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Explain Galileo’s major achievements in the science of mechanics

Open Posted By: surajrudrajnv33 Date: 16/12/2020 Graduate Rewriting & Paraphrasing

8. Explain Galileo’s major achievements in the science of mechanics (Read Cardwell’s article, and also use information in PPT 20).

  1. a)  Explain his achievements in kinematics.
  2. b)  Explain his impact on machines
  3. c)  Explain his achievements in material science.

Must be 600-750 words

Try to keep a logical track in your explanations: Start with a short but clear reference to the background of the topic, then explain the topic as clear as you can, and finally, specify its importance/influence. In this final section, do not employ general expressions such as “the discovery of X had a profound influence on Y”, or “many fields in physics benefited from the invention of X”. You have to explicitly mention the results.

Category: Accounting & Finance Subjects: Behavioral Finance Deadline: 12 Hours Budget: $120 - $180 Pages: 2-3 Pages (Short Assignment)

Attachment 1

The Scientific Revolution - 1 ~1500 - ~1700 AD

Bacon and Galileo

• Questions:

• What happened during the Scientific Revolution?

• What were the connections between Scientific Revolution and the Industrial Revolution? And,

• How did technological knowledge develop and diffuse after the 1700s?

300s BC 200s AD 500s 800s 1200s 1500s 1700s

Hellenistic Period

Roman Period

Islamic Era

Christianity

Ptolemy Galen Archimedes Euclid Apollonius Hipparchus

Cicero Posidonius Varro Pliny Martinus- Capella

St. Benedict Isidore of Seville Bede Gerber t/ Anselm

The House of Wisdom Khawarizmi

Ibn Sina (Avicenna) Ibn Haytham

Ibn Rushd (Averroes) Battani

Tusi

The Scientific Revolution

Aristotelianism

Earth

Celestial Region

Terrestrial Region

Aristotle’s Cosmos

Water

Air Fire

Two different regions

Two different substance(s)

Two different concepts of motion

Two different concepts of change

TWO DIFFERENT PHYSICAL CONSTITUTIONS

TWO DIFFERENT PHYSICAL BEHAVIOURS

Epistemology / Logic

Syllogism \si-lə-ji-zəm\ a deductive scheme of a formal argument consisting of a major and a minor

premise and a conclusion

There is no change in celestial bodies (except positional change) (major premise) >> It is already known.

The shape, size and brightness of comets are changing (minor premise) >> known from

observation/experience Comets are not celestial

(conclusion)

The purpose of this philosophical scheme was to understand in the most fundamental way what things were and why they behaved as they did.

• The Goal of Science: – Describe nature as it is.

– Aristotelian philosophy was aimed at Explanation.

– Aristotle wanted to know things by knowing why things were the way they were.

– The intent of scholastic Aristotelians was to understand phenomena that were already known.

– No space for new discoveries.

• Copernicus: On the Revolution (1543) – Planets (including the earth) are moving

around the sun >> solved the problem of annual changes in the celestial sphere, including the retrograde motion (> next slide), and the seasons

– The earth not only moves around the sun, it rotates around its axis >> solved the problem of diurnal motion of the celestial sphere

– The axis of rotation of the earth is not perpendicular to the plane of the solar system >> solved the problem of seasons, and the way that celestial motions happen

The axis of the earth is not vertical to the ecliptic.

Copernicus explained the seasons based on earth’s axial tilt.

As the earth overtakes other planets, in its path around the sun, those planets appear to retrogress.

The Retrograde Motion of Mars within 4 months

• Tycho Brahe (1546- 1601)

– 1572 Supernova – Great Comet of 1577

– Observational and mathematical verification of celestial origin of comets and supernovae

• Kepler’s Laws (Early 17th century)

– I. The orbits of the planets are ellipses, with the Sun at one focus of the ellipse.

– II. The line joining the planet to the Sun sweeps out equal areas in equal times as the planet travels around the ellipse.

– III. The ratio of the squares of the revolutionary periods for two planets is equal to the ratio of the cubes of their semi- major axes.

The End of uniform circular motion! New problems….

• Francis Bacon (1561-1626): – Torture nature to extract her secrets! – Experimental philosophy

– Experimental investigation relies on the notion that what nature can made to do, rather than what it usually does by itself.

– Experimental philosophy: Employment of empirical data in order to perform research on philosophical questions and understanding the cause of natural phenomena

Francis Bacon Major writings: New Atlantis New Organon

• Francis Bacon distinguished between two different categories of inventions: –Science-based inventions, and –Empirical inventions

• Of all the inventions that Bacon discusses three seem to be of particular importance:

• Gunpowder, Printing, the Compass

• Bacon: With the advancement of science must come new opportunities for invention.

• Bacon argues that there are four major hindrances to the advancement of science and technics:

• Idols of the Tribe (humanity’s psychological and physical limitations)

• Idols of the Cave (limitations imposed by education and society)

• Idols of the Marketplace (ambiguities resulting from the nature of languages…)

• Idols of the Theater (intellectual systems that control our thoughts)

• The four Idols create a limiting framework to exercise inventions and discoveries.

• Bacon proposes a reformed inductive method to verify facts and make scientific statements.

• In The New Atlantis (1627) Bacon describes Solomon's House, a research establishment, wherein science is a collaborative undertaking, conducted in a rational and impersonal way, for the material benefit of mankind.

Baconian Induction vs. Aristotelian Deduction

SPECIFIC INSTANCE https://www.youtube.com/watch?v=WAdpPABoTzE

GENERALIZATION

DEDUCTIVE Top Down

INDUCTIVE Bottom Up

Baconian Induction vs. Aristotelian Deduction

Deductive Reasoning: Certainty Inductive Reasoning: Probability

• Galileo Galilei (1564-1642) –Telescopic observation

of astronomical phenomena –The surface of the moon –Sunspots –The satellites of Jupiter –The milky way –Saturn’s rings –Phases of Venus

• Galileo: Dialogue on the Two Chief World Systems (1632) in Italian – Actors: Salviati / Sagredo / Simplicio

• Step by step comparison of the old and new astronomy

• Discourse on Two New Sciences (1638) – Kinematics and the strength of materials

• Mathematical analysis of motion, force and the strength of materials

Problem: What load, W, can the beam carry when it is horizontal with one end mortised into the wall?

• Discourse on Two New Sciences (1638) – Kinematics and the strength of materials

• Galileo explores the general topics of cohesion of bodies and the breaking strength of materials.

• He wonders, for example, about size effect (the theory of scaling or scale effect) and why one cannot build a wooden boat weighing a million tons.

• He asks what makes a marble column hold together.

• Galileo presents an extraordinary matter theory (involving infinities of infinitesimals),

• He explores the coherence of bodies, surface tension, the nature of fluids, condensation and rarefaction, the weight of air, the propagation of light, …

• He suggests experimental methods to study the strength of materials and study properties of materials

• He mathematically determines the effects of the internal stresses induced by external loads and by the intrinsic heaviness of the beam itself.

Galileo studied local motion - motion in the neighborhood of the earth.

Galileo overthrew the traditional Aristotelian conception that the rate at which a body falls is proportional to its weight.

Galileo discovered that the distance a body falls in free fall remains proportional to the square of the time of fall

Distance S ∝ t2

S = ½ gt2

For Galileo, all bodies (independent of their weight) fall at the same accelerated rate in a vacuum.

Galileo on projectile motion

What was Aristotle’s idea?

With the same initial velocity, complimentary angels produce the same range.

From Galileo's 1638 treatise Discourse concerning Two New Sciences.

Galileo distinguished two separate components in a projectile:

- A horizontal, non- changing motion - A vertical motion, accelerating downward

- The Concept of inertia - Rotation of the earth and Inertia

Galileo: a scientist and an engineer Galileo as an Engineer: Employment of scientific rules in machines

Galileo’s lever principle applied to pulleys

Galileo: a scientist and an engineer

Galileo: Calculation of the performance and the efficiency of any real machine

Before Galileo, machines were judged qualitatively, after him they could be assessed quantitatively

Galileo: Quantitative measurement of work, force, friction, load…

Attachment 2

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