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Aristotle’s laws of motion

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Aristotle (Ἀριστοτέλης) 384–322 BCE was a Greek philosopher and scientist born in the city of Stagira, in classical Greece.

Aristotle bust

At 17 years of age, he joined Plato’s Academy in Athens and remained there until the age of thirty-seven (c. 347 BCE)

ancient-athens-map

His writings cover many subjects – including physics, biology, zoology, logic, ethics, poetry, theater, music, linguistics, and politics. They constitute the first comprehensive system of Western philosophy.

Shortly after Plato died, Aristotle left Athens and, at the request of Philip of Macedon, tutored Alexander the Great beginning in 343 BC.

Aristotle’s views on physical science profoundly shaped medieval scholarship. Their influence extended from Late Antiquity and the Early Middle Ages into the Renaissance, and were not replaced systematically until the Enlightenment and theories such as classical mechanics.

  • excerpted and adapted from Aristotle. (2016, October 20). Wikipedia, The Free Encyclopedia.

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Aristotle’s laws of motion

Aristotle bust
Aristotle set out 3 laws of motion, based on observations (but not on experiment)

* objects fall at a constant rate, that depends on their size and weight.

* there is a difference between “violent motion” versus “natural motion”

* objects in the heavens (the celestial sphere) move in circular motion,
without any external force compelling them to do so.
objects on Earth (the terrestrial sphere) move in straight lines,
unless forced to move in a circular motion.

Here is the modern, correct view of how gravity accelerates objects of different masses. (Does the mass and size affect the speed at which they fall?)

Yet here is Aristotle’s view of how gravity accelerates objects of different masses. (How does this differ from the previous animation?)

Aristotles view of gravity

What about pushing and pulling?

Natural vs Unnatural Motion

For objects on Earth, Aristotle thought that objects moved by people (“unnatural motion”) would move in a straight line, and when that “unnatural force” ran out, then natural motion would take over.

So what would happen if a canon fired a cannonball? Aristotle supposed that it would move in a straight line (due to the unnatural force), and then would fall straight down (due to a different, natural force.)

aristotle-idea-of-cannonball-not-projectile-motion

For Aristotle, once “violent motion” (from people) extinguished itself, natural motion takes over, and then the cannon ball falls to its natural place, the earth.

An animation of what this would look like.

However, as Galielo showed in the 1500’s, Aristotle’s view isn’t correct at all.  Anyone who watches an archer fire an arrow into the air, and carefully observes, would see that this doesn’t happen.

Galileo showed that the vertical motion (up/down) and horizontal motion (size-to-side) are independent.

When you fire an arrow, cannonball, or pop-fly in baseball, into the air, what happens?

The vertical motion slowly decreases, reaches zero (at the peak), and then increases in the opposite (downward) direction.

The horizontal motion actually stays constant (doesn’t speed up, or slow down.)

projectile-motion-canon-on-cliff

Heavenly forces vs terrestrial forces

Aristotle thought that heavenly (celestial) objects, by their nature, forever moved in circles – without any external force acting on them.

Earthly (terrestrial) objects were believed to have a separate set of laws of motion. Earthly objects supposedly would always stop moving, of their own accord, on their own.

As we will learn, there aren’t really 2 sets of laws (heavenly and earthly); rather, the laws of nature are the same everywhere:

* objects naturally travel only in straight lines.
* for objects to have a circular motion requires some external force,
keeping them pulled into a circular path

How could one of the greatest thinkers of the classical world be in error?
The ancient Greeks had a preference for attempting to find truth
through logic alone. Greeks viewed observations of the physical world
as a valid way  to learn, but held this to be inferior to intellect.

Also, Aristotle never ran experiments, so he was very limited in
what he could observe.
In the medieval era, Galileo (and others) ran controlled experiments.
The results of these experiments were analyzed with math.

Their findings ended the acceptance of Aristotelian physics.

Galileo learned critical thinking skills from his father, Vincenzo

Galileo and Einstein: History of Physics – Prof Michael Fowler

Vincenzo Galilei, father of Galileo.

Vincenzo Galilei, father of Galileo.

Galileo continued his father’s tradition of critical inquiry

Galileo rolled balls along surfaces tilted at different angles.

a. When ball rolls downward, it moves with Earth’s gravity, and its speed increases.

b. When ball rolls upward, it moves against gravity and loses speed.

c. When ball rolls on level plane, it doesn’t move with or against gravity.

 Galileo rolls balls slope

a. The ball rolls down the incline, and then up the opposite incline,
and reaches its initial height.

b. As the angle of the upward incline is reduced,
the ball rolls a greater distance before reaching its initial height.

c. If there is no friction, then the ball will never stop – unless it hits something.

Galileo rolls balls no friction never stops

Galileo’s conclusion was supported by another line of reasoning.

He described two inclined planes facing each other, as in Figure 3.4.
A ball released to roll down one plane would roll up the other to reach nearly the same height.
The smoother the planes were, the more nearly equal would be the initial and final heights.
He noted that the ball tended to attain the same height,
even when the second plane was longer,
and inclined at a smaller angle than the first plane.
Always, the ball went farther and tended to reach the same height.

Inclined Plane – Galileo’s Battle for the Heavens PBS NOVA

Video clip: Galileo’s inclined plane PBS media

Advanced: Similar studies with the moment of inertia

Rolling balls, cylinders and tubes down inclined plane: Moment of Inertia

http://makeagif.com/i/sWbNgM

 

Something special: The brachistochrone – curve of quickest descent. And the tautochrone- the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point.

brachistochrone-and-tautochrone-curve

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Aristotle’s laws of motion.

Excerpted from a lecture by Professor Michael Fowler, U. Va. Physics, 9/3/2008

http://galileoandeinstein.physics.virginia.edu/lectures/aristot2.html

What Aristotle achieved in those years in Athens was to begin a school of organized scientific inquiry on a scale far exceeding anything that had gone before. He first clearly defined what was scientific knowledge, and why it should be sought. In other words, he single-handedly invented science as the collective, organized enterprise it is today. Plato’s Academy had the equivalent of a university mathematics department, Aristotle had the first science department, truly excellent in biology, but, as we shall see, a little weak in physics.

After Aristotle, there was no comparable professional science enterprise for over 2,000 years, and his work was of such quality that it was accepted by all, and had long been a part of the official orthodoxy of the Christian Church 2,000 years later. This was unfortunate, because when Galileo questioned some of the assertions concerning simple physics, he quickly found himself in serious trouble with the Church.
Aristotle’s method of investigation:

defining the subject matter

considering the difficulties involved, by reviewing the generally accepted views on the subject, and suggestions of earlier writers

presenting his own arguments and solutions

This is the pattern modern research papers follow, Aristotle was laying down the standard professional approach to scientific research.

Aristotle often refuted an opposing argument by showing that it led to an absurd conclusion, this is called reductio ad absurdum (reducing something to absurdity). As we shall see later, Galileo used exactly this kind of argument against Aristotle himself, to the great annoyance of Aristotelians [people who fully agreed with Aristotle] 2,000 years after Aristotle.

[Aristotle himself likely would not have minded later thinkers disagreeing with him; in his lifetime Aristotle would change his mind, if he found new information or a more logical argument.]

In contrast to Plato, who felt the only worthwhile science to be the contemplation of abstract forms, Aristotle practiced detailed observation and dissection of plants and animals, to try to understand how each fitted into the grand scheme of nature, and the importance of the different organs of animals.

It is essential to realize that the world Aristotle saw around him in everyday life was very different indeed from that we see today. Every modern child has since birth seen cars and planes moving around, and soon finds out that these things are not alive, like people and animals. In contrast, most of the motion seen in fourth century Greece was people, animals and birds, all very much alive. This motion all had a purpose, the animal was moving to someplace it would rather be, for some reason, so the motion was directed by the animal’s will.

For Aristotle, this motion was therefore fulfilling the “nature” of the animal, just as its natural growth fulfilled the nature of the animal.

To account for motion of things obviously not alive, such as a stone dropped from the hand, Aristotle extended the concept of the “nature” of something to inanimate matter. He suggested that the motion of such inanimate objects could be understood by postulating that elements tend to seek their natural place in the order of things:

So earth moves downwards most strongly,
water flows downwards too, but not so strongly, since a stone will fall through water.
In contrast, air moves up (bubbles in water),
and fire goes upwards most strongly of all, since it shoots upward through air.

This general theory of how elements move has to be elaborated, of course, when applied to real materials, which are mixtures of elements. He would conclude that wood has both earth and air in it, since it does not sink in water.

Natural Motion and Violent Motion

Things also move because they are pushed. A stone’s natural tendency, if left alone and unsupported, is to fall, but we can lift it, or even throw it through the air.

Aristotle termed such forced motion “violent” motion as opposed to natural motion.

The term “violent” just means that some external force is applied to it.

Aristotle was the first to think quantitatively about the speeds involved in these movements. He made two quantitative assertions about how things fall (natural motion):

Heavier things fall faster, the speed being proportional to the weight.

The speed of fall of a given object depends inversely on the density of the medium it is falling through.

So, for example, the same body will fall twice as fast through a medium of half the density.

Notice that these rules have a certain elegance, an appealing quantitative simplicity. And, if you drop a stone and a piece of paper, it’s clear that the heavier thing does fall faster, and a stone falling through water is definitely slowed down by the water, so the rules at first appear plausible.

The surprising thing is, in view of Aristotle’s painstaking observations of so many things, he didn’t check out these rules in any serious way.

It would not have taken long to find out if half a brick fell at half the speed of a whole brick, for example. Obviously, this was not something he considered important.

From the second assertion above, he concluded that a vacuum cannot exist, because if it did, since it has zero density, all bodies would fall through it at infinite speed which is clearly nonsense.

For violent motion, Aristotle stated that the speed of the moving object was in direct proportion to the applied force.

This means first that if you stop pushing, the object stops moving.

This certainly sounds like a reasonable rule for, say,
pushing a box of books across a carpet, or an ox dragging a plough through a field.

(This intuitively appealing picture, however, fails to take account of
the large frictional force between the box and the carpet.
If you put the box on a sled and pushed it across ice,
it wouldn’t stop when you stop pushing.
Centuries later, Galileo realized the importance of friction in these situations.)

Learning Standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework
HS-PS2-1. Analyze data to support the claim that Newton’s second law of motion is a
mathematical model describing change in motion (the acceleration) of objects when
acted on by a net force.

HS-PS2-10(MA). Use free-body force diagrams, algebraic expressions, and Newton’s laws of motion to predict changes to velocity and acceleration for an object moving in one dimension in various situations

Massachusetts History and Social Science Curriculum Framework

The roots of Western civilization: Ancient Greece, C. 800-300 BCE.
7.34 Describe the purposes and functions of development of Greek institutions such as the lyceum, the gymnasium, and the Library of Alexandria, and identify the major accomplishments of the ancient Greeks.

WHI.33 Summarize how the Scientific Revolution and the scientific method led to new theories of the universe and describe the accomplishments of leading figures of the Scientific Revolution, including Bacon, Copernicus, Descartes, Galileo, Kepler, and
Newton.

A FRAMEWORK FOR K-12 SCIENCE EDUCATION: Practices, Crosscutting Concepts, and Core Ideas
PS2.A: FORCES AND MOTION
How can one predict an object’s continued motion, changes in motion, or stability?

Interactions of an object with another object can be explained and predicted using the concept of forces, which can cause a change in motion of one or both of the interacting objects… At the macroscale, the motion of an object subject to forces is governed by Newton’s second law of motion… An understanding of the forces between objects is important for describing how their motions change, as well as for predicting stability or instability in systems at any scale.

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