Mechanics: From Aristotle to Einstein.
Chapter 1
Machanics Before Galileo
Meaning of mechanics:
Atomists (pre-Socratic) view on physics:
Plato:
Aristotle’s position was between the two (Plato and the atomists):
Meaning of mechanics:
- Area concerned with construction, design and operation of machines.
- Area that treats motions and tendencies in material bodies.
Atomists (pre-Socratic) view on physics:
- There was no distinction between terrestrial and celestial regions.
- Both regions were filled with atoms and the void.
Plato:
- Ultimate elements of physical bodies are geometrical.
- Divided the celestial realm.
- Importance of sense experience.
Aristotle’s position was between the two (Plato and the atomists):
- Celestial and terrestrial realms were different.
- Celestial bodies are perfect and move eternally.
- All terrestrial bodes were composed of Earth, Air, Fire or Water (Copernican).
- The bodies move to their natural places: earth falls to earth. Firer and air rise.
“Again, things which are thrown are in motion, though that which pushed them is not touching them, either because of mutual replacements, as some say, or because the air that has been pushed pushes (them) with a motion which is faster than the locomotion of the things pushed, that is, the locomotion with which those things travel to their proper place.”
If you throw a ball in the air, it will keep going in the air, because the force of air is stronger than that of the ball which is trying to return to its place, so it will push the ball forward in the air.
Aristotle did not believe in the existence of the void space. (it made no logical sense to speak of nothing, because the speed of a body in a void would be infinite).
It is thought that during the Medieval period, there were no contributions to science and that science was left apart. This is not entirely true, but there were contributions by Pierre Duhem and Nicole Oresme.
If you throw a ball in the air, it will keep going in the air, because the force of air is stronger than that of the ball which is trying to return to its place, so it will push the ball forward in the air.
Aristotle did not believe in the existence of the void space. (it made no logical sense to speak of nothing, because the speed of a body in a void would be infinite).
It is thought that during the Medieval period, there were no contributions to science and that science was left apart. This is not entirely true, but there were contributions by Pierre Duhem and Nicole Oresme.
Chapter 2
Galileo and Terrestrial Mechanics
Aristotle: Against the notion that void is necessary for motion.
(Simplicio) he says that motion destroys the void.
Galileo challenges Aristotle’s doctrine on the basis of an experiment.
Free-fall:
“When we hold and then simultaneously release a heavy and a light ball, we in fact most invariably release the lighter ball sooner, giving it a small head start.” (Due to differential motion fatigue in our hands.)
Bodies in free fall move in such a way that their speed at any point is proportional to their times of fall.
Isochronism of the pendulum:
The time of swing of any pendulum is the same, no matter what weight or material of the pendulum bob may be and no matter what the size of the arc through which it swings is.
The only thing that may make a difference is the length of the chord.
Aristotle: Against the notion that void is necessary for motion.
(Simplicio) he says that motion destroys the void.
Galileo challenges Aristotle’s doctrine on the basis of an experiment.
Free-fall:
“When we hold and then simultaneously release a heavy and a light ball, we in fact most invariably release the lighter ball sooner, giving it a small head start.” (Due to differential motion fatigue in our hands.)
Bodies in free fall move in such a way that their speed at any point is proportional to their times of fall.
Isochronism of the pendulum:
The time of swing of any pendulum is the same, no matter what weight or material of the pendulum bob may be and no matter what the size of the arc through which it swings is.
The only thing that may make a difference is the length of the chord.
THIRD DAY
On Local Motion
There are many essential things that yet haven’t been remarked or demonstrated regarding motion, like:
Galileo’s treatise is divided into three parts:
Naturally accelerated motion:
I like the way he tries not to invent the definition of accelerated motion, but tries to capture the essence of it.
Equable movement: when is equal times, equal spaces are traversed.
Remarks:
“If the moveable were to continue its motion ay the degree of momentum of speed acquired in the first little part of time, and were to extend its motion successfully and equably with that degree, this movement would be twice as slow as that of the degree of speed obtained in two little parts of time.”
Assuming that the intensification of speed is made according to the extension of time.
Even though the moveable object passes through each degree, it only passes there without remaining there beyond and instant.
Uniformly accelerated motion: that in which the speed goes increasing according to the increase of space traversed.
DEFINITION:
“We shall call that motion equably or uniformly accelerated which, abandoning rest, adds on to itself equal momenta of swiftness in equal times.”
The one true assumption:
Postulate: “ I assume that the degrees of speed acquired by the moveable over different inclinations of planes are equal whenever the heights of those planes are equal.”
On Local Motion
There are many essential things that yet haven’t been remarked or demonstrated regarding motion, like:
- In heavy falling objects continually accelerate; there is no proportion for the acceleration that takes place.
- Spaces run through in equal times by a moveable descending from the rest, maintain themselves the same rule as do the odd numbers following upon unity.
- Missiles or projectiles trace out a curve line; no one has proved it is a parabola.
Galileo’s treatise is divided into three parts:
- Equable or uniform motion
- Motion of naturally accelerated
- Violent motion projectiles
Naturally accelerated motion:
I like the way he tries not to invent the definition of accelerated motion, but tries to capture the essence of it.
Equable movement: when is equal times, equal spaces are traversed.
Remarks:
“If the moveable were to continue its motion ay the degree of momentum of speed acquired in the first little part of time, and were to extend its motion successfully and equably with that degree, this movement would be twice as slow as that of the degree of speed obtained in two little parts of time.”
Assuming that the intensification of speed is made according to the extension of time.
Even though the moveable object passes through each degree, it only passes there without remaining there beyond and instant.
Uniformly accelerated motion: that in which the speed goes increasing according to the increase of space traversed.
DEFINITION:
“We shall call that motion equably or uniformly accelerated which, abandoning rest, adds on to itself equal momenta of swiftness in equal times.”
The one true assumption:
Postulate: “ I assume that the degrees of speed acquired by the moveable over different inclinations of planes are equal whenever the heights of those planes are equal.”
Propositions