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Micro-world Macro-world Fall 2009 Instr: Stephen L. Olsen
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What does “Physics” mean? Greek: φίσίσ phisis “things” “logic” “The logic of things” or “How things work” Chinese: 物理 WU LI Nature
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What kind of “things”? Ordinary-sized objects: : apples : footballs : ukuleles : etc.
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Gigantic things Earth Sun galaxies etc.
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Very tiny things molecules atoms cells quarks
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Galileo Galilei 1562 - 1642 1 st “modern” scientist
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Example of how Galileo thought: His experiments on motion on inclined planes
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What if the 2 nd track was horizontal?
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Aristotle ~300 BC Forces are needed to keep objects in motion. A constant force will have a constant motion. Physics book VII chapter 5
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Galileo’s big idea Forces are not needed to keep objects in motion. They are only needed to change the state of motion.
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Actually, Galileo wasn’t first Mozi ( 墨子 ) ~400BC If there is no opposing force, motion will never stop. before Aristotle!
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Object sliding on a surface If there were no friction the book would keep sliding.
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Angels are not needed to keep planets moving in their orbits
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Law of inertia Discovered by Galileo, but as written by Newton: Every object perseveres in its state of rest, or of uniform motion in a straight line, unless it is so compelled to change that state of motion by forces impressed thereon.
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Comment on the Law of Inertia No mention of balls & tracks Applies to ordinary objects & also huge objects like galaxies and tiny objects like atoms & quarks Galileo knew nothing of galaxies or quarks, but, thanks to his imagination, his insight, based on observations of ordinary objects, proved to be a universal truth.
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Units & Reference Frames Required for measurements/observations
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English units King’s foot 12 inches = 1ft 5280 ft = 1 mile
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One meter of length 1 meter = 40 inches (1.1 yds) 10,000,000m 1m About the distance from nose to the outstretched finger (of a pretty big guy).
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Centimeters & millimeters 1 centimeter = 1/100 meters ( radius of a penny) 1 millimeter = 1/1000 meters ( thickness of a dime) means “approximately equal to” 1cm 1mm
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1km 5/8 mile 1000 m = 1 kilometer (km)
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Motion depends on the circumstances of the observer (I) To us, both the red & blue cars move forward To someone in the red car, the blue car is going backwards backwardforward
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Reference frames aka Coordinate systems x z y To describe the position of an object: You need to define a coordinate system (reference frame) & determine 3 coordinates e.g. x, y & z Choices of location of the coordinate system & directions of the axes are up the observer. z x-axis (e.g. the 1 st baseline) y-axis (e.g. the 3 rd baseline) z-axis (vertical) reference point (e.g. home plate)
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Motion depends on the circumstances of the observer (II) In the fish’s reference frame, it is the ground that is moving x z y
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Some distances Nose to finger~1m Back of the room~10m SNU library~100m SNU main gate~1000m Incheon ~50000m Center of the Earth~6400000m Earth to Moon ~385000000m Earth to Sun ~150000000000m Next star ~40000000000000000m We are only out to the next star & we are already running out of space
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Some small sizes radius of a 10 won coin~0.01 m thickness of a 10 won coin~0.001 m thickness of a human hair ~0.000075 m diameter of a red blood cell~0.00000002 m size of hydrogen atom ~0.00000000006 m size of hydrogen nucleus ~0.0000000000000001 m Again, the numbers become unwieldy & use up a lot of space
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Exponential logic
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Exponential logic powers of “2”
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Area of a sheet of paper 28 cm 21.5 cm Area =28 cm x 21.5 cm = 600 cm 2 Cut it in half
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Area of the remaining sheet after 1 cut 28 cm 21.5 cm Area =28 cm x 21.5 cm Cut it in half again 2 2 2 = 600 cm 2 =300 cm 2 = 600 (1/2)cm 2
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Area of the remaining sheet after 2 cuts 28 cm 21.5 cm Area =28 cm x 21.5 cm Cut it in half again 2 2 2 2 = 600 cm 2 2x2 =600 cm 2 x(1/2) 2 =150cm 2
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Area of the remaining sheet after 3 cuts 28 cm 21.5 cm Area =28 cm x 21.5 cm Cut it in half again 2 2x2 2 2 1212 = 600 cm 2 2x2x2 =600 cm 2 x(1/2) 3 =75cm 2
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After 12 times 28 cm 21.5 cm Area =28 cm x 21.5 cm 2626 2626 2626 2626 =0.15 cm 2 Smallest piece of paper I can handle = 600 cm 2 2 6 x2 6 =600 cm 2 x(1/2) 12 = 600 cm 2 4096
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Imagine we did it 70 times 28 cm 21.5 cm Area =28 cm x 21.5 cm 2 35 1,180,591,620,717,411,3??,??? = 5.1 x10 -19 cm 2 (about ½ the area of an atom) =600 cm 2 x = 600 cm 2 2 35 x2 35 =600 cm 2 x(1/2) 70 1
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1 1,180,591,620,717,411,3??,??? is unwieldy ( 다루기 힘든, 꼴 사나운 ) (1/2) 70 Is more tractable Difficult to manage Tractable easy to manage
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Powers of 10 $ 100.0 = $ 10.00 x 10 Move the decimal point 1 place to the left multiply by 10 & $0.01 = $00.1 x 1/10 Move the decimal point 1 place to the right divide by 10 & “penny” “dime”
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Positive powers of 10 150000000000150000000000.15000000000.0 x 10 1 1500000000.00 x 10 2 150000000.000 x 10 3 15000000.0000 x 10 4 1500000.00000 x 10 5 150000.000000 x 10 6 15000.0000000 x 10 7 1500.00000000 x 10 8 150.0000000000 x 10 9 15.0000000000 x 10 10 1.50000000000 x 10 11 = 1.5 x 10 11 1500000000.00 x 10x10 11 jumps to the left +11 in the exponent
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Some distances Nose to finger~1 m The back of the room~10 m SNU Library ~100 m SNU Main gate~1000 m Incheon~50000 m Center of Earth ~6400000 m Earth to Moon ~386,000,000 m Earth to Sun~150000000000 m Next star~40000000000000000 m ~5.0 x 10 4 m ~6.4 x 10 6 m ~3.86 x 10 8 m ~1.5 x 10 11 m ~4.0 x 10 16 m
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nomenclature 10 3 = 1 thousand (kilo) 10 6 = 1 million (mega) 10 9 = 1 billion (giga) 10 12 = 1 trillion (tera)
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Small numbers 1 penny = $0.01 1 dime= $0.10 1 penny = 1/10 th of a dime $0.01 = $0.10x(1 /10) Moving the decimal point 1 place to the right is the same as multiplying by 10
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Negative powers of 10 0.0000000000600.0000000006 x 1/1000.0000000006 x 10 -1 000.000000006 x 10 -1 x10 -1 000.000000006 x 10 -2 0000.00000006 x 10 -3 00000.0000006 x 10 -4 000000.000006 x 10 -5 0000000.00006 x 10 -6 00000000.0006 x 10 -7 000000000.006 x 10 -8 0000000000.06 x 10 -9 00000000000.6 x 10 -10 000000000006.x 10 -11 = 6.0 x 10 -11 11 jumps to the right -11 in the exponent
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Some small sizes radius of a 10 won coin~0.01 m thickness of a 10 won coin~0.001 m thickness of a human hair ~0.000075 m diameter of a red blood cell~0.00000002 m size of hydrogen atom ~0.00000000006 m size of hydrogen nucleus ~0.000000000000001 m ~7.5 x 10 -5 m ~2.0 x 10 -8 m ~6.0 x 10 -11 m ~1.0 x 10 -15 m
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More nomenclature 10 -2 = centi- 10 -3 = milli- 10 -6 = micro- ( ) 10 -9 = nano- 10 -12 = pico-
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exponents are very important Distance to the Sun: 1.5 x 10 11 m Distance to next star: 4 x 10 16 m Exponents differ by 5 Light from the sun takes 8 minutes to get here Light from the next star takes 4 years to get here 8 minutes from now 4 years from now?
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Multiplying large numbers Use the rule: (A x 10 a ) x (B x 10 b ) Number of people In the US x average income/person 301,000,000 x $ 40,100 = 3.01x10 8 x $ 4.01x10 4 = (3.01 x $4.01) x (10 8 x 10 4 ) = $12.1 x 10 8+4 =$12.1 x 10 12 = $1.21 x 10 13 on 1/8/07 10 a+b =(AxB) x (10 a x 10 b ) Sum of everyone’s income
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dividing large numbers = US national debt # of persons in US on 818/07 Ax10 a Bx10 b x= = x 10 a x 10 -b $8,598,000,000,000 301,000,000 persons $8.60 x 10 12 3.01 x 10 8 persons == $8.60 10 12 3.01 10 8 persons x = $2.86 x 10 12- 8 / person move b upstairs = $2.86 x 10 4 / person (= $28,600/ person ) ABAB ABAB 10 a 10 b & change sign 10 a-b
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$28,600 (ladies not included)
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