and Atoms Stars IST 2420
Class 7, October 20 Fall 2008
Instructor: David Bowen Course web site: www.is.wayne.edu/drbowen/aasf08
Agenda
Assignments and passbacks Reminders: Online Grade Reports, Grade What-If, Essay grades Readings: "Watershed" Preview: Galileo Review: Boyle's Law Upcoming assignments Essay 2 Review for Midterm
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Handouts & Announcements
Initial the sign in sheet
Due tonight
Report for Lab 8 Part 2
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Coming up...
Tonight:
o Stay in 122 Cohn for the whole class period o Review session for Midterm
One hour, at the end of class (replaces lab)
Next week: Midterm
o One hour at the start of class o 3 to 5 questions from the list o Regular class, with lab, after Exam
Only assignment (except for studying): read Manual for Experiment 13
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Information sheet for Midterm
Will get clean copy on Exam Many basic facts Direct answers for many questions Must use your own words no credit for simply copying from the information sheet
10/13/08 10/20/08
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Grade What-If (repeat)
What is your average now?
o What grade are you headed for? o What do you have to improve to get a better grade?
It's the Grade What-If (doing what-if with your Atoms and Stars grade)
o On the course web site o Save to a disk drive if you want to save results o Early in semester to work on course grade
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Essays back...
Diskettes and flash drives being passed back, grade on there Also a file with the details
o AAS_W08_ESSAY_1_YTIG.doc
"YTI" = "Your Three Initials" "_" if no middle initial on file with WSU G = "graded," comments and grades in [ ]
These grades, like all here, can be discussed This assignment, like all here, can be redone 10/20/08 Atoms and Stars, Class 7 7
Problems in Essays
Several people are writing in their essays that Copi's seven steps say how to perform an experiment. This is incorrect. Show me the step(s) that says(say) how to perform an experiment. Torricelli the person
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o They do say that an experiment should be performed, but not how to do one.
o Torricellian another person, anyone who believes Torricelli or thinks like him
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Problems in Essays
Pay attention to these:
o Aristotle was not a scientist, although many people wrote that he was. o Aristotle did not do experiments, although many people wrote that he did.
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Missing a Class...
No excuses needed BUT you are still responsible for the material (standard for College level).
To make up the grade, write a two-page summary of the NOTES (see Syllabus for details).
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o Syllabus: get the notes, read them (and other assignments), and get any questions cleared up before the next class.
o Missing one or two classes lowers your grade by only a small amount.
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The Watershed
Chapter 6. The Giving of the Laws 1609 The New Astronomy with first two laws
o Precise verifiable mathematical laws, divorced from theology and spheres o Solar system: free-floating bodies in space moved by forces between them
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The Watershed
Brahe "gave" Mars to Kepler the most elliptical.
o Brahe and others could not make it fit
Copernican orbits centered on earth's orbit, not sun, but sun supposed to cause orbits K saw balance between a force in sun (today, gravity) and a force in the planet (today, inertia or resistance to motion)
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Ellipse
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Drawing an Ellipse
Two pins, a loop and a pen to draw an ellipse Distance from yellow pin (focus) to ellipse + distance from blue pin (the other ellipse) = a constant From Wikipedia
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The Watershed
Plane of Mars orbit passed through sun, angle between Mars plane and earth's fixed Initially kept circular orbits but threw out constant speed
o reasoned that force varied with distance from sun, so speed could also
Verified hypothesis with four of Brahe's positions, but added two did not work
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The Watershed
Insisted on both the facts and the theory
o A break with previous civilizations Alfred North Whitehead o Even a break with K's Mysterium Cosmographicum o Koestler: Made necessary by change from fitting to geometrical theories towards physical causes
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The Watershed
Started over, threw out circular motion as well Did not assume shapes of orbits as his predecessors did
o Only three points determine a circle o Calculated enough points to show the shape, had to start with earth since Mars seen from earth o Work on Second Law had many errors but still worked at the end
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The Watershed
Developed new methods, refined his skills Returned to shapes of orbits, showed Mars orbit not a circle Frightened by abandoning circular orbits Convinced himself by combining force of sun and force of planet that orbit was eggshaped (bigger at one end)
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Used ellipse as an aid to calculations for years while insisting orbit was egg-shaped Calculations were laying the foundation for calculus (invented by Newton later) theory of area of irregular shapes Clued in by numerical relationship which seemed at first like a coincidence K: "The roads that lead man to knowledge are a wondrous as that knowledge itself."
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The Watershed
The Watershed
Rejected an orbit because he had made a mistake in calculations and also didn't realize it was an ellipse, tried an ellipse and came back to that equation
o = "eccentricity"
But rest was mopping up
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o "Ah what a foolish bird I have been"
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The Watershed
Kepler saw no particular reason for these laws, or egg, did not make sense until Newton
o Ashamed of abandoning circular orbits
Prouder of orbits based on five regular solids Unique in devotion to both theory and observation, even switching back and forth Also deep immersion, knowing the numbers
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The Watershed
Removed astronomy from geometry to physics motion and its causes looked at it in a new frame
o Koestler: essence of creativity
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The Watershed
Chapter 7. Kepler Depressed Publishing difficulties, difficulties getting Brahe's data, getting paid, etc. (Tengnagle) Broke with King, didn't give edition to King but sold it to publishers in lieu of salary Not a friendly reception: friends but no colleagues
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The Watershed
Germans did not recognize significance, but English did, most importantly, Newton Kepler getting known, somewhat happier but always complaining about health, money King Rudolph (patron) getting eccentric, isolated, brother grabbing kingdom Kepler saw a second exile coming
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The Watershed
Chapter 9: Chaos and Harmony Galileo invented telescope, but Kepler explained how it worked 1610: Dioptrice
o Very and straightforward plain
1611 King Rudolph abdicated (died a year later), wife and child dead (K still kept title) Modest provincial mathematicus post in Linz, upper Austria, but he got the salary
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The Watershed
Religious problems disagreed with doctrines the Lutherans later abandoned
o Mother accused of witchcraft in Leonburg, threatened with burning at the stake 1615 1621 o Accused of the evil eye, entering houses through locked doors and more o K shot back as Imperial Mathematicus, demanded he receive all documents, etc.
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The Watershed
o Mother transferred to Wuerttemburg, led to torture chamber, refused to confess, failed "weeping test," was released (Pg 220) a year later o Could not return to Leonburg threatened with lynching
1618 Kepler discovered 3rd law (t2 r3) more straightforwardly, with only one backtrack
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The Watershed
Contribution of Kepler was methods; did not abandon mysticism Without calculus, Kepler could not see the connections between his three laws Koestler: "...Kepler set out to discover India and found America." Quote from Heinrich Herz (discovered radio waves) Pg 225
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The Watershed
King Wallenstein wanted Kepler for astrological advice, but Kepler felt this was unethical, avoided it.
o King got planetary positions from Kepler, gave them to his other astrologers o Kepler dismissed
Wandered, looking for a position, trying to get money owed him Died in Ratisbon, Germany 1630
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Readings Galileo and Later
The Rise of Science (the core of this course) Copernicus Brahe Kepler Galileo Descartes Bacon Newton
1450 1500 1550 1600 1650 1700 1750
The Greeks
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Galileo: Preview (Q25)
Astronomical observations with telescope
o Mountains on moon (not perfect) o Discovered Moons of Jupiter (Earth not unique) o Saw phases of Venus, argued (falsely) these were incompatible with geocentrism (Q26)
Argued (falsely) that tides on Earth incompatible with geocentrism (Q26) Sensational book brought attention
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Galileo (continued) (Q25)
Publicly supported Copernicus, Church said he had to be evenhanded with Ptolemy
o Put Pope's words in mouth of "Simplicius"
Church (Inquisition) put him on trial, forced him to stop saying the Earth moved, put him under house arrest
o He transformed his career o Apparently disagreed, privately
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Boyle's Law (cont'd)
Boyle's Law is an example of "the new Physics" Q12
o Makes specific mathematical predictions o Exhibits mathematical regularities in nature
(Modern changes:
o o
Correct when atoms in gas are far apart Pressures higher than this when atoms close)
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Boyle's Law (cont'd)
Mathematically: P1 V1 = P2 V2 Q13
o P: Pressure o V: Volume o 1: "sub 1" means time 1 - before (a change any change) o 2: "sub 2" means time 2 - after (the same change)
Assumes temperature the same at time 1 and time 2 Will always be the case in problems for this course A more general law if temperature changes
o Ignore the pressure and volume units (no unit conversions here)
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Boyle's Law (cont'd)
Mathematically: P1 V1 = P2 V2 Problem: given numbers for any three of P1, V1, P2, V2, find the fourth number Method Q13c:
Check: multiply both sides afterwards
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1.Identify what each of the three given numbers is 2.Substitute numbers into Boyle's Law 3.Multiply two numbers on same side 4.Divide to yield answer (get unknown by itself) o Know you are right
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Boyle's Law Examples
Example 6: A gas with a volume of 20 quarts and a pressure of 1.5 atmospheres is compressed to a pressure of 6 atmospheres. Find its new volume.
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Boyle's Law Examples (cont'd)
Example 7: A gas with a volume of 3 quarts and a pressure of 4 atmospheres beforehand is expanded to a volume of 6 quarts. Find its pressure after the expansion. Example 8: A gas with an earlier pressure of 2 inches of Mercury and a volume of 6 cubic feet is compressed to a pressure of 3 inches of Mercury. Find its volume a...