhup.edu/~dsimanek
......................................................................

18. Who first proposed the experiment of dropping two balls of
different weight from a high tower to test Aristotle's assertion that
they'd fall at equal speeds?

The Byzantine scholar John Philoponus (or John the Grammarian) (6th
century CE) described such an experiment:

For if you let fall from the same height two weights of which one
is many times as heavy as the other, you will see that the ratio of
times required for the motion does not depend on the ratio of the
weights but that the difference in time is a very small one. And
so, if the difference in weights is not considerable, that is, if
one is, let us say, double the other, there will be no difference,
or else an imperceptible difference, in time, though the difference
in weight is by no means negligible, with one body weighing twice
as much as the other. [26]

One of Tartaglia's pupils, Giovanni Benedetti, in 1533, proposed the
experiment of dropping two balls, one heavy and one light, from a
tower to test Aristotle's assertion that they would fall with equal
velocities. Flemish engineer Simon Stevin did the experiment and
published the results in 1586. There was very little difference in how
fast the balls fell. Stevin includes an experimental detail of
considerable importance, determining the simultaneity of landing by
the sound as they hit a board:

My experience against Aristotle is the following. Let us take (as
the very learned Mr Jan Cornets de Groot, most industrious
investigator of the secrets of nature and myself have done) two
spheres of lead, the one ten times larger and heavier than the
other, and drop them together from a height of 30 feet onto a board
or something on which they will give a perceptible sound. Then it
will be found that the lighter will not be ten times longer on its
way than the heavier but that they will fall together onto the
board so simultaneously that their two sounds seem to be one and
the same rap. [27]

Galileo described the experiment in his Dialogues of two New Sciences,
and refers several times in other writings to having done such an
experiment from a high tower, but never names a particular tower.
Here's Galileo's account:

But I, Simplicio, who have made the test can assure you that a
cannon ball weighing one or two hundred pounds or even more, will
not reach the ground by as much as a span ahead of a musket ball
weighing only half a pound, provided both are dropped from a height
of 200 cubits...the larger outstrips the smaller by two
finger-breadths, that is, when the larger has reached the ground,
the other is short of it by two finger-breadths.

The well-known and often-repeated story that Galileo did this
experiment from the Leaning Tower of Pisa can be traced back to just
one uncorroborated source: Vincenzo Vivani, Galileo's last pupil and
biographer. Vivani's account describes this as a public demonstration,
with the entire university specially assembled by Galileo to observe
it. Galileo would have been in his twenties and a professor at Pisa
then. No university record confirms this event, nor does anyone who
might have been there, other than Vivani, mention it. [28]

F. S. Taylor says ``As Professor Lane Cooper has pointed out in an
entertaining pamphlet, [29] the versions of the story differ widely.
Sometimes they are one pound and 100 pounds, sometimes they are one
pound and ten pounds; one ingenious author makes Galileo enclose
different materials in equal-sized boxes, presumably to make their
air-resistance the same.'' This shows how colorful fables are
embellished and amplified by authors indifferent to historical
accuracy.