Part 2. Cartes to Newton

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FRICTIONThe Discovery of


The Discovery of Friction

One important breakthrough in the study of motion is the discovery of friction in the seventeenth century. Friction is a resistance force between a moving object and the surface it moves on or the medium it moves in. It tends to stop motion. The basic nature of friction was first made aware by Leonardo Da Vinci (1452-1519) 200 years before Newton even defined what force is. However Leonardo did not published his findings and the credit of discovering friction was awarded to the architect Guillaume Amontons(1663-1705).

Oops!


The Unseen Genie

Friction is like an unseen genie, when you rub against a surface, it comes up and opposes your action. It suffices here to say that the magnitude of the force depends directly on the weight of the object and the nature of the surface. For example, on a rough surface, it will be hard to slide on; but on ice, one can glide effortlessly. Readers who are interested may look up the internet or read from common text books.


Different Game for Aristotle

Had Aristotle been aware of friction in his time, he would not have made so many wrong concepts about motion, because if there were no friction in the world, anything that starts moving would never stop. No more or further force is necessary.

Oh what a different gameI could have played!

No friction


RENE DESCARTESThe Laws of


René Descartes

René Descartes (1596–1650) was a French philosopher and mathematician who developed a theory known as the mechanical philosophy. This philosophy was highly influential until superseded by Newton's methodology.

Carte’s achievement has be so well received in his time that he has been dubbed the father of modern philosophy, and much subsequent Western philosophy is a response to his writings,[which are studied closely even to this day. In particular, his Meditations on First Philosophy continues to be a standard text at most university philosophy departments. Wikipedia


Definition of Motion

In the study of mechanics, Descartes provided the first distinctly modern formulation of laws of nature and a conservation principle of motion.

He accepted the existence of inertial motion (uniform or non-accelerating motion) or bodily rest as natural bodily states.

He regarded motion as “the action by which some body is transferred from one place to another”.


Size and Velocity

The quantity of motion of a body is the size of the body times its speed. This is not to be identified with momentum (mass x velocity), because for Descartes, size and mass are not distinct concepts; at the same time, for Descartes, speed (scalar) and velocity (vector) are not distinct concepts.


Conservation of MotionDescartes also envisioned the conservation of quantity of motion as one of the fundamental governing principles of the entire cosmos. When God created the universe, he reasoned, a certain finite amount of motion (quantity of motion) was conferred to its material occupants; a quantity, moreover, that God continuously preserves at each succeeding moment. Part 2, Article 36.

Due to the immutability and constancy of God, the total quantity of motion of bodies in the universe is conserved.


Conservation of Transference

It is obvious that when God first created the world, He not only moved its parts in various ways, but also simultaneously caused some of the parts to push others and to transfer their motion to these others. So in now maintaining the world by the same action and with the same laws with which He created it, He conserves motion; not always contained in the same parts of matter, but transferred from some parts to others depending on the ways in which they come in contact.

As to the cause of motion, Descartes believed that God is the primary cause, the rest are secondary causes. He said: Part II, Article 62.


Summary of Descartes’s Law of Motion

According to Descartes, motion is governed by the following laws:

1. Each and every thing, as far as it can, always continues in its same state – in motion or at rest.

2. This natural tendency to preserve the present state can be affected by “external causes”.

The second law holds that “all movement is, of itself, along straight lines” (Pr II 39) It also deals with circular motion and is not in our discussion here.This law is as close to Newtons laws as any pre-Newtonian philosopher can get. The renowned historian of science Clifford Truesdell (1919-2000) had observed, “[Descartes' physics] is the beginning of theory in the modern sense”


Nature of Impetus

As to the nature of motion and the transferred substance, Descartes declared that motion and rest are primitive states of material bodies. It does not need of further explanation. So from Descartes, we still do not get any clue as to what impetus or momentum is.

?


GALILEO GALILEEThe Resourceful


Galileo Galilei

Galileo Galilei (1564-1642) was an Italian physicist, mathematician, engineer, astronomer, and philosopher who played a major role in the scientific revolution during the Renaissance.

His achievements include improvements to the telescope so much so that data could be collected to support Copernicanism. Galileo has been variously called the “father of modern observational astronomy”, the "father of modern physics”, the “father of science”, and “the father of modern science”. When Newton said that he could see further because he was on the shoulder of giants.” Galileo is no doubt the giant he referred to.


Inertia

One of Galileo’s important contributions to the idea of motion is the discovery of inertia. The word ‘inertia’ comes from the Latin word, iners, which means idle, sluggish. It describes the quality of an object to resist changes to its state of motion. If you want to move an object, you feel its resistance and you need an effort to change it.

Inertia is the tendency of matter to resist changes in its velocity. Inertia look slightly different from impetus. Inertia is an intrinsic property of matter. It is that property of matter which opposes changes in velocity.

Inertia Force


Experiment to Prove Inertia

The proof of this idea was that if a ball rolled down one ramp, its inertia would cause it to roll up an opposite ramp of equal height. If the ramps are placed close to each other, the motion will go on for some time before being stopped by the effects of friction.


Conservation of InertiaIf we lower the slope of the second ramp, the ball will actually travel farther up the ramp, but to the same height. Using this logic, as the ramp approaches a level surface, the ball will roll forever.

The theory of inertia says that an object’s inertia has the tendency to maintain its state of motion. The more inertia an object has, the harder it is to change its state of motion.


Galilean Law of Inertia

Inertia is also something innate with a moving object. Galileo's Principle of Inertia stated: “A body moving on a level surface will continue in the same direction at constant speed unless disturbed.”

This principle was later incorporated into Newton's laws of motion (first law).


The Law of Inertia

In popular culture we often see this Law written as:An object at rest will tend to remain at rest unless acted upon by an outside force. An object in a constant state of motion will tend to remain in that state of motion unless acted upon by an outside force.


The Kinetic Piece

Inertia

Thus Galileo succeeded in adding another piece of our motion puzzle.

VelocityForce Impetus


THREE LAWS OF MOTIONIsaac Newton’s


Sir Isaac Newton

Sir Isaac Newton (1642 – 1727) was an English physicist and mathematician (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time and as a key figure in the scientific revolution. His discovery of the law of gravity and the laws in mechanics laid the foundations for classical mechanics. He also made seminal contributions to optics, and he shares credit with Gottfried Leibniz for the development of calculus. Wikipedia.


Principia Mathematica

The most important document in the field of physics was published in 1686 by Sir Isaac Newton through the Royal Society in his book entitled:“Philosophiae Naturalis Principia Mathematica” Which in modern day English is:“The Mathematical Principles of Natural Science”. Since then the kinetic behavior of a particle is completely and satisfactorily describable by his three basic theorems.

Title page of the first edition of the Principia.


On the Shoulders of Giants

The Principia has long been recognized as one of the intellectual landmarks in the history of physics. It is the first book to show clearly the close relationship between mathematics and formal logic. . . . No other book has such an influence on the subsequent history of mathematical philosophy. A. N. Whitehead and Bertrand Russell: Principia Mathematica. Cambridge University Press. 1910.

Newton was rather modest with his own achievements. In his letter to Robert Hooke in February 1676, he wrote:

If I have seen further it is by standing on the shoulders of giants.


Epitaph

The English poet Alexander Pope wrote this famous epitaph:

Nature and nature’s law hid in night;

God said “Let Newton be” and all was light.

Figure drawing by William Blake (1757-1827). Depicting Newton as God the geometer. Originally meant to degrade Newton as a devilish draftsman.


Newton’s Three Laws of motion

In forms slightly different from the original versions, Newton’s laws of motion can be stated as follows:

Law No. ❶ : A particle in rest will remain forever at rest, and a particle in uniform rectilinear motion will continue to move on forever at constant speed in the same direction. It will change its state of motion only and only when it is compelled to do so by forces impressed on it.

Law No. ❷ :When a particle is acted on by an external force, it accelerates. The acceleration is proportional to the magnitude of the applied force 𝑭𝑭 and is in the same direction as the applied force. If the particle has a mass of 𝑚𝑚 and the applied force is represented by the vector 𝐹𝐹, then: 𝑭𝑭 = 𝑚𝑚𝒂𝒂.

Law No. ❸: Whenever one body exerts a force F onto a second body, the second body exerts the force −F on the first body. 𝑭𝑭 and −F are equal in magnitude and opposite in sense.


Foundation of Classical Mechanics

This is the first time in history that the kinetic behavior of a particle is completely and satisfactorily describable by the three theorems. Since Newton’s time these theorems of force and motion had become the very foundation of classical mechanics and accredited the status of laws.


Complete Foundation

Later on in the nineteenth century, classical mechanics was further enhanced by Albert Einstein’s special relativity and general relativity. For motion of objects with a high velocity approaching the speed of light, relativity consideration is employed. Besides a small doubt about Einstein’s theory, classical mechanics is said to be complete.


IMPETUS

IMPETUS+ Sustaine

d Motion

INERTIA

Unexpected Guests

We shall deal with this gentleman in a

later section on Relative Motion.

HIG

H SPEED

Part 2. Cartes to Newton

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