so far chapter 3: idea 2 the universe is a mechanism run

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Chapter 3: Idea 2

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Newtonian Mechanics and Causality

The Universe is a mechanism run by rules

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run by rules.

So far...

• Finished Universe-shaking Idea #1– Copernican Astronomy– the first step in the Scientific Revolution

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the first step in the Scientific Revolution

• Followed an historical approach– people attempting to explain what they observed– This was the origins of science

Historical Approach

• From the ancient Greeks– Aristotle: Geocentric Theory– Ptolemy: Modified Geocentric Theory

• Equant, Eccentric, Epicycle, Deferent

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• To the more modern– Copernicus: Heliocentric Theory– Brahe: Great data and the Compromise Theory– Galileo: Refuted Aristotle systematically– Kepler: 3 Laws of Planetary Motion

• All these attempts were descriptive only!– Described motions and positions of Planets– Said little or nothing about the causes of motion

• They did not explain anything!

Historical Approach

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They did not explain anything!

• Had to wait for the development of Physics!– Physics tries to explain, not just describe!– Idea #2 is about the development of a branch of

Physics known as Mechanics

Mechanics

• Concerned with Motion

• The causes and the description of Motion– Motion of ALL objects

• Earthbound and celestial

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a t bou d a d ce est a• From baseballs, projectiles, and rockets• To planets, stars, and comets

• Based on the work of one man– Isaac Newton

Isaac Newton

• His successful theories– completely revolutionized the way we think

about science and our place in the Universe

C fi d l i id

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• Confirmed two new revolutionary ideas– That Science is based on a few basic rules

• Fundamental principles– That Science can explain how the Universe

works

Aristotelian Physics

• Let’s continue our historical approach…

• We’ll trace the history of the important i f h i

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science of Mechanics

• As before, our story begins with the Ancient Greeks (again!!??)

Aristotle’s Methods

• Greeks inherited knowledge– from Egyptian and Mesopotamian cultures

• They acquired vast amounts of info

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y q– in Astronomy, Agriculture, and Science

• The older cultures made no attempt– to explain or understand the information

• This was generally left to Religion

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• For example– To the Egyptians

• The Sun rode a God’s chariot across the sky


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• An intellectual dead end– Either you believe it or you don’t– No need to explain it

• The Ancient Greeks were the first– to try to use logical arguments to describe things

• They were not always correct (as we have seen)


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)– did not base descriptions on empirical data

• But they were logical– started with a set of reasonable assumptions– followed them to their logical conclusions

• The great contribution of the Greeks– The goal of science is to describe “appearances”

• To describe what is observed in terms of basic principles

• To describe, not explain!


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• Their method is mostly due to Aristotle– Make observations leading to hypotheses– Adjust hypotheses as needed– until the observations are “understood”

• Student of Plato

Aristotle (384 - 322 BC)

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• Teacher of Alexander the Great

• Father was a physician to a Macedonian king

• Aristotle spent his life studying– Biology and Natural Philosophy

• What we would call “Physical Science” today

Aristotle

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• First to classify animals by species• First to dissect animals systematically

• He was the first to try to describe how the Universe works

• Tried to describe how Universe works– created a comprehensive system based on a set of

simple assumptions• we could call it a “unified physical theory”

F d d hi h l d l lib

Aristotle

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• Founded his own school and personal library

• Most volumes of his work ended up at the great library at Alexandria– Library was destroyed several times

• starting in ~50 BC

• His lectures were collected into 150 volumes

• Contained essentially all human knowledge up to that time

Aristotle

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– Science, Literature, Politics, Ethics, Logic

• Only about 50 volumes have survived– found by the Romans around 80 AD

• Aristotle believed all earthly matter...– all the stuff here on the Earth

• ...was composed of four “prime substances”– what he called “elements”

Prime Substances

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what he called elements

• The four elements: Earth, Water, Air, Fire

• He used this idea– to describe the basic properties of matter

• Described an object’s different characteristics– such as weight, hardness, buoyancy, motions

• An object’s characteristics depended

Prime Substances

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– on how much of each element it had

• For example– Heavy objects: mostly earth and water– Light objects: mostly air and fire

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Prime Substances

• Aristotle believed all celestial matter...– the stuff in the heavens

• ...was composed of ether

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p

• Only heavenly objects were made of “ether”– no earthly objects had any ether because there

was no ether on the Earth

Motion According to Aristotle

• Described the motions of objects using the basic natures of the four elements

• Each element had a basic nature

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– which determined how it moved

• An object’s motion is determined – by how much of each element it had

Aristotle listed 4 basic kinds of motion

• Alteration

• Natural Local Motion

Motion According to Aristotle

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• Natural Local Motion

• Horizontal Motion– also called Violent Motion

• Celestial Motion

• Alteration means change– To Aristotle, “motion equals change”

• Examplesleaves turning color iron rusting colors fading

Alteration

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– leaves turning color, iron rusting, colors fading

• Today, these are in the realm of Chemistry

• To us, motion involves physical displacement– motion from “here to there”

• The key to Aristotle’s ideas on motion

• NLM is always either Up or Down

Natural Local Motion (NLM)

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• Most objects go Down when released– stones, apples, sand, etc.

• Some objects go Up when released– smoke, fire, hot gases

• These motions are “natural” motions– the “natural” motions of these objects due to the

dominant nature of the objects

Natural Local Motion

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• An object’s dominant nature is determined– by the elements that comprise it

• These motions happen spontaneously– The object does not need to be pushed or pulled

• An object’s natural motion is always– toward their “natural” resting place– trying to achieve the “natural” order


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• Objects move “naturally” because they are striving to be more “perfect”

• To Aristotle, perfection occurs when all objects are in their proper place

• Natural motion ↔ Dominant nature

• Earth and Water– move “naturally” Down toward the Earth’s


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center

• Air and Fire– move “naturally” Up away from the Earth’s

center

• Once objects attain their “natural” place they stop moving

• He predicted heavier objects would fall faster than lighter ones


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t a g te o es– more eagerly striving to achieve their proper

place

• This is not consistent with experiment– It is wrong! (Prove with simple demo)

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• Drop a piece of paper– it falls slowly– made of Earth and Air– competing Up and Down natures

Natural Local Motion: an Example

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p g p

• Crunch it up: squeeze the air out– it falls faster– much less “Up” element available– Down nature more dominant

• Correctly predicted objects in a vacuum fall at same speed– Objects fall slower in a denser medium

• But for the wrong reason


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• But for the wrong reason– thought objects in a vacuum fell at infinite speed– which is impossible

• infinite speed ⇒ no time elapses ⇒ two places at once– therefore a vacuum is impossible

• “nature abhors a vacuum”

• Divided into two basic types

• Objects that are pushed or pulled– wagons, people walking, shopping carts

Horizontal Motion

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• Objects that are thrown or struck– projectiles– He asked “what keeps the projectile going?”– There is a better, more fruitful question...later

• These are “unnatural” motions– do not arise from the nature of the object– do no occur spontaneously when object released

Horizontal Motion

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• Horizontal motion requires a push or a pull– A push or a pull causes motion– No push or pull ⇒ no motion

• This is according to Aristotle remember...

• Antiperistasis– Aristotle’s explanation of Projectile Motion– Since the projectile keeps moving after release

there must be something pushing it!

Horizontal Motion

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• Air in front is pushed aside– comes around to fill temporary void

• created as back vacates last position

– pushes projectile forward

• Motion of the heavens– obey completely different laws of motion

• Celestial objects

Celestial Motion

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j– Massless spheres, made of ether– They were “perfect”

• Perfect spheres moving in perfect circles

• The heavens are perfect, Earth is not!

• On Earth, we have a mixture of elements– that are not in their “natural” place

Celestial Motion

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– but are trying to attain perfection

• In the heavens, everything is perfect and therefore unchanging– Why change if you’re perfect...

• Largely discredited and discarded– at the time of Newton

• He still made major contributions– particularly the method of observe and describe

Aristotle’s Physics

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p ybased on a few simple assumptions and logic

• His system was– reasonable, self-consistent, logical– Accepted as correct for nearly 2000 years

It took a long, long time...

• …but the cracks began to show!

• First recorded serious criticism– around 500 AD (some 800 years later)– a scholarly idea going unchallenged - amazing!

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a scholarly idea going unchallenged - amazing!

• Then trouble in human civilization…– The fall of the Roman empire– The destruction of the great Library of

Alexandria

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• Led to the Dark Ages– No significant scientific progress in Europe for

700 years!!

• Then the Renaissance (around 1200 AD)– the “re-birth”

A i G k d f h h

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• A recommitment to Greek modes of thought– Philosophy, Art, Science

• Aristotle’s system became “church dogma”– a set of ideas proclaimed by the church as true– OK to study them, not OK to refute them

• Around 1300 AD…

• The idea of Antiperistasis discredited

• Consider a spear sharpened at both ends– one end moves through the air

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one end moves through the air– but the other is pushed by the air?

• Or a millwheel– no “back end”, like a Frisbee

• Also by 1300 AD…

• Only two different kinds of motion were believed to exist

– Uniform Motion

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• straight line, constant speed

– Uniformly Accelerated Motion• speed changes at a constant rate

• Motion at a constant speed – in a constant direction

• Travel the same distancei h f i

Uniform Motion

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– in the same amount of time

• Distance traveled each second is the same– twice as much time ⇒ twice as much distance

• Example: 65 mi/hr

– You travel 65 miles each and every hour– If you travel for twice as much time– you will travel twice as far (130 miles)

Uniform Motion

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y ( )

• The distance traveled is proportional to time

d t∝

• Motion with a changing speed– speed changes at a constant rate

• If the speed is increasingl f h i h f i

Uniformly Accelerated Motion

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– travel further in the same amount of time– that’s what “faster” means

• The distance traveled each second increases– twice as much time ⇒ four times the distance

• Example: 0 to 60 in 6 seconds– after 1 second, you’re going 10 mi/hr and have

covered 7.3 ft– after 2 seconds, you’re going 20 mi/hr and have

covered 29 ft


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– after 6 seconds, you’re going 60 mi/hr and have covered 264 ft

• Distance traveled proportional to time squared

d t∝ 2

Graphical Representation of MotionSpeed Uniformly Accelerated Motion

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Time

Uniform Motion

Speed versus Time Graph

Summary of MotionUniform Motion

Dist

ance

Spee

d

Acc

eler

atio

n

Time Time Time

Constant = 0

Constant ≠ 0α t

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Time Time Time

Dist

ance

Spee

d

Acc

eler

atio

n

Time Time Time

Constant ≠ 0α t2 α t

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Two important unanswered questions!

• What kind of motion do falling objects undergo?– Objects that are dropped

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• What kind of motion do projectiles undergo?– Objects that are thrown or struck

Galilean Mechanics

• These two unanswered questions– were 2000 years old– Been around since the time of Aristotle

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• Finally answered by Galileo– After a systematic analysis based on

experimentation– The scientific method in action!

• Contributed to Physics too– refuted Aristotle’s Physics

Galileo Galilei (1564-1642)

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• Answered our questions– Dropped objects– Projectiles

• One of the most prominent scholars of his day

• Was a believer in the Copernican system– After he looked through the telescope in 1610

Galileo Galilei

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g p• systematically!

– And believed his own eyes

• Did not publish until he had solid evidence– Science!

• Became interested in how objects fall– while a student at the University of Pisa– He was studying medicine at the time

Galileo Galilei

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• Did not drop stuff from the Leaning Tower– That experiment would have been inconclusive

because of air resistance

• Aristotle– believed a heavier object falls faster– twice as heavy ⇒ falls twice as fast

• This would not have happened if he had actually tried to do an experiment!

Galileo Galilei

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actually tried to do an experiment!– which he did not do

• Galileo– suspected the two should fall at same speed– Correct, if there is no air resistance

• This was verified experimentally– over 300 years later on the Moon!

• An Apollo astronaut dropped two objectsf h d h

Galileo Galilei

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– a feather and a hammer

• Moon has no atmosphere– so there is no air resistance– and they fell together, as predicted

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• He was convinced Aristotle was wrong– about falling objects and projectiles

• But he had a serious measuring problem

Galileo Galilei

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– no accurate clocks– falling process too fast

• Used Inclined Planes– a long ramp!

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• Inclined planes were a great idea!– Same process: falling under influence of Gravity

• Cleverly “watered down” gravity

Falling Bodies

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– The object falls slower

• Makes experiment more accurate– takes more time to fall– reduces air resistance

Falling Bodies

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½ second 5 seconds

• The results for the motion of objects– falling under influence of Gravity

• Uniformly Accelerated Motion!

Falling Bodies

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– Correct answer to 2000 year old question

• Galileo correctly analyzed the problem– tried to minimize air resistance and friction– to better understand the fundamental motion


• Twice as much timet i f t

Falling Bodies

4.9 m

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– twice as fast– four times as far

• Three times as much time– three times as fast– nine times as far

19.6 m

44.1 m

• Galileo asked the right question about the motion of objects– Why do they stop?

• Understood the roles of resistive effects

Falling Bodies

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• Understood the roles of resistive effects– They stop because of air resistance and friction

• Designed an appropriate experiment– Did not just pick examples that supported his

point of view

• Galileo understood that air resistance– was a result of motion– not a cause of motion– Air resistance impedes motion!

Falling Bodies

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• To understand motion– you need to avoid air resistance and minimize

friction

• Used gently inclined, polished ramps!

• Aristotle– objects fall at different

constant speeds

Falling Bodies

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• Heavy objects– fall faster

• Lighter objects– fall slower

Falling Bodies

• Galileo– all objects fall at the

same changing speed

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• Object’s weight does not matter– if air resistance is

eliminated

Falling Bodies

• Real Life– air resistance matters!

• Resistive forceeventually stops

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– eventually stops acceleration

• Terminal Velocity– depends on Mass– We’ll ask Newton why

Aristotle

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• Galileo drew two conclusions– from his work with inclined planes

• A ball dropped from resti l i

Projectile Motion

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– experiences a constant acceleration– Uniformly Accelerated Motion

• A ball rolling on a flat horizontal surface– experiences no acceleration– Uniform Motion!

• The logic…

• Roll a ball down a ramp– It speeds up - a positive acceleration

R ll b ll

Projectile Motion

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• Roll a ball up a ramp– It slows down - a negative acceleration

• Roll a ball horizontally– The speed stays the same - NO acceleration– Uniform Motion!

• Recall Aristotle’s question– What keeps a projectile going?

• Galileo realized this is the wrong question

Projectile Motion

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• Galileo’s better question– What stops a projectile?

• Answer: nothing!

• The natural thing for a moving object moving horizontally– is to keep moving!– with Uniform Motion

Projectile Motion

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• In other words– once it is moving horizontally– it keeps moving horizontally– Until something stops it!

• In modern terms– this is called “Inertia”

• Inertia is the tendency of an object to resist changes in its motion

Projectile Motion

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• The more mass an object has– the more Inertia it has– the more difficult it is to change its motion– Pushing a boulder is much harder than pushing

a pebble!

• Galileo’s conclusion– Projectile Motion is a combination of motions

• The projectile moves 2-dimensionally

Projectile Motion

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• The horizontal motion is– Uniform Motion

• The vertical motion is– Uniformly Accelerated Motion

• The two motions are independent– they do not influence each other– they can be analyzed separately

Projectile Motion

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• This is called the Superposition Principle

• The Horizontal motion– does not alter the Vertical motion

• Demonstration

• Shoot two balls simultaneously– drop one straight down– project the other horizontally

Projectile Motion

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project the other horizontally

• What happens?– Dropped ball lands first?– Projected ball lands first?– They land at the same time?

100

120

140

160

180

Projectile Motion

Same Height

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0

20

40

60

80

0 1 2 3 4 5 6Range

9

Projectile Motion

• They land at the same time!– Happens for all Projectiles

• Galileo correctly analyzed these motions and gave us a description

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gave us a description

• The explanation was soon to follow– but first we need some mathematical background

Logic, Mathematics, and Science

• This is the part you’ve been dreading– The Math part

• We need to discuss two things

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• We need to discuss two things...– Logic– Mathematics

• …before we can talk about modern Science.

• Mathematics– An important tool of Science– Called the “language” of Science

h i b h f h i

Mathematics

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• Three important branches of Mathematics– Calculus– Analytic Geometry– Vectors

• We are not going to do any Math– This is not a Math class. Phew!

• This is a Physics class– We must try to understand Mathematics

Mathematics

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We must try to understand Mathematics– as the study of order and relationship

• Physics is about problem solving– Math is the tool used to solve the problems

• Sometimes the solution has to wait– for the Mathematical tool to be invented

• Recall Kepler and his wine jugs

Mathematics

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– without Calculus ⇒ a very difficult problem– with it ⇒ an undergraduate homework problem

• Recall Kepler and the Logarithms– made analysis of Mars’ orbit doable

• Two kinds of Logic used in Science– Induction– Deduction

Logic

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• Newton realized something important!– Both kinds of Logic are needed to do Science– They are used in combination

• to determine the physical laws of nature

• Induction– the process of extracting a general rule from

the results of a series of experiments

l l f h i

Inductive Logic

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• Data → a general law of Physics

• There isn’t any line of reasoning– you simply notice a pattern in a body of data

• The more data you have– the more obvious the pattern– the more reliable the general rule

Inductive Logic

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• If you have enough data– you notice the correct pattern– induce the correct general rule

• Inductive logic is never predictive– The general law describes the existing data– it says nothing about any new data

l

Inductive Logic

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• Example: Surveys– Collect data by asking people questions– Make a general rule

• “Most people like red lollipops”– Says nothing about what the next person likes

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• Deduction– Start with a basic premise

• An hypothesis or an educated guess– “Most people like red lollipops”

– Logically argue that certain other results follow

Deductive Logic

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Logically argue that certain other results follow• If this happens, then that must happen

– “So most people should like red licorice too”

– Take it to its logical conclusion• Therefore the end result is something

– “Most people like red licorice”

• There is a danger here– The premise might not be physically realistic

• Not connected to physical reality

A bad premise results in a bad conclusion

Deductive Logic

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– A bad premise results in a bad conclusion• no matter how correct and clever the logic

– What we used to call “GIGO”• Garbage In Garbage Out

• Example: High school geometry proofs– Those step-by-step exercises you loved– Apply the rules of geometry

• from Euclid, another of those Ancient Greeks

Deductive Logic

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• Example: Sherlock Holmes– “Elementary my dear Watson”

• “The description of geometrical shapes with mathematical formulas”

• Many shapes have mathematical descriptions

Analytic Geometry

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– Circles and Ellipses are but two examples– some examples on page 82 of text

• And here are a few more…

Centered Circle: ( )r Rθ =

45°

90°

135°

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0 0.5 1 1.50°180°

225°

270°

315°

( )r aθ θ= cosOff-centered Circle:

45°

90°

135°

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00.510°180°

225°

270°

315°

45°

90°

135°

Ellipse: ( )r Rθ εε θ

=+

+1

1 cos

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01230°180°

225°

270°

315°

45°

90°

135°

( )r R aθ θ= + cosCardioid:

89

00.511.520°180°

225°

270°

315°

Rose: ( )r aθ θ= sin2

45°

90°

135°

90

01230°180°

225°

270°

315°

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• The shapes are often useful to Science– Kepler and his ellipses opened the door for Newton

• The shapes are sometimes related to Physics

Analytic Geometry

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The shapes are sometimes related to Physics– The elliptical shape of planetary orbits– used by Newton to figure out Gravity

• We have used graphs to describe motion– Uniform and Uniformly Accelerated Motion

• Each graph has a mathematical formula

Analytic Geometry

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Each graph has a mathematical formula– Speed versus Time– Distance versus Time

• Mathematics describes physical reality

• Invented independently – by Isaac Newton and Gottfried Leibnitz

• Mathematical techniques

Calculus

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– for calculating quantities that are changing

• Relates properties of graphs– to actual physical quantities– like speed, distance, and acceleration

• Distance versus Time graph– Speed of object = Slope of graph

• Speed versus Time graph

Calculus

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– Acceleration of object = Slope of graph– Distance Traveled = Area under the curve

• We get information about the real world– from simple graphs

Calculus

tanc

e

∆y

95

Time

Dis

t

Slope = ∆y/∆x = speed of object

∆y

∆x

Calculus

Spee

d

Slope = acceleration of object

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STime

Area = total distance traveled

• Sometimes number just don’t add up

• For example….– If I walk 5 steps and stop

Vectors

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– Then I walk 12 steps and stop– How far from where I started do I end up?

• Answer: It depends!– On which direction I walked.

Vectors

5 12 17+ →

5 12 7+ →

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5 12 7+ →

5 12 13+ →

• Vectors have two parts– Magnitude

• tells “how much” of the vector there is

– Direction

Vectors

99

• tells “which way” the vector points

• Need both to describe many quantities– such as Force (which way you push matters)– and velocity

12

• Numbers that add up the “usual” way– are called Scalars

• These are the numbers you’ve used

Scalars

100

– your whole life (temperature, money)

• When you figure out your average grade– add the scores and divide– you’re manipulating Scalars

Newtonian Mechanics

• We are now ready to discuss the work of Isaac Newton

C ll d “th t t i t ll t h li d”

101

• Called “the greatest intellect who ever lived”

• The man who invented theoretical Physics

Isaac Newton (1642 - 1727)

• Born in Woolsthorpe, Lincolnshire, England

• Born on Christmas day– same year Galileo died

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same year Galileo died– another symbolic transition

• Invented the idea of a “clockwork” Universe– one that runs by rules

Isaac Newton

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• The dominant scientist of his generation– like Galileo the generation before

• Born into a family of dirt farmers– Father died three months before he was born

Isaac Newton

104

– Mother noted that he would not be a good farmer

– Considered an average student• did show exceptional mathematical ability

– and a strange boy• did many unusual projects on his own

• His uncle was a faculty member of Trinity College– had connections!

• Enrolled in Cambridge University in 1660

Isaac Newton

105

g y– Graduated in 1665

• Returned to his boyhood home on the farm– during the time of the Great Plague– Cities like London were not safe

• And set the world on its ear!

• Had such a great year in 1666– it is called his “miracle year”

“ i i b li ” i L i

Isaac Newton

106

– or “annis mirabelis” in Latin

• What he did in 1666 was amazing!– Only one other year like it in history– Only Einstein’s work in 1905 can compare

• In his “miracle year”, Newton discovered– the Binomial Theorem: (x + y)n

– the Calculus– the Spectrum of White Light (the rainbow)– the Laws of Mechanics

Isaac Newton

107

– the Universal Law of Gravitation

• And did not tell anyone!– Even though all are “hall of fame” quality work!– due to his being ridiculed over an earlier optics

paper

• Eventually Published the Principia Mathematicain 1687, some 20 years later!!!– “Mathematical Principles of Natural Philosophy”– Codified all of Galileo’s results into physical laws

Isaac Newton

108

– Explained as well as described!

• Newton invents Physics!– The most important work in the history of physics– and the theoretical part of the scientific method

13

• On a personal level– Newton was a petty, jealous, egomaniac– extremely sensitive to criticism

• Never married

Isaac Newton

109

– only one traumatic romance when young

• The original absentminded scientist– Occasionally forgot to eat for days at a time– Lived with his Niece, who took care of him

• Fought Leibnitz bitterly over priority– for the invention of the calculus, even though

he was already famous– Abused his position as President of the Royal

Society to smear Leibnitz professionally

Isaac Newton

110

• Stole theories about optics?– The controversy between Newton and Hooke– Contemporaries and rivals– Hooke attacked Newton his entire career

Three Laws and Gravity

• Newton explains motion– He answers the “how” question

• His answer:Three Laws of Motion

111

– Three Laws of Motion– Law of Universal Gravitation

• Including the actual version– Of the “Newton and the Apple” story

The Principia Mathematica

• The Principia was Newton’s masterpiece

• In it he starts with the basics– sets forth Definitions and Assumptions

112

• Introduces his famous Laws of Motion– uses them to explain Galileo’s results

• Applies them to the Moon– derives Law of Universal Gravitation

• Mass– “How much stuff” there is in an object– Different than weight

• Weight depends on where you are (vector)

Definitions

113

Weight depends on where you are (vector)– A person that weighs 180 pounds on Earth

weighs only 30 pounds on the Moon– and is weightless in orbit

• Mass is a property of the object (scalar)

• Motion– Product of Mass times Velocity– Today we call this “Momentum” (vector)

F ( t )

Definitions

114

• Force (vector)– An action that changes the Motion– Can change the Speed and/or Direction of an

object

• Newton next introduces his three– “fundamental quantities”– Must be measurable and objective– Does not depend on point of view of observer

Fundamental Quantities

115

• The three:Length: 1 meter = 1 yard + 3.37 inches

Mass: 1 kilogram weighs 2.2 pounds on EarthTime: 1 second = 1 second

• All other physical quantities– are combinations of these three

• Velocity = Length ÷ TimeTh ’ h il h miles/

Fundamental Quantities

116

– That’s how we get miles per hour: miles/hour

• Momentum = Mass × Velocity

• Force = Momentum ÷ Time

• Newton presented this Three Laws in terms of these carefully defined quantities

• The Three Laws become the basis of Physics f th t 250

Newton’s Laws of Motion

117

for the next 250 years

• Until the 20th century and the next “revolution”– Relativity and Quantum Mechanics

14

Newton’s First Law

• The Inertia Law“An object will continue in a state of uniformmotion unless acted upon by a net force.”

hi i h lil i

118

• This is the answer to Galileo’s question– Why does an object stop?– Because a net force acted on it

• Changed its motion from moving to stopped


F2F1

Fnet

119

F3

F4

Fnet = F1 + F2 + F3 + F4

(added as vectors)

• Uniform Motion– Motion at a constant speed in a straight line– This includes “at rest”, which is a constant

speed of zero


120

• Net Force– If two forces cancel out, there is no net force– Must have a non-zero net force to change the

motion of an object

• No Net Force– No change in the object’s motion– Speed does not change– Direction does not change


121

g

• Net Force– Change in Speed and/or Direction– Circular motion at constant Speed

• This defines the concept of Inertia– The tendency of an object to resist changes in its

current state of motion

• If an object is stopped, it tends to stay stopped


122

• If an object is moving, it tends to keep moving

• Unless a Net Force acts on it!– This is why you get injured in a car accident!

• We now know “what” happens– but we don’t know “how much”...


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• That’s what the second law is for!

• The Acceleration Law“The change in motion equals the net force and isin the same direction as the net force”

Newton’s Second Law

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• Perhaps the second most famous equation

F ma=

• The “F” is the Net Force– The vector sum of all the applied forces

• The “a” is the Acceleration


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– Acceleration is the rate of change of velocity

• The “m” is the object’s Mass– The property that determines Inertia

• The Second Law is a recipe– for how much change in motion is produced by

a certain amount of net force

• Relates cause and effect


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Relates cause and effect– Cause: a net force– Effect: a change in motion, an Acceleration!

• The connection: the object’s Mass!

15

• A more useful form:


FCause = Net Force

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am

=Effect = Acceleration

Object’s property: Mass

• More Net Force– produces more change– and a bigger Acceleration


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• More Mass– get less change for the same Net Force– and a smaller Acceleration

• Suppose we kick a soccer ball– apply a large Force to a small Mass– results in a large Acceleration– the ball goes zooming off


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• Apply the same kick to a bowling ball– same Force, much larger Mass– results in a smaller Acceleration– the ball does not move very much (ouch!!)

• The Interaction Law“The force exerted by one object on a second isequal and opposite to the force exerted by thesecond on the first”

Newton’s Third Law

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• I push it! It pushes me back!– That’s why you hurt your foot kicking the bowling ball!

• Explains how forces are transferred– between interacting objects

• We need the 3rd Law to explain...

• How I walk across the floor


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– My foot pushes the floor– The floor pushes back on my feet– I walk across the floor

• How a rocket moves– The rocket pushes gases out the back– The gases push back on the rocket– The rocket accelerates


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The rocket accelerates

• Rocket science is not rocket science!

• Children’s balloons work the same way

• Sometimes called the Action/Reaction Law“For every action there is an equal and oppositereaction”

• The Action


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– Object 1 exerts a force on Object 2

• The Reaction– Object 2 exerts a force of equal magnitude but

in the opposite direction on Object 1

• Once Newton invented Physics– he needed a Physics problem to solve

• Turned his attention to falling objects

The Law of Universal Gravitation

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g j– He figured Earth attracts the object– so Gravity is a Force that produces an

Acceleration– “drop” ⇒ speed changes from zero to not zero

• He knew the acceleration due to Gravity on the Earth’s surface: 1 g = 9.80 m/s2

• It is a constant

Gravitation

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– just like Galileo said it was!

• Newton thought that Gravity also– extends out to the Moon’s motion– and influences the Moon’s motion

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• Newton arrived at this conclusion– by shooting an imaginary cannon

• Shoot the cannon horizontallyh b ll f ll P j il M i

Gravitation

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– the ball follows Projectile Motion

• Shoot it faster, it goes farther

• Shoot it fast enough– it goes all the way around, like the Moon!

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• Newton used his new Physics– and calculated the Moon’s acceleration– as it moves in its circular orbit around Earth

Hi t lt

Gravitation

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• His correct result:

a gg

Moon =

=

13600

1602

• Newton knew the Earth’s radius– actually measured by ancient Greeks

• Eratosthenes

Gravitation

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– Walked from Syene (Aswan) to Alexandria, Egypt

– and counted his steps for 500 miles!

• Measured the angle of a stick’s shadow– and correctly calculated the Earth’s radius

Eratosthenes’ Journey

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The Earth’s RadiusWalked 787 kilometers (km)- yielded a radius of 6441 km- actual value 6380 km

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• He also knew the distance– from the Earth to the Moon

• About 60 Earth radii

Gravitation

r RMoon Earth= 60

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• Measured during Lunar eclipse– by size of Earth’s shadow

on Moon

Moon is 60 times further from Earth’s center than we are on the surface

r RMoon Earth= 60a gM = 12

Gravitation

• This was an important clue– about the nature of the Gravitational Force

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Moon Earth60a gMoon 602

• Gravity is an inverse-square force!

FrG ≈1

2

• Inverse-square– How Gravitational Force changes with distance

• If we double the distance

Inverse-square Forces

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– the Gravitational Force is one-quarter

• If we move 60 times further away– the Gravitational Force is 1/602 as strong

17

• Next Newton invoked his Third Law– The Earth’s pulls on the Moon– the Moon must pull back with equal force

Gravitation

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• Weight is proportional to mass– and weight is just the force of Gravity

• Gravitation must depend on both masses

• Newton then generalized it– If Gravity works for the Earth and the Moon– then why not for the Sun and the Earth– and Jupiter and its moons

Gravitation

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and Jupiter and its moons

• Gravity works for any two objects with mass!– It is Universal!

• Every object attracts every other object with a force proportional to the product of the massesand inversely proportional to the square of the distance between their centers The attractive


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distance between their centers. The attractive force acts along the line joining the centers.

F G m mrG = 1 2

2

• “Every object”– this is the “Universal” part– So there is one constant for all objects: G


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• “Proportional to the product of the masses”– This is the “m1 m2” part– Each mass contributes to the Force– More mass produces more Gravity

• But why? We still don’t know!!!

• “Inversely proportional to the square of the distance”– this is the part


12r

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• Newton then took his new Law of Gravitation– and combined it with his Second Law of Motion– and solved some problems!

• This was highly successful!– Newton used his Gravitation and the 2nd Law

• to theoretically derive all of Kepler’s Laws• An amazing confirmation of Newton’s work


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– Used to predict locations of new planets• Uranus found in 1781• Neptune found in 1846

– Still successfully used today• for baseballs and rockets to Mars...

• Newton’s work had huge implications! – The Universe is a giant clock-work Machine!– that is run by rules– Newton showed the rules are discoverable!

Isaac Newton

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• Knowable and Understandable

• Based on cause and effect– Forces cause changes in Motion– and the rules that relate the two!

• Newton’s theory is deterministic– Same input always produces the same results

– The results are completely determined by input• How far the ball goes depends on how you throw it

Isaac Newton

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ow a t e ba goes depe ds o ow you t ow t

• If Newton is right– the current state of the Universe

• was determined by its beginning• So there is no free will!

– We’ll see if he’s correct later in the course…

so far chapter 3: idea 2 the universe is a mechanism run

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