77
(a) Galileo’s experiments show that all
falling objects have the same motion
if air resistance is negligible.
Aristotle said that heavier objects fell
faster than lighter ones. If two rocks
are tied together, that makes an extra-
heavy rock, (b), which should fall
faster. But Aristotle’s theory would also
predict that the light rock would hold
back the heavy rock, resulting in a
slower fall, (c).
Its speed increases at a steady rate, so in the next second it will travel 19 cm.
(b)(c)
Section 3.1The Motion of Falling Objects
Self-Check
An object is rolling down an incline. After it has been rolling for a short time, it
is found to travel 13 cm during a certain one-second interval. During the
second after that, if goes 16 cm. How many cm will it travel in the second after
that.
A contradiction in Aristotle’s reasoning
Galileo’s inclined-plane experiment disproved the long-accepted claim
by Aristotle that a falling object had a definite “natural falling speed”
proportional to its weight. Galileo had found that the speed just kept on
increasing, and weight was irrelevant as long as air friction was negligible.
Not only did Galileo prove experimentally that Aristotle had been wrong,
but he also pointed out a logical contradiction in Aristotle’s own reasoning.
Simplicio, the stupid character, mouths the accepted Aristotelian wisdom:
S
IMPLICIO
: There can be no doubt but that a particular body ... has a
fixed velocity which is determined by nature...
S
ALVIATI
: If then we take two bodies whose natural speeds are
different, it is clear that, [according to Aristotle], on uniting the two, the
more rapid one will be partly held back by the slower, and the slower
will be somewhat hastened by the swifter. Do you not agree with me
in this opinion.
S
IMPLICIO
: You are unquestionably right.
S
ALVIATI
: But if this is true, and if a large stone moves with a speed of,
say, eight [unspecified units] while a smaller moves with a speed of
four, then when they are united, the system will move with a speed
less than eight; but the two stones when tied together make a stone
larger than that which before moved with a speed of eight. Hence the
heavier body moves with less speed than the lighter; an effect which
is contrary to your supposition. Thus you see how, from your
assumption that the heavier body moves more rapidly than the lighter
one, I infer that the heavier body moves more slowly.
[tr. Crew and De Salvio]
What is gravity.
The physicist Richard Feynman liked to tell a story about how when he
was a little kid, he asked his father, “Why do things fall.” As an adult, he
praised his father for answering, “Nobody knows why things fall. It’s a deep
mystery, and the smartest people in the world don’t know the basic reason
for it.” Contrast that with the average person’s off-the-cuff answer, “Oh, it’s
because of gravity.” Feynman liked his father’s answer, because his father
realized that simply giving a name to something didn’t mean that you
understood it. The radical thing about Galileo’s and Newton’s approach to
science was that they concentrated first on describing mathematically what
really did happen, rather than spending a lot of time on untestable specula-
tion such as Aristotle’s statement that “Things fall because they are trying to
reach their natural place in contact with the earth.” That doesn’t mean that
science can never answer the “why” questions. Over the next month or two
as you delve deeper into physics, you will learn that there are more funda-
mental reasons why all falling objects have v-t graphs with the same slope,
regardless of their mass. Nevertheless, the methods of science always impose
limits on how deep our explanation can go.