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The Flying Circus of Physics\\/ITH ANSWERS »
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NOW -with Answers
The flying circus of physics“IITH ANSWERS
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II ing circus ofphysicsThe
WITH NSWERS‘.-';_{"’3-‘I» :_:/4l.'.'I'.-',-'13.‘; '~- ~.-,_\ * ==$:Z1.~§f~'1>?¢'-'.~1;t;/ “ * ‘ -‘4 .~ :"t~?3~.'}“3f.'\'\“?/ /.-&‘,g~’-Z~?;:i§_‘=w?.-;‘I-F,‘ ,_;-I'-'({-1~.'-r_4-?\,'-.x\ r~
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I
JOHN WILEY 8| SONS, New York - Chlchester - Brisbane - Toronto
Copyright © 1975. 1977 by John Wiley & Sons, Inc.All rights reserved. Published simultaneously in Canada.
Reproduction or translation oi any part oi this work beyondthat permitted by Sections 107 or I08 oi the 1976 United StatesCopyright Act without the permission oi the copyright owneris unlawlul. Requests ior permission or iunher informationshould be addressed to the Permissions Department, JohnVlfiley & Sons, lnc.
Library of Congress Cataloging in Publication Data:
Walker. Jearl. 1945-The iiying circus oi Physics.Bibliography1. Physics-Problems, exercises, etcl. Title.QC32.W2 530 75-5670ISBN O-47t»02984-xPrinted in the United States of America
3029282726252423
for elizabeth
Preface
These problems are for fun. I never meant them to be takentoo seriously. Some you will find easy enough to answer.Others are enormously difficult, and grown men and womenmake their livings trying to answer them. But even thesetough ones are for fun. I am not so interested in how manyyou can answer as I am in getting you to worry over them.
What I mainly want to show here is that physics is not some-thing that has to be done in a physics building. Physics andphysics problems are in the real, everyday world that we live,work, love, and die in. And I hope that this book will captureyou enough that you begin to find your own flying circus ofphysics in your own world. If you start thinking about phys-ics when you are cooking, flying, or just lazing next to astream, then l will feel the book was worthwhile. Please let meknow what physics you do find, along with any corrections orcomments on the book.‘ However, please take all this as beingjust for fun.
Jearl Walker
My grandmother’: houseAledo, Texas, 1977
‘Physics Department, Cleveland State University, Cleveland, Ohio 44115.
i i
Acknowledgments
I should in no way give the impression that this book was written by mealone. Lots of people contributed, helped, argued, criticized, encour-aged, and understood. Since I was a graduate student at the Universityof Maryland when I wrote the book, I must thank Howard Laster andHarry Kriemelmeyer for their willingness to support a graduate studentwith such an offbeat idea. Dick Berg, also at Maryland, contributedmany ideas and hours of discussion. Sherman Poultney not only gaveme several good problems but also was understanding when my disserta-tion occasionally lfrequently) fell victim to my book. My wife,Elizabeth, typed and edited the manuscript. Art West, who was also agraduate student at the time, gave very valuable and detailed sugges-tions on the semifinal version. However, it was Joanne Murray whotoiled through my morass of the English language and read and editedmany versions of the manuscript. I am especially indebted to her. Ialso thank Don Deneck, Edwin Taylor, George Arfken, Ralph Llewellyn,and A. A, Strassenburg who thoughtfully read the manuscript andoffered many very valuable suggestions.
Jearl Walker
1 Hiding under the covers,listening for the monsters1
1.11.2
1.3
1.4
1.51.61.71.8
1.91.101.11
1.12
1.131.141.151.161.171.181.191.201.211.221.23
1 .24
1.251.261.27
Squealing chalk 3A finger on the wine glass3Two-headed drumvibrations 3Bass pressed into records3Whistling sand 3Booming sand dunes 3Chladni figures 4Pickin' the banio andfingering the harp 4String telephone 4Bowing a violin 4Plucking a rubber band5The sounds of boilingwater 5Murmuring brook 5Walking in the snow 5Silence after a snowfall 5Ripping cloth 5Knuckle cracking 6Snap, crackle, and pop 6Noise of melting ice 6An ear to the ground 6Voice pitch and helium 6Tapping coffee cup 6Orchestra warmup andpitch changes 7Bending to the ground tohear an airplane 7Culvert whistlers 7Music hall acoustics 7Acoustics of aconfessional 7
1 .28
1 .29
1.301.31
1.321.331.341.351.361.37
1.38
1.39
1.40
1 .411 .421 .43
1.44
1.45
1.461.47
1.48
1.491 .50
1 .511.521 .531 .541.55
Sound travel on a coolday 8Silent zones of anexplosion 8Echoes 8The mysterious whisperinggallery 9Musical echoes 10Tornado sounds 10Echo Bridge 10Sound travel in wind 11Brontides 11Shadowing a seagull‘s cry11Lightning without thunder12Submarine lurking in theshadows 12Cracking a door againstthe noise 12Feedback ringing 12Foghorns 13Whispering around a head13End effects on open-ended pipes 13Getting sick frominfrasound 13Noisy water pipes 13Piles and ripples of aKundt tube 14Pouring water from abottle 14Seashell roar 14Talking and whispering14Shower singing 15A shattering singer 15Howling wind 15Twirl-a-tune 15Whistling wires 16
Contents
1.561.57
1.581.59
1.601.611.62
1 .631.64
1.65
1.661.67
1.68
1.691.701.711.72
1.731.741.75
1.76
1 .77
The whistling teapot 16Blowing on a Coke bottle16Police whistle 17Whistling through yourlips 17Gramophone horns 17Vortex whistle 17Sizes of woofers andtweeters 17The cheerleading horn 18Bass from small speakers18Screams of race cars andartillery shells 18Bat sonar 18Hearing Brownian motion18When the cops stop theparty 19V-2 rocket sounds 19Cocktail party effect 19Taping your voice 19Fixing the direction of asound 20Sonic booms 20Sounds of thunder 20Hearing aurora and frozenwords 20Dark shadows on clouds21Whip crack 21
2 The walrus speaks ofclassical mechanics 22
2.1
2.2
Run or walk in the rain?23Catching a fly ball 23
2.3
2.4
2.52.6
2.72.82.9
2.102.112.12
2.132.142.15
2.1 62.172.18
2.192.202.21
2.22
2.23
2.242.252.26
2.272.282.292.302.31
Running a yellow light23Getting the bat there intime 23Turn or stop 24The secret of the golfswing 24Jumping beans 24Jumping 24Throwing the Babe a slowone 25Karate punch 25Hammers 25Softballs and hardballs25Heavy bats 25Jerking chair 25Click beetle's somersault26The weight of time 26Pressure regulator 26The superball as a deadlyweapon 27Locking brakes 27Wide slicks on cars 27Friction in drag racing27Sliding stick across fingers28Accelerating and brakingin a turn 28Starting a car 28Left on the ice 28Turning a car, bike, andtrain 29Pool shots 29Superball tricks 30Bike design 30I-lula-Hoop 31Keeping a bike upright31
2.322.332.342.352.362.372.382.392.402.412.42
2.432.442.452.462.472.48
2.492.50
2.512.52
2.53
2.54
2.552.562.57
2.582.592.602.61
2.62
Cowboy rope tricks 31Spinning a book 31Fiddlesticks 32Eskimo roll 32Large diameter tires 32Car in icy skid 32Tire balancing 32Tearing toilet paper 32Skipping rocks 33Car differential 34Racing car engine mount34Tightrope walk 34Carnival bottle swing 34Falling cat 34Ski turns 34Yo-yo 35Slapping the mat in iudo35Bullet spin and drift 35The leaning tower ofbooks 35Falling chimneys 36The Falkland Islandsbattle and Big Bertha 36Beer's law of river erosion36A new twist on thetwirling ice skater 36Boomerangs 37Swinging 37Soldiers marching acrossfootbridge 37Incense swing 38Road corrugation 38A ship's antiroll tank 39lnverted pendulum,unicycle riders 39Spring pendulum 39
2.63
2.642.65
2.66
2.672.682.692.702.712.722.732.74
2.75
2.762.77
2.782.79
The bell that wouldn'tring 40Swinging watches 40Earth vibrations nearwaterfalls 40Stinging hands fromhitting the ball 40The archer's paradox 40Magic windmill 41Personalities of tops 42Diabolos 42Spinning eggs 42The rebellious celts 42Tippy tops 43Seeing only one side ofmoon 43Spy satellites over Moscow43Moon trip figure 8 44Earth and sun pull onmoon 44Making a map of India 44Air drag speeds upsatellite 44
3 Heat fantasies and othercheap thrills of the night 45
3.1
3.2
3.3
3.43.5
3.6
3.7
The well-built stewardess46Making cakes at highaltitudes 46The Swiss cottage baro-meter 46Wells and storms 46One balloon blowing upanother balloon 46Champagne recompression47Emergency ascent 47
3.83.9
3.10
3.113.123.133.143.153.163.17
3.18
3.193.20
3.213.22
3.23
3.243.253.263.27
3.283.293.303.313.323.333.343.353.36
3.373.38
Blow-holes 47Decompression schedule48Hot water turning itselfoff 48Bursting pipes 48Fever thermometer 49Heating a rubber band 49Watch speed 49U—tube oscillations 49Bike pump heating up 50West-slope hill growth50The Chinook and goingmad 50Coke fog 51Convertible cooling effect51Death Valley 51Mountain top coldness51Holding a cloud together51Mushroom clouds 51Holes in the clouds 51Mountain clouds 52Spherical cloud of A-bomb blast 52Burning off clouds 52Mamma 53Cause of fog 53Breath condensation 53Contrails and distrails 53Salt water bubbles 53Fireplace draft 54Open-air fires 54Cigarette smoke stream54Stack plumes 55Shades of ice coverings55
3.393.40
3.41
3.42
3.433.443.453.463.473.483.49
3.503.513.52
3.533.543.55
3.563.57
3.583.59
3.603.61
3.623.633.643.65
3.663.673.68
Freezing water 55Freezing hot and coldwater 55Worldwide thunderstormactivity 56Getting stuck by the cold56Wrapping ice 56Pond freeze 56Skiing 56Ice skating 57Snow avalanche 57Making a snowball 57Snow tires and sand forice 58Salting ice 58Antifreeze coolant 58Feeling cool while wet58Carburetor icing 58Eating polar ice 59A pan top for boilingwater 59Briefly opening oven 59Water tub saving thevegetables 59lcehouse orientation 59Heating meat with a“Sizzle Stik" 60The highest mountain 60The boiling water ordeal60Boiling point of water 60A pudd|e's salt ring 61Dunking bird 61Dancing drops on hotskillet 62Geysers 62Percolator 63Single—pipe radiators 63
3.69
3.703.71
3.723.733.74
3.753.76
3.773.783.79
3.803.813.82
3.833.84
3.853.86
3.87
3.88
3.89
3.903.913.92
3.933.94
3.95
Licking a red-hot steelbar 63Banging radiator pipes 64Wrapping food withaluminum foil 64Old incandescent bulb 64How hot is red hot? 64Cool room withrefrigerator 64Black pie pans 65Archimedes's death ray65Toy putt-putt boat 65Feeling cold obiects 65White clothes in the tropics66Cast-iron cookery 66The season lag 66Temperature of space walk67Greenhouse 67Why do you feel cold?67Wrapping steam pipes 68Thunderstorm winddirection 68Silvery waves from yourfinger 68Insect plumes over trees68Shrimp plumes and Ferriswheel rides 69Heat stroke 69Cooling a coffee 70Polariod colordevelopment 70Heat islands 70Total kinetic energy'in aheated room 70Smudge pots in theorchard 71
3.96
3.973.983.99
3.100
3.1013.102
3.1033.104
3.105
3.106
3.107
3.1083.1093.110
3.1113.1123.113
3.114
3.1153.116
A warm blanket of snow71Fires from A-bombs 71Growing crystals 71Snowflake symmetry 71Two attractive Cheerios71Cultivating farmland 71Wall curvatures of a liquidsurface 72Rising sap in trees 72Ice columns growing inground 72Growing stones in thegarden 72Winter buckling of roads73Shorting out a masonrywall 73Soap bubbles 73Inverted soap bubbles 74A candle’: flickeringdeath 74Dustexplosion 74Davy mine lamps 74Mud polygons and dryingcracks 75Thermal ground cracks75Stone nets 75Life and the Second Law75
4 The madness of stirring tea76
4.1
4.2
Holding back the NorthSea 77Breathing through air tube77
4.3
4.44.5
4.64.74.84.9
4.104.11
4.124.134.144.15
4.16
4.174.184.19
4.20
4.21
4.22
4.23
4.24
4.254.264.27
4.28
4.29
Measuring blood pressure77Last lock in Panama 77Panama Canal ocean levels77Hourglass's bouyancy 77Boat sinking in pool 77Coiled water hose 78Floating ship in dry dock78Submarine stability 78Floating bar orientation78Fish ascent, descent 79lnverted water glass 79Floating bodies 79Stability of an invertedglass of water 79The perpetual saltfountain 79Salt fingers 80Salt oscillator 80Narrowing of falling waterstream 80Beachball in an air stream80Toy with suspended ball81Ball balanced on a wateriet 81Egg pulled up by water81Spoon in a faucet stream82Water tube spray guns 82Passing trains 82Ventilator tops and prairiedog holes 82Insects rupturing onwindshields 83Flapping flags 83
4.30
4.314.32
4.334.344.354.364.374.38
4.39
4.40
4.414.424.434.44
4.45
4.464.474.48
4.494.504.514.524.53
4.544.554.564.574.584.59
4.60
Wings and fans on racingcars 83Lifting an airplane 84Pulling out of nose dive84Sailing into the wind 84Frisbee 84Manpowered flight 85Golf ball top spin 85Flettner’s strange ship 85Winds through a building86Curve, drop, and knuckleballs 86Curves with smooth balls86Building waves 86Monster ocean waves 86Whitecaps 87Boat speed andhydroplaning 87Whirligig beetle waves87Ship waves 88Edge waves 88Swing of waves to shore89Surf skimmer 89Surfing 89Bow-riding porpoises 89Ocean tides 90Tides: sun versus moon90Tidal friction effects 90Seiches 91Tidal bores 91Bay of Fundy tide 92Sink hydraulic iump 93Standing waves in fallingstream 93Beach cusps 93
4.614.62
4.634.644.65
4.664.674.68
4.694.704.714.724.734.74
4.754.76
4.77
4.784.794.80
4.81
4.824.83
4.84
4.854.86
4.874.88
4.89
Ekman spiral 93Stronger ocean currentsin the west 94Tea leaves 94River meander 94Rising ball in rotatingwater 94Taylor's ink walls 95Bathtub vortex 95Tornadoes and waterspouts 95Soda water tornado 95Coffee cup vortex 95Dust devils 95Fire vortices 96Steam devil 96Vortex rings from fallingdrops 96Ghost wakes 96Hot and cold air vortextube 97Birds flying in V formation97Sinking coin 97Tailgating race cars 97Several sinking objectsinteracting 98Stange air bubbles inwater 98Fish schooling 99Wind gusts on building99Tacoma Narrows Bridgecollapse 99Air turbulence 100Watch speed on a mountaintop 100Wire mesh on faucet 100Fast swimming pools100Nappe oscillations 100
4.904.91
4.92
4.934.94
4.954.964.97
4.984.99
4.1004.101
4.102
4.1034.1044.1054.1064.1074.1084.1094.1104.111
4.112
4.1134.1144.1154.116
4.1174.1184.1194.1204.121
Parachute holes 101Speed of a drifting boat101The gaps in snow fences101Snow drifts 101Streamlined airplane wings101Skiing aerodynamics 102Dimpled golf balls 102Flight of the plucked bird102Bird soaring 103Kites 103Cloud streets 103Coffee laced with polygons104Longitudinal sand dunestreets 104Smoke ring tricks 105Sand ripples 105Siphons 106Marching sand dunes 106The Crapper 106Street oil stains 107Lake surface lines 107Milk‘s clear band 107Spreading olive oil onwater 107Marine organic streaks108Splashing milk drops 108Water bells 108Water sheets 109Gluing water streams109Pepper and soap 109Pouring from a can 109Tears of whiskey 110Aquaplaning cars 110Floating water drops 110
4.1224.1 234.124
4.1254.126
4.127
4.1284.1 294.1 304.1 31
Soup swirl reversal 110A leaping liquid 110Rod-climbing egg whites110Liquid rope coils 111Thixotropic margarine111Die-swelling Silly Putty111Bouncing putty 112Self.—siphoning fluids 112Quicksand 112Unmixing a dye solution112
5 She comes in colorseverywhere 114
5.15.25.3
5.4
5.55.6
5.75.85.9
5.105.1 15.125.1 3
5.145.15
5.165.17
Swimming goggles 115The invisible man 115Playing with a pencil inthe tub 115Coin's image in water115Distance of a fish 116Ghosting in double-walledwindows 1 16Mountain looming 116Fata Morgana 116Oasis mirage 117Wall mirage 117Paper doll mirage 118One-way mirrors 118Red moon during lunareclipse 118Ghost mirage 118Number of images in twomirrors 1 19The green flash 119Bouncing a light beam1 19
5.18
5.19
5.20
5.215.225.235.245.255.265.275.28
5.29
5.305.31
5.325.335.345.35
5.365.375.385.395.405.415.425.435.445.455.465.475.48
5.49
Flattened sun and moon120Blue ribbon on sea horizon12030° reflection off the sea120Lunar light triangles 120Shiny black cloth 120Inverted shadows 121Pinhole camera 121Eclipse leaf shadows 121Heiligenschein 121Bike reflectors 121Brown spots on leaves1 22Rays around your head'sshadow 122Cats’ eyes in the dark 122Brightness of falling rain122Rainbow colors 122Pure reds in rainbows 123Supernumerary bows 123Dark sky between bows123Rainbow polarization 123Lunar rainbows 123Rainbow distance 123Rainbow pillar 123Reflected rainbows 124Dewbows 124Sun dogs 124The 22° halo 125Fogbovvs 125Sun pillars 125Other arcs and halos 126Crown flash 127Polarization for car lights127Polarized glasses and glare127
5.505.51
5.52
5.53
5.54
5.55
5.565.575.585.595.605.61
5.625.63
5.64
5.655.66
5.67
5.68
5.69
5.705.71
5.725.73
5.74
5.75
Sky polarization 127Colored frost flowers127Cellphane between twopolarizing filters 127Spots on rear window128Optical activity of Karosyrup 128Animal navigation bypolarized light 128Magic sun stones 129Haidinger's brush 129Sunset colors 129The blue sky 130Twilight purple light 130Zenith blue enhancement130Belt of Venus 130Green street lights and redChristmas trees 130Brightness of daytime sky130Yellow ski goggles 131Stars seen through shafts131Colors of lakes and oceans131Color of overcast sky131Seeing the dark part of themoon 131White clouds 131Sunlight scattered byclouds 131Maps in the sky 132Mother-of-pearl clouds133Young's dusty mirror1 33Searchlight beams 133
5.76
5.77
5.785.795.805.815.825.835.845.855.865.87
5.88
5.89
5.90
5.91
5.92
5.935.945.955.965.975.985 .99
5.100
5.101
5.1025.1035.104
Zodiacal light andgegenschein 133Windshield light streaks134Color of a city haze 134Glory 134Corona 135Frosty glass corona 135Bishop's Ring 135Streetlight corona 135Blue moons 135Yellow fog lights 135Blue hazes 136Shadows in muddy water136Color of milk in water136Color of cigarette smoke136Color of campfire smoke136Oil slick and soap filmcolors 136Color effects afterswimming 136Liquid crystals 137Butterfly colors 137Dark lines in a fork 137Eye floaters 137Points on a star 137Poisson spot 138Eclipse shadow bands138Sunset shadow bands138Bands around a lake'sreflection 138Star twinkle 138Bleaching by light 139Optical levitation 139
5.105
5.1065.1075.1085.109
5.1105.111
5.112
5.1135.114
5.1155.1165.117
5.118
5.119
5.1205.1215.1225.123
5.124
5.125
5.1265.1275.128
5.1 29
5.1 30
Lights through a screen139Star color 140Luminous tornado 140Sugar glow 140Suntans and sunburns140Fireflies 141Other luminescentorganisms 141Photosensitive sunglasses142Black-light posters 142Fluorescent lightconversion 142Speckle patterns 142Humming and vision 142Sunglasses and motiondistortion 143Top patterns before TVscreen 143A stargazer's eye jump143Retinal blue arcs 143Phosphenes 144Streetlamp sequence 144Spots before your eyes145Purkinie's shadow figures145Early morning shadows inyour eyes 145Purkinie color effect 145Mach bands 146Seeing the colors of yourmind 147Making colors with a finger147Colors in a black andwhite disc 147
5.131
5.1325.133
5.1345.1355.1365.1375.138
5.1395.140
5.1 41
5.142
Color effects fromfluorescent lights 148Floating TV pictures 1483-D movies, cards, andposters 148Enlarging the moon 149Rays of Buddha 149Moon-to-sun line 149Bent search beams 150Rear lights and a redlight 150Snowblindness 150Resolution of earth objectsby astronauts 150A Christmas baIl'sreflection 150Moire patterns 151
6 The electrician's evil and thering's magic 152
6.16.26.3
6.46.56.6
6.7
6.86.9
6.10
6.116.126.136.14
Electrocution 153Frog legs 153Getting stuck to electricwire 153Electric eel 153Microwave cooking 154Time to turn on light154Shocking walk on rug154Kelvin water dropper 154Electrical field and waterstreams 155Snow charging wire fences155Scotch tape glow 155Sifting sugar 155Gas truck chains 155Charge in shower 155
6.15
6.16
6.17
6.186.19
6.20
6.21
6.22
6.236.24
6.25
6.266.27
6.286.29
6. 306. 316.326. 336.346.356.366.376.386.396.406.416.42
Happiness and negativecharge 155Fall through the floor156Sand castles and crumbs156Food wrap 156Magnetic—field dollar bill156Bubbles moved bymagnetic field 156Electromagnetic levitation156Turning in the shade of amagnetic field 156Car speedometer 157Perpetual magnetic motion157Radio, TV receptionrange 157Crystal radio 158Airplane interference withTV 158AM car antenna 158Multiple stations on radio158Auroral displays 158Whistlers 160Lightning 160Earth's field 160Lightning forms 161Ball lightning 161H-bomblightning 162Volcaniclightning 162Earthquake lightning 162Franklin'skite 162Lightning rod 163Lightning and trees 163Lightning strikes to aircraft163
6.43
6.446.45
6.466.47
6.486.496.50
Rain gush after lightning164Clothes thrown off 164Ground fields in lightninghit 164st. Elmo's fire 165Living through lightning165Andes glow 165Electrical pinwheel 165Power-line blues 166
7 The walrus has his last sayand leaves us assorted goodies167
7.17.2
7.37.47.57.67.77.8
7.9
7.10
7.11
7.12
7.13
7.14
7.15
UFO propulsion 168Violating the virgin sky168Olber's paradox 169Noctilucent clouds 169Water witching 170Snow waves 170Fixed-point theorem 170The great leap downward171Beating and heating eggwhites 171Pulling off Scotch tape171Footprints in the sand172Balloon filled with waterand sand 172Buying a sack of corn172Radiation levels in anairplane 172Flashes seen by astronauts172
7.16
7.177.18
7.197.207.217.227.237.24
X rays in the art museum173Nuclear-blast fireball 173Defensive shields in Dune173Friction 173The flowing roof 173Cracks 174Chrome corrosion 174Polishing 174Sticky fingers 174
Bibliography 176Index 219Answers 225
The flying circus of physicsWITH ANSWERS
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frictionf8SOl'\3l'\C8
1.1Squealing chalk
Why does a piece of chalk producea hideous squeal if you hold it in-correctly? Why does the orienta-tion of the chalk matter, and whatdetermines the pitch you hear?
Why do squeaky doors squeak?Why do tires squeal on a car thatis drag racing from a dead stop?
1 dwrough 3'.
1850081168
vibration
friction
1.2A finger on the wine glass
Why does a wine glass sing whenyou draw a wet finger around itsedge? What exactly excites theglass, and why should the finger bewet and greaseless? What deter-mines the pitch? ls the vibrationof the rim longitudinal or trans-verse? Finally, why does thewine show an antinode" in itsvibrational pattern 45° behind youfinger?
124, p. 154.
Exceptionally good references: Weath
I
er(a journal), Jones (82), Bragg (159).‘The numbers following the problemsrefer to the bibliography at the end ofthe book."An antinode is where the vibrationalmotion is maximum.
1.3Two—headed drum vibrations
If a two—headed drum, such as theIndian tom-tom, is struck on onehead, both heads will oscillatealthough they may not both beoscillating at any given instant.Apparently the oscillation is fedfrom one to the other, and eachperiodically almost ceases to move.Why does this happen? Wouldn'tyou have guessed that the mem-branes would oscillate in sympathyWhat determines the frequencywith which the energy is fed backand forth?
124, p. 149; 126, p. 474.
?
shearing
1 .5Whistling sand
In various parts of the world, suchas on some English beaches, thereare sands that whistle when theyare walked on. A scraping soundseems plausible, but I can't imaginewhat would cause a whistle. Dothe sand grains have some uniqueshape so that the sand resonates?
81, p. 145' 144, Chapter 17;145, p. 140; 146 through 150,-1483.
oscillationsshearing
harmonic motion
1.4Bass pressed into records
If I tum down the volume on myrecord player and just listen to thesound coming directly from thestylus, I can hear high frequencieswhenever they occur in the music,but there is almost no bass. Am-plifiers take this weaker bass intoaccount and amplify the low fre-quencies much more than thehigh. Is there any practical reasonfor reducing the strength of thebass pressed into records?
143.
1.6Booming sand dunes
Even more curious is the"booming" occasionally heardfrom sand dunes. Suddenly,in the quiet of the desert, a dunebegins to boom so furiously thatone might have to shout to beheard by his companions. Theclue to this may lie in the ac-companying avalanche on theleeward (downwind) side of thedune. Then again, there is nothingunusual about such avalanches forthat is precisely how the dune it-self flows across the desert floor.Under some conditions could oneof these avalanches cause a largevibration of the sand and thusproduce the booming?
144, Chapter 17; 146; 150.
Hiding under the covers. listening for monsters 3
vibration string vibration
standing waves
1.7Chladni figures
Chladni figures are made with ametal disc supported at its centerand sprinkled with sand. As abowstring is drawn across an edge,the sand jumps into some geomet-ric design on the plate (Figure1.7). Why? Nothing to it, yousay? It is just simple standingwaves set up on the plate by the
using the same bowing motion,you get one design with sand andanother design with a finer dust?You can even mix them up before-hand; they'll separate into theirown designs as you bow the plate.
81, pp. 129-131; 82, pp. 172-180; 124, pp. 61-62.‘ 127, pp.172-176; 128. PP- 130- 131;130 through 138; 139, p. 207;141, pp. 178-190; 142, pp. 88-91; 1529; 1551.bowing? Well, then tell me why,
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Bowing a plate to get Chladni figures. (Some of these may require thesupport of the plate in places other than the center.)
1.8Pickin' the banjo and fingering thehaveWhy does the banjo produce atwangy sound and the harp a softmellow sound? One differencebetween the two instruments isthat the banjo is plucked witha pick but the harp is plucked witha finger. How does this makea difference?
82, pp. 283 fi5' 128, pp. 92-93;145, p. 89.
string vibrationl'€$Ol'l8I'l@
1.9String telephone
l-low does the string telephone thatyou played with as a child work?How does the pitch heard in thereceiving can depend on the tight-ness and density of the string andthe size of the can? Approximatelyhow much more energy is transmit-ted with the string telephone thanwithout it?
82, pp. 103- 104.
string vibrationfriction
1.10Bowing a violin
Plucking a string, as a guitarplayer does, seems a straightfor-ward way to excite vibrations in it.
4 The flying circus of plsyolco
But how does the apparentlysmooth motion of bowing excitethe vibrations of a violin string?Does the sound's pitch depend onthe pressure or speed of the bowing?
82, pp. 219-221, 291-800,‘ 124,pp. 98 ff,‘ 126, pp. 453-456; 127,pp. 101-103; 128, pp. 93-94;145, pp. 89-99; 151, PP. 90-93;152, pp. 167-170; 153; 1552.
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Figure I 10string vibration
1.11Piucking a rubber band
Ifyou tighten a guitar string, youraise its pitch. What happens ifyou do the same with a rubberband stretched between thumband forefinger? Does its pitchchange when it is stretchedfarther? No, the pitch remainsfairly unchanged; or, if it doeschange, it becomes lower rathertitan higher. Why is there a dif-ference between rubber bands andguitar strings?
vibration SiFOSS
phase change phase change
1.12The sounds of boiling water
sound of the water tells me henit has begun to boll. First there isa hising that grows and then diesout as a harsher sound takes over.Just as the water begins really toboil, the sound becomes sof r.Can you explain these sounds,especially the softening as thewater begins to boil?
,57|. ,581p- ppc 88'
89,‘ 160, P. 168.
When I heat water for coffee, thew
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1.14Walking in the snow
Sometimes snow crackles whenyou walk in it, but only when thetemperature is far enough belowfreezing. What causes the noise,and why does its productiondepend on the temperature? Atapproximately what temperaturewill the snow begin to crackle?
164, p. 440; 165, p. 144; 166‘.
absorption
154; 155, pp. 186- 187.
vibration
1.13Murmuring brook
At some time in your life you'veprobably spent e sunny afternoonlying in the grass, listening tothe murmur of a brook. Why dobrooks murmur? Why do water-falls and cataracts roar?
What is responsible for thespritely sound of a just-openedsoft drink? Look into a clearsoft drink and try correlatingthe noise with the creation, move-ment, or bursting of the bubbles.
145, p. 140,’ 159,PP. 129- 130;161 through 163.
1 . 15Silence after a snowfall
Why is it so quiet just after a snow-fall? There aren't as many peopleand cars outside as usual, but thatalone doesn't explain such quiet-ness. Where does the energy ofthe outdoor noise go? Why doesthe snow have to be fresh?
A similar sound reduction occursin freshly dug snow tunnels inAntarctic expeditions: thespeakers must shout to be heardif they are more than 15 feetapart. Again, what happens tothe sound energy?
165, p. 134; 167.
1.16Ripping cloth
Why is it that when you tear apiece of cloth faster, the pitch ofthe ripping is higher?
Hiding under the covers, listening for monotere 5
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Figure 1.18"Listen. There it is again. ‘Snap, crackle, pop.
1.17Knuckle cracking
What makes the cracking soundwhen you crack your knuckles?Why must you wait a while beforeyou can get that cracking again?
1 68.
1.18Snap, crackle, and pop
Why exactly do Rice Krispies*go “snap, crackle, and pop" whenyou pour in the milk?
1.19Noise of melting ice
Piop an ice cube or two into yourfavorite drink, and you’ll hearfirst a cracking and then a“frying” sound. What causes thesenoises? Actually, not all ice will
‘A breakfast cereal from the KelloggCompany.
ftlwfli//.!i'* -0/time i
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produce the “frying” sound. Whyis that?
icebergs melting in their south-ward drift also make frying noisesthat can be heard by submarineand ship crews. The sound is called“bergy seltzer."
169.
propagation
1.21Voice pitch and helium
When people inhale helium gas,why dues the pitch of their voicesincrease?
One should be very, verycautious in inhaling helium. Onecan suffocate with the heliumwhile feeling no discomfort be-cause there is no carbon dioxideaccumulation in the lungs. Never,never inhale hydrogen or pureoxygen. Hydrogen is explosiveand oxygen supports burning.Even a spark from your clothescan lead to death.
170, p. 219; 171, pp. 16'-17.
speed of sound
acoustic conduction
1.20An ear to the ground
Why did Indian scouts in the oldWesterns fall to their knees andpress their ears against the groundto detect distant, and unseen,riders? If they could hear thedistant pounding of hoovesthrough the ground, why couldn'tthey hear it through the air?
124, p. 21.
1.22Tapping coffee cup
As you stir instant cream or in-stant coffee into a cup of water,tap the side with your spoon. Thepitch of the tapping changesradically as the powder is addedand then during the stirring. Why?
Tap the side of a glass of beeras the head goes down. Again, thepitch changes. Why?
You may have a tendency toanswer that the foam or the powderdamp the oscillations caused bythe tapping, but even if that is true,would that change the pitch oronly the amplitude?
159. P. 1551' 173.
6 The flying circus of physics
speed of soundand temperature
interference covered with nooks and cran-
1.23Orchestra warmup and pitchchanges
Why does the pitch of the wind' ramstruments increase as an orchestwarms up? Why does the pitch ofthe string instruments decrease?
124, pp. 49-50,‘ 126, p. 498;172.
wavegu ides nies that reflect the sound in
interference
1.24Bending to the ground to hear anairplane
I have read that if I put my headclose to the ground while listeningto an airplane fly by, the pitch ofthe airplane's noise may seam toincrease. Similarly, if i stand bya wall near a waterfall, l may hear,in addition to the normal soundof the waterfall, a softer back-ground sound. The closer I standto the wall, the higher the pitch ofthe extra sound. in either case,why would I hear a soundwhose pitch depends on the near-ness of my ear to the solid struc-ture?
82, pp. 98- 100,‘ 145. P. 59,’ 174through 180.
1.25Culvert whistlers
Stand in front of a long concreteculvert and clap you hands sharply.You will hear not only the echoof your clap, but also a “zroom,"which starts at a high pitch anddrops to a low pitch within afraction of a second.* What'sresponsible for the “zroom"?
101,- 1&2.
1 .26Music hall acoustics
Why are concert halls generallynarrow with high ceilings? Ifechoes are undesirable shouldn'tthe walls and ceiling be close tothe listener? That way thelistener will not be able to distin-guish the direct sound from thereflected sound. What is theminimum time difference betweentwo sounds that the listener n,in fact, distinguish? Why doesa hall full of peopla sound muchbetter than an empty hall?
lf echoas are to be eliminated,why aren't the walls and ceilingscovered with material that willabsorb the sound? Granted thatthe hall's baauty might be de-stroyed, it still appears that hallsare designed so as not to elimin-ate all sound raflections. In fact,the walls and cailings may be
‘Crawford i181) has described these as
every which way. On the otherhand, a hall with no reflectionsis said to be acoustilly dead.
124, Chapter 13,' 127, pp. 531-540; 128, Chapter 10; 142,Chapter 14; 145, pp. 279-293;152, Chapter 9; 158, pp. 60.9-616; 170. PP. 265-266; 171,pp. 44-50; 183, pp. 123- 180.‘184, Chapter 14; 185, Chapter11; 186, Chapter 8; 187, pp.291-300; 188 through 195 1528.
reflection
focusing
1.27Acoustics of a confessional
Some rooms are especially notedfor their strange acoustics; someeven provide a focusing of thesound. Such focusing was ap-parently used in the "Ear ofDionysius" in the dungeons ofSyracuse where the acousticssomehow fed words and evenwhispers of the prisoners into aconcealed tube to be heard by thetyrant.
For an example in recent times,the dome covering the old Hall ofRepresentatives in the Capitolbuilding (Washington, D.C.) wouldreflect even a whisper from oneside of the chamber in such a waythat it would be audible on theopposite side. More than oncethis was rumored to have em-
being analogous to atmospheric whistlers party SBCPBIS I0 their 00119391195.(see Prob. 6.31). The Cathedral of Girgenti in
Hiding under the covers. listening for monsters 7
barrassed representatives whispering
Sicily provided even more severeembarassment. Its shape is that ofan ellipsoid of revolution, so thatsound produced at one focus ofthe ellipsoid is nearly as loud atthe other focus. Soon after it wasbuilt one focus was unknowinglychosen for the position of theconfessional.
The focus was discovered byaccident, and for some timethe person who discoveredit took pleasure in hearing,and in bringing his friendsto hear, utterances in-tended for the priestalone. One day, it is said,his own wife occupiedthe penitential stool, andboth he and his friends werethus made acquainted withsecrets which were thereverse of amusing to oneof the party (141).13.9, p. 194; 14 1, p. 48; 1.97,Utapter 11.
1.29Silent zones of an explosion
During World War ll it was oftennoticed that as one would drivetoward a distant artillery piece,the roar of its fire would disap-pear at certain distances (Figure1.29). Why were there suchsilent zones?
Sound travel over large distancesis also curious. For example,
during World War l people on theEnglish shore could hear gunfirefrom installations in France. Whatconditions permit such an enormoussound range?
150; 165, pp. 135 ff; 187, p. 137;214, p. 2; 215, pp. 23-25 218'217, pp. 9-14; 218; 219, pp.291-293; 313, pp. 71 ff.
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i§1F”“‘r”5§ "2- Mr- -'Figure 1.29
propagation
refraction
1.28Sound travel on a cool day
Why does sound travel farther on acool day than on a warm day? Thisis especially noticeable over calmwater or a frozen lake. The rangeof sounds in the desert, on theother hand, may be noticeablylimited.
81, pp. 34-35 82, p. 107;124, p. 17,‘ 127, pp. 322-325'142, pp. 1 17-1 18,‘ 185, PP.
309-311,’ 186, pp. 66-67,‘ 187,p. 137; 207, pp. 50-52,‘ 209,pp. 24-25' 210, p. 600; 211,pp. 474-475' 212,‘ 213, pp. 49-52.
a higher pitch than that of theinitial sound. Also, why does ahigh-pitched sound usually pro-duce a louder, more distinctecho than a low-pitched sound?l-low close to the reflecting
reflectionwall can you stand and still hearan echo?
Rayleigh scattering
1.30Echoes
I am sure you can explain echoes-they are reflections of the soundwaves by some distant object,right? Then explain why someechoes retum to the speaker with
81, p. 31,‘ 82, pp. 86-87,‘ 127,pp. 311-313,‘ 142, p. 132; 164,p. 426,‘ 182,‘ 1.98, pp. 147-154,‘206.
8 The Ilylng circus of phyelco
Rayleigh wavesintensity and distancereflection
1.31The mysterious whispering gallery
lt was Rayleigh who first explainedthe mysterious whispering galleryin the dome of London's St. Paul'sCathedral. In this large gallerythere is a peculiar auclibility forwhispers. For instance, if a friendwere to whisper to the wall some-where around the gallery, youwould be able to hear his whisperno matter where you might standalong the gallery (Figure 1.31a).Strangely enough, you will hearhim better the more he faces thewall and the closer he is to it.
ls this iust a straightforward re-flection and focusing problem?Rayleigh made a large model ofthe gallery to find out. He placeda birdcall at one point along themodel gallery and a flame atanother point. When sound wavesfrom the birdcall impinged on theflame, the flame would flare, andso the flame was his sound detec-tor. You are probably temptedto draw the sound rays shown inFigure 1.31b. But before you
Z7— -4: lie”_
Figure 1.31bRayleigh ‘s model of whisperinggallery. Birdcall causes flame toflare.
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Figure 1.31aCutaway view of whisperinggallery.
fie?
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Figure 1.31cWith thin screen placed near thewall, birdcall cannot make flameflare.put too much faith in them, sup-pose a narrow screen were to beplaced at some intermediate poinalong the inside perimeter of the 81, pp. 32-33; 82, pp. 87-92;metal sheet (as shown in Figure 127, pp, 315-316; 198, pp, 126-1.310, but exactly where along 129; 199 through 205,
I
the perimeter doesn't matter). lfyour idea about the rays is correct,the flame should still flare be-cause the screen is out of the way,right? Well, as a matter of fact,when Rayleigh inserted a screen,the flame did not flare. Thescreen must somehow have blockedthe sound waves. But how? Afterall, it was only a narrow screenplaced seemingly well out of theway of the sound rays. This resultgave Rayleigh a clue to the natureof the whispering gallery.
lfldiag under the covers. listening for monsters 9
interference reflection
1.32Musical echoes
What causes the musical echo youcan sometimes hear when youmake a noise near a fence or aflight of stairs? Can you calculatethe pitch of the echo?
81, p. 32; 127, pp. 313-314,’145, p. 13,‘ 164, pp. 426-427,‘182,’ 206',’ 207, pp. 47-48,‘ 208.
Rayleigh waves
tu rbulence
refraction
1.33Tornado sounds
My grandmother could alwaysforecast a tornado by thedeathly silence that would sud-denly fall before the appearanceof the tornado. Why the silence?When the twister hit, there wouldbe a deafening roar much like ajet plane's. Why the roar? Finally,there are reports that in thetornado's center it is, again, deathlyquiet. Can this be true? Wouldn'tyou hear at least the furious de-struction taking place outside thecenter?
165, pp. 144-145; 223, pp. 67,83; 224 through 226.
1.34Echo Bridge
The whispering gallery effect maybe responsible for some of thesounds you can hear beneath abridge arch. If you stand near thewall of such an arch (Figure 1.34)and whisper faintly, you will heartwo echoes; a loud handclap will
yield many echoes. Can you ac-count for these echoes? They canresult either from normal reflec-tions off the water or from thewhispering gallery effect, or fromboth.
82, p. 87,’ 202,‘ 203.
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Figure I. 34Echo bridge.
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10 The flying circus of physics
refraction
1.35Sound travel in wind
Why is it easier to hear a distantfriend yell if you are downwindrather than upwind? ls it because,as is commonly thought, there is agreater attenuation in the upwinddirection?
81. PP. 33-34; 82, pp. 107-108; 124, pp. 17- 18,’ 127,pp. 322-325’ 142, pp. 119-121,‘ 185, pp. 11- 13, 311,‘ 185.pp. 65-57,’ 187, p. 137,’ 207,pp. 52-53; 210, pp. 599-500;212; 213. PP. 52-55' 222.
the people ascribe the sounds to Can you think of other possiblethe gods. In other places, how- 9XP|a"aT»i°"5?ever, they are now probably dis-missed as sonic booms.
One is tempted to identify these
164, p. 442,‘ 227; 1611, SectionGS.
mysterious sounds as distant ,See Prob 1 38thunder, but thunder is normallynot heard at distances greaterthan 15 miles‘. Besides, thesesounds are heard on clear days.
diffraction
propagation
1.36Brontides
Throughout history there havebeen tales of mysterious soundsfrom the sky, rumblings, and shortcracklings when the sky is per-fectly clear and there are noobvious noise sources. Thesenoises—called brontides, mist-poeffers, or Barisal guns -areheard virtually everywhere: overflatland, over water, and in themountains. In a study of 200Dutch mistpoeffers it was foundthat the sound came most oftenin the morning and afternoon, lessoften at noon, and hardly everduring the night. In some placesthey are far from rare. For ex-ample, near the Bay of Bengalthey are heard so frequently that
1.37Shadowing a seagull’s cry
For an example of quiet "shadows"behind objects, let me offer thefollowing story (see Figure 1.37).
In the spring the seagulls resortin large numbers to the mossto lay their eggs and when theyoung birds are able to fly,the air is filled with theirshrill screams. There is a roadat a little distance from thenests and by the side of theroad there is sometimes a rowof stacks of peat. The lengthof one of these stacks is manytimes as great as the wave-
length of the scream of thebirds and consequently a goodsound shadow is fonned. Op-posite the gap between twostacks the sound is unpleasant-ly loud; opposite the stack it-self there is almost completesilence, and the change fromsound to silence is quite sud-den (234).
Would there be a quiet region ifseagulls cried in a deep voice ratherthan their shrill one?
128, p. 18; 234, p. 103.
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__ _ __-_ 3,119“: ___ '1;-:<-~¢: _m " - ' —_._ __ ~_ ._ - _ . _____. , ~—---.._i___ - 3 *-"""'-""-"__.?_..-.i-_,
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Figure 1.37
Hiding under the covers. listening for monsters 11
refraction diffraction
1.38Lightning without thunder
Often a lightning stroke appearsunaccompanied by thunder. ln
about 15 miles from the lightning
a great distance for sound toNo, artillery fire and explosionscan certainly be heard beyond 15miles. Why not thunder as well?
82, pp. 114-116,‘ 142, p. 113,’1 - I PP164 pp 441-442 219, . 304-
.30% 220, p. 196.‘ 221.
fact, thunder is rarely heard beyond
flash. Why? Is 15 miles really suchtravel? -
1.40Cracking a door against the noise
If I close my door, which leadsto a very noisy hall, my room iskept quiet. If l open the doorwide, though, it is hard to thinkwith all the noise. How aboutcracking the door iust a little?That certainly should be almostthe same as closing it all the way.Yet, I try it and discover the noiseto be almost as bad as with thedoor wide open. Why does even asmall crack make such a dispro-portionate dlfference in the noiselevel of my room?
128, p. 19,’ 155, p. 177.
1.41Feedback ringing
There was an era in rock and rollwhen feedback was used extensively to give a psychedelic quality tothe music. A guitar player wouldplay facing into his own speaker,and the speaker output would bepicked up and reamplified by hiselectric guitar. That same type ofringing can be heard if a radioannouncer holds a radio tuned tohis own station near his micro-phone. In either case what causesthe ringing?
refraction
1.39Submarine lurking in the shadows
'l'hough sonar systems are powerful a sonar unit and a sub at about the detected. What causes thoseenough to detect submarines at same depth (Figure 1.39). For shadows?very large distances, they are usually some reason other than just absorp-limiled I0 Only several thousand tion, sound radiated toward the sub '7" pp‘ 864$ 785' p‘ 235meters (in the tropics to even less never reaches it; the sub is said to 217’ pp‘ '6' 7'9" 228' pp‘ 376'than 3130- c°1‘15id°l'- f°l' °*3mP1°. be in a shadow area and won't be 379; 229 mmugh 232'
Buoy
Figure 1.39
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12 Tboflylngdlcuoofphydco
diffraction
1.42Foghorns
Foghoms should be designed tospread their sound over a widehorizontal field, wasting as littleas possible upward. Doesn't itseem strange, then, that rectangu-lar foghorns are oriented withthe long sides of their openingsvertical (Figure 1.42). Isn't thatorientation precisely the wrongone?
142, pp. 124- 125' 145, p.167,‘ 159, PP. 159- 160,‘ 235,pp. 78-79; 236.
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diffraction
even if the whisper is as loud ashis nonnal voice?
159, pp. 85-86; 198, p. 127;237, p. 188; 238, pp. 47-48;239, p. 220.
l'8SO|'lBl‘iCB
1.44End effects on open-ended pipes
Why is there an antinode of airmovement (and a node of pres-sure) at each end of an open pipewhen standing sound waves areset up inside? Since there is anode at e closed end, there shouldbe an antinode at an open end,right? Can you actually showwhy there is an antinode there?As e matter of tact, the antinodeis not precisely at the open end,and where it really is depends onseveral parameters of the pipe(width, for example). Will thisdeparture from simple theoryeffect the practical use of pipesin such things as organs?
82, pp. 136- 139,‘ 126. Pp.4.93-496; 127, pp. 181- 182,‘145. PP. 153-165 240,‘ 241.
1.43Whispering around a head
You can hear a friend's normalvoice reasonably well whether heis facing you or turned away.Why is it that you can hear hiswhisper only if he is facing you,
resonant oscillation
1.45Getting sick from infrasound
infrasound (sound of a subaudiblefrequency) can make you nauseousand dizzy. . . it can even kill you.Now that its danger is being re-
cognized, infrasound is being dis-covered in many common set-tings: near aircraft, in cars at highspeeds, near ocean surfs, in thunder-stonns, and near tornados, forexample. It may even warnanimals and some especially sensi-tive people of an impendingearthquake. Why does infrasoundaffect people and animals thisway? In particular, how can itcause such things as intemalbleeding?
171.99. 139- 147; 1489through 1491; 1534 through1536‘.
vibrationcavitationFQSOIIBOCG
1.46Noisy water pipes
Why do the pipes sometimes groanand grumble when I turn on andoff my water faucet? Why doesn'tit happen all the time? Whereexactly does the noise originate:in the faucet, the pipe immediate-ly behind it, or a turn in the pipesomewhere down the line? Why isthere rumbling only with certainflow rates? Finally, why can theproblem be alleviated by adding avertical pipe of trapped air to thewater pipe?
183, p. 46; 251; 252.
Illdlng under the covers. listening for monsters 13
IBSOHBIICQ TQSOHGHCG
vortex motion cavitation
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1 .48Pouring water from a bottle
As water is poured from a bottle,the pitch of the pouring noisedecreases. As water is poured backin, the opposite change in pitchoccurs. Why?
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1 .49Seashell roar
What causes the ocean roar thatyou hear in a seashell?
82, pp. 196-1.97,‘ 141, pp. 253-254,‘ 150; 238, pp. 57-58, 55.
1.41 With a loudspeaker as an exciter, resonance
Piles and ripples of a Kundt tube
The Kundt tube has long been asimple demonstration of acousticstanding waves, but can you reallyexplain how it works? It consistsof along glass tube containingsome light powder (cork dust orlycopodium powder, for example).The tube is corked at one endand sealed at the other with abrass rod (Figure l.47a). Whenthe rod is stroked with a rosin-coated chamois, not only does therod squeal, but also the dust in thetube collects in periodic piles alongthe tube. Standing sound wavesmust do this to the dust, but how?Moreover, if one of the piles of
thin discs ofdust form across thetube ’s cross section.
powder is examined closely, it isfound to contain a series of ripplesIf standing waves make the piles,what makes the ripples?
If the rod is replaced by a puretone loudspeaker, discs form inbetween the piles (Figure 1.47b).Each disc resembles a very thinbarrier extending across the tube.What generates them?
82, pp. 208-214; 124, pp. 113-114; 127 pp 188-191 255-258
vibration
1.50Talking and whispering
What determines the pitch of yourvoice? Why are women's voiceshigher than men's? Many youngmen go through a stage in whichtheir voices change. What causesthat? How do you switch from anormal voice to a whisper?
81 pp. 113-114' 124 pp. 75-774 2_ 2' - _' _ 1 132-1.26; 127.1111. 202-211; 141,7 , 1 8, pp. 22-23, 130, 141,pp. 244-253; 145, pp. 220-222.‘207, pp. 151- 156; 243 through250.’ 1517.
pp. 238-244; 142, pp. 179- 181;145, pp. 254-255’ 151, pp. 175-177; 238, Chapter 7; 239;253, p. 387,‘ 254.
14 The flying circus of physics
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1.51Shower singing
Why does your singing sound somuch richer and fuller in theshower (Figure 1.51)?
1.52A shattering singer
Champagne glasses can be shatteredby opera singers who sing at somehigh pitch with great power. Whydoes the glass shatter, and whymust a particular pitch be sung?Why does it take several secondsbefore the glass shatters?
1.53
Howling wind
Monster movies always have ahowling wind as a background
III!!!_)'4.
sound to the sinister deeds of themonster. How does wind howl?
150; 154, pp. 442-443.
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Bernoulli effect
1.54Twirl-a-tune
A musical toy called "Twirl-a-tune"' is a surprisingly simpletoy: it's nothing but a flexible,corrugated plastic tube mademuch like a vacuum cleaner hoseand open at both ends. Whenheld by one end and whirled about(Figure 1.54), it produces amusical tone. At higher speeds,you get higher pitched tones; thetransition from pitch to pitch isnot smooth but takes place injumps. A gathering of manytwirlers can produce quite a
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sound, and the fairies in a partic-ular English presentatlon ofA Midsummer Night's Dream evengave a chorus of such twirlingtubes to enhance their magic(I588). How are the tones made,and why are the pitch changesdiscrete?
The tendency will be to dismissthe questions by pointing to thestandard textbook example ofsound resonance in open-endedpipes. But here you will first haveto understand why there is anysound at all and why the sound'sfrequency range depends on thewhirling speed. Also, you shouldfigure out which way the air movesthrough the tube. Only then canyou use the textbook explanationof why only certain frequencieswill be stored and built up insidethe tube.
Will the centrifugal force on thetube affect the frequency of thesound?
1588.‘Avalon industries, lnc., 95 LorimerSt., Brooklyn, New York 11206; seeRel, 1588 for other trade names.
Hiding under the covers 15
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vortex formation feedback
1.55Whistling wires
Why do telephone wires whistlein the wind? Why did the aeo-lian harps of ancient Greece singwhen left in the wind? In partic-ular, do the wires or strings them-selves have to move in order toproduce the sound? If theymove, do they move in the planeof the wind or perpendicular toit? What determines the pitch youhear?
Suppose you were to simulatethe wind whistling through tele-phone wires by waving a fork withlong, thin prongs. Which waywould you wave it, in the plane ofthe prongs or perpendicular to thatplane? Try it both ways.
What causes the sighing of treesin winter and the murmur of anentire forest? Do all trees sigh atthe same pitch?
82, pp. 304-313? 124, pp. 114-116; 126. pp. 480-482; 127,pp. 218-220; 142, p. 215; 145,pp. 149-152; 150; 155, PP. 188-189; 164, PP. 443-448; 165,p. 144; 207, PP. 156-157; 256,pp. 126-128; 257, PP. 123-130;258 through 261.
1 .56The whistling teapot
Other types of whistles use anobstruction in the way of the airstream. For example, an edgetone can be produced by direct»ing an air stream onto a wedge(Figure 1.560). Similarly, aring tone is made by placing a ringin the stream path (Figure 1.56 b).The most familiar of all is thecommon teapot whistle that hasa hole in the stream’s way andthat produces what is called ahole tone (Figure 1.56c). In eachexample the whistling sound de-pends on the obstructing object,but how? What really produces thewhistling you hear when your tea-pct bolls?124, PP. 116 ff; 126, PP. 482-485;127, pp. 220-23; 142, P. 216;145, PP. 169-174; 151, pp. 95-97; 257, pp. 130- 138,‘ 258; 263through 269.
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sound from vortices
1.57Blowing on a Coke bottle
Making a Coke bottle hum byblowing across its opening is anexample of still another type ofwhistle. Not only is there an ob-struction, the edge of the bottle,but there is also a cavity adjacentto the obstruction. Flutes, record-ers, and organ pipes are other
examples of the same kind ofwhistle.
Why do such devices produceparticular frequencies? In otherwords, how do the fingering ofholes on the cavity (as in the caseof the flute) and the change of airpressure across the obstructiondetermine the different frequenc-ies that can be made? ln the caseof the Coke bottle, does thebottle's mouth size affect thefrequency? How about shape?Suppose I partially fill a bottle
16 Theflplngclreuaofphyotco
with water, excite it with tuningforks to find its resonant frequency,and then tilt the bottle. The in-ternal shape changes, of course,but does the resonant frequency?
142, p. 163; 151, pp. 95-97;15.9, pp. 74-75; 170, pp. 218-219.‘ 258; 310; 1553.
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1.58Police whistle
How does an American policewhistle work? As above, there isan edge across which air is blownand there is an adjacent cavity.Thereisalsoasmallballinthatcavity. What does the ball do forthe whistling? Why won't thewhistle work underwater?
258.
1.59Whistling through your lips
Finally we come to the mostcommon whistle of them all,although perhaps the most difficulto explain: whistling through yourlips. What's responsible for thissound? Can you whistle under-water?
82.‘ 258.
1 .60Gramophone horns
Remember the old gramophoneswith their cranks and big horns?
Why did they have homs? Did thehorns concentrate sound in a cer-tain direction? Why did they usean expanding horn and not just astraight tube? The point was thatif the sound box's diaphragmcoupled directly to the room's airwithout the intervening horn,there was poor sound emission.What can an expanding horn do incoupling the sound box with theair?
124, pp. 212-214; 185, pp. 208-209.
vibrationacoustic impedancepower
1.62Sizes of woofers and tweeters
Why is the woofer (low frequencyspeaker) so much larger than thetweeter (high frequency speaker)in most hi-fi systems?
128, p. 148; 187, pp. 272-273,280; 228. pp. 174- 175.
sound from vortioes
1 .61Vortex whistle
'I‘he vortex whistle (Figure 1.61)produces sound when you blowthrough a tube that juts out froma round cavity. Apparently vor-tices are set up in the cavity and,when they emerge from a centralhole, a whistling sound is made.Unlike the common “policewhistle," the vortex whistle pro-
duces a frequency that dependson the presure with which thewhistle is blown. Hence, by vary-lng the pressure, you can playtunes on it. What produces thewhistling sound, and why doesthe frequency depend on the pressure?
258,‘ 262.
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26, I8 (I954).Vortex whistle (after Bernard Vonnegut, J. Acoustical Soc. Amen,
llldlng under the oovoro. listening for monsters 17
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spherical and plane wavesintensity versus rangeimpedance
1.63The cheerleading horn
How does a cheerleader's hornmake the yell louder in one direc-tion? Do multiple reflections in-side the horn limit the directionof spreading? This may seemreasonable, but considering thesize of the horn compared tothe wavelengths of the sound,how can there possibly be sucha concentrating effect due to in-ternal reflections? So, again,why is the yell louder in the direc-tion of the horn?
127. PP. 205-207; 142, p. 111,‘145, PP. 239-240,’ 159.Pp. 12-13; 213, P. 47,‘ 235, p. 78; 242.
400-402,‘ 128, pp. 31-32, 56-59; 151, pp. 117-120,’ 152, pp.105- 108; 170,Pp. 40-42; 184,pp. 403-406; 209, pp. 179-187; 228. pp. 253-256; 237,pp. 66-63; 256, PP. 231-245270, pp. 129- 133; 271, pp. 50-52; 272, Chapter 7, pp. 41 1-413; 273 through 279.
Doppler shift
combination tonesnonlinear response
1.64Bass from small speakers
Isn't it surprising that telephones,high fidelity earphones, and smalltransistor radios can reproducebass (see Prob. 162)? The speakein them are so small, yet one doeshear bass from them. The hornson early gramophones shouldn'thave been able to handle lowfrequencies either. In both cases,why is bass heard?
82, pp. 256-261; 124, pp. 29-32, 84-87, 165, 214; 127, pp.
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1.65Screams of race cars,artilleryshells
Why does the pitch of a racecar's scream change as the carspeeds past you? Surely the noisethrown forward is no differentfrom that thrown backward.
On the battlefield men canpredict the danger of an incomingshell by the scream it makes.Not only do they listen for thechange in loudness but also thepitch and its change. What doesthe pitch tell them?
128, p. 19.
thus finding the distance to areflecting obiect? Does it detectthe Doppler shift (frequency shift)if either it or the obiect is movinOr does it locate the obiect by
g?
triangulation of the return sound,much as we perceive depth withbinocular vision? Maybe it iseven more complicated becausesome bats chirp, that is, each soundpulse sweeps from about 20 kHzdown to 15 kHz. How can suchchirp be used to extract more in-formation about the object?
What is the smallest insect thata bat can detect using a constantfrequency pulse of 20 kHz?
142 pp 353-354 280 throu. - .' gh284; 1493 through 1497.
Brownian motionhearing
Doppler shiftranging
1.66Bat sonar
To find their way and to locateinsects, most bats emit a high fre-quency sound and then detect theecho. What does a bat actuallydo with the echo? Does it emita sound pulse and time its return,
1.67Hearing Brownian motion
Hearing involves detection of airpressure variations, right? Well,the air next to the eardrum is con-tinually fluctuating in pressure.How large are those fluctuationsthe ear drum, and are they largeenough to be heard? if they are,then why don't you hear them?Shouldn’t there be a continuousroar in your ears?
311.
on
18 The flying circus of physics
acoustic power shock wave hearing
signal-to- noise ratio
1.68When the cops stop the party
Some cocktail parties are quiet;others are loud. Can you roughlycalculate the critical number ofguests beyond which the party be-comes loud? You might take thetransition point as when the back-ground noise on your listener be-comes as great as your volume onhim.
Suppose the guests are called toattention by the hostess, and then,afterwards, allowed to resume theirconversations. About how muchtime will pass before the party be-comes loud again?
285.
1.69V-2 rocket sounds
If you were being fired on withartillery shells, you would firsthear the shelI's scream, then itsexplosion, and finally the roar ofthe gun. But in the V—2 rocketattacks on London during WorldWar II, the first two sounds camein reverse sequence: first the
1.70Cocktail party effect
How can you distinguish thewords of one person when there isa lot of background noise? If youtape a friend talking to you at aloud party, it's likely that on tapeyou won’: be able to hear him atall, much less understand thewords. Why the difference?
explosion, and slightly later the _ _rocket's whine. Why the difference? 171'p' 62' 238’pp' '5 16' 286'
142, p. 153. acoustic conduction
hearing
1.71Taping your voice
If you've ever taped your ownvoice, you were probably sur-prised by how thin it sounded
5 5W'_§_£\-\_';""- when you played it back. Other“' uemmr. - -Y"-“"'~‘5°°E I-lIlN5\1An\'s‘ people recorded their voice and
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you. But yours. . .it iust wasn tright. What was wrong?
312.
Hiding under the covers. listening for monsters 19
acoustic conduction 5|1°¢|< WW9hearing reflection
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1.72Fixing the direction of a sound
Since you have two ears insteadof one, you can locate the direc-tion of a sound as well as just hearthe sound. If you were to plotyour ability to fix the direction ofa pure tone versus the frequencyof that tone, you would find thatyour ability is reasonably constant
uency (Hz)
te
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with frequency except in the re-gion of 2 to 4 kl-lz (Figure 1.72).Why does your ability get worsein that particular region, whereasit is better for both higher andlower frequency tones?
1554; 1555.
1.74Sounds of thunder
When I was little my mother toldrne that thunder had something todo with lightning. How is thunderproduced, and why does it last forsuch a relatively long time? Mustit always boom? I've read that ifyou stand within 100 yards of thelightning flash you first hear aclick, then a crack (as in a whipcrack), and finally the rumbling.What causes the click and thecrack? If you're a little furtheraway you'll hear a swish insteadof the sharp click? Why a swish?
82, pp. 1 14-1 16; 220, Chapter 6,pp. 195- 199,‘ 29.9, pp. 124- 127;300, pp. 162- 163;301, pp. 66-67; 302 dtrough 305,‘ 1617.
sound propagationattenuation
ShOC|< WBVBS Why not always two? Does therefraction boom depend on the aircraft's
1.73Sonic booms
What causes the sonic boomsproduced by supersonic aircraft?Is the boom produced only whenthe plane first breaks the soundbarrier? Does it depend on theengine noise? Sometimes youhear not just one boom but tworight in succession. Why two?
plane is climbing, diving, orturning? Under some circumstances the aircraft may generatea “superboom”-an especially intense shock wave. Under otherconditions a boom will be made bthe plane but will never reach theground. What probably happensit?
288 through 298.
altitude? Does it matter if the
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to
1.75Hearing aurora and frozen words
is it possible to hear aurora*?There have been reports ofcracklings or swishings (soundinglike “burning gras and spray")coordinated with changes in thelight intensity of aurora. Whileit is hard to imagine how soundmade at such a high altitude (above70 km) could reach an observer onthe ground with any appreciablepower simply because of the at-
20 The flying dicta of physics
tenuaiion over such a large distance,recently an explanation alongthis line was proposed: electronsfrom the aurora would excitewhat are called plasma acousticwaves that would create nomialacoustic waves. Regardless of theactual mechanism, however, couldyou hear a sound made so high?What exactly happens to theacoustic power when the soundtravels downward through theatmosphere?
Another interesting explanationhas been that “What one hears isone’s own breath that freezes inthe cold air" (Figure 1.75). Whenthe air is calm and very cold, canyou actually hear the collision ofice crystals formed from yourbreath? If this is ever posible, howcold must it be?
1506 through 1511; 1532.‘See Prob. 6.30.
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1.76Dark shadows on clouds
During the fighting near theSiegfried Line in World War ll,U. S. troops spotted dark shadowscrossing over white cirrus clouds.These shadows were arcs whosecenters lay on the German side,supposedly being caused by theheavy artillery. Why were theseshadows produced? Would youexpect the shadows to comesingly or always in pairs? Finally,was the cloud background necessary?
142, p. 754; 306 through 308.
1.77Whip crack
What makes the sound when a whipis cracked? Try to support anyguess with rough numbers.
82, p. 30; 159, p. 184; 288,’30.9.
Illdlng under the covers, listening for monsters 21
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force equation of motiondisplacement energy
V6|0¢llY momentumaccelerationcross sectipnflux
2.1Run or walk in the rain
Should you run or walk whenyou have to cross the street in therain without an umbrella? Runningmeans spending less time in therain, but, on the other hand, sinceyou are running into some rain,you might end up wetter than ifyou had walked. Try to do a roughcalculation, taking your body as arectangular object. Using such amodel, can you tell if your answer(whether to mn or walk) dependson whether the rain is falling ver-tically or at a slant?
2.2
Catching a fly ball
If in baseball a highly hit ball—a“high fly"—is knocked to yourpart of the outfield, there are twothings you could do. You coulddash over to the correct place andwait to catch the ball, If you do,I'll ask you how you guessed wherethe hall was to come down. Or,you might run over at a more or
less constant speed, arriving just intime to make the catch. In thatcase I'll ask you how you deter-mined the correct running speed.Experience helps, of course, butyou must also have an intuitivefeel for the physics involved in thehall's flight. What tips you off asto where to go and how fast torun?
121. / W2%ass‘o’
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2.3Running a yellow light
Every driver will occasionally haveto make a quick decision whetheror not to stop at a yellow light.His intuition about this has beenbuilt up by many tests and somemistakes, but a calculation mightreveal some situations whereintuition will not help.
For some given light durationand intersection size, what com-binations of initial speed anddistance require you to stop (orrun a red light)? What range ofspeed and distance would allowyou to make it through in time?Notice that for a certain range ofthese parameters you can chooseeither to stop or not. But thereis also a range in which you cando neither in time, in which caseyou may be in a lot of trouble.
1 23.
2Q4
Getting the bat there in time
To make a hard line drive you mustget the bat into the proper positionfor the collision with the thrownball. l-low much error can youstand, both in the vertical direc-tion and in time, and still be ableto get the hit? For example,would it be all right if your timingis off by some small amount suchas 0.01 second?
4.
Exceptionally good reference:Crabtree (36).
The walrus speaks of classical mechanics 23
2.5‘him or stop
It is hard to find any physics of amore real-world nature than thatwhich involves your own death.For example, suppose you suddenly(ind yourself driving toward abrick wall on the far side of aT-intersection (Figure 2.5). Whatshould you do? Use your brakesfully, without skidding, whilesteering straight ahead? Tum atfull speed? Or tum while applyingyour brakes as well as you can?
Consider this question in parts.First, assume you can stop the carin time by braking and steeringstraight. Would tuming insteadalso save you? Right now you'llprobably want to think about thiswith ideal conditions. Later youcan throw in the possibility ofaskld, differences in road handling
between front and rear tires, andbrake fade. What if the straight-ahead option won't stop you intime? Should you bother tuming,or are you doomed to an earlydeath?
If you were to find a large objectin the road, would it be better toattempt a head-on stop or to try tosteer around it? Of course, theanswer will depend on the object'ssize.
Don ’t answer quickly in any ofthese cases, for even though youmay be very experienced, yourintuition may be wrong. If it iswrong, the question becomes farmore relevant.
122.
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Figure 2. 5Tum or stop for the brick wail?
2.6The secret of the golf swing
How should you swing a golfclub in order to impart maximumspeed to the ball? While manygolfers might prefer to keep theproblem in the realm of the eso-teric, we should be able to con-sider it using some physics. Whatshould the initial backswing anglebe? When should you relax yourwrists? Should the club, arms,and ball be along a straight linewhen contact with the ball ismade?
5,’ 6; 1613.
momentum transfercenter of mass motion
2.7Jumping beans
Why do jumping beans jump?There they are, lying quietly inyour hand, when suddenly,every few seconds, they jump intothe air. Can you convince a friendthey violate conservation of mo-mentum?
7,’ 8,‘ 9, p. 238.
2.8Jumping
How high can you jump? Can youcalculate the height? Would yoube able to jump higher if your legswere longer? ls there any initial
24 The flying circus ofphysics
orientation or way of swinging the‘arms that would increase yourjump?
How far can you jump? Someathletes bicycle their legs as theyfly through the air; does thisreally help? At what angle is itbest to leave the ground? At theangle (45°l that maximizes therange of a projectile?
Why do pole vaulters and broadjumpers charge forward for thejump but high jumpers approachthe jump much slower? Shouldn'tall three obtain the maximumpossible speed before they leavethe ground?
Can you jump as high or as far ona seacoast beach as you can on amountain? if the height above sealevel makes a difference, some
paring record jumps at variousaltitudes.
10 through 13.
2.9Throwing the Babe a slow one
Pitchers sometimes threw BabeRuth slow balls because theythought it would be harder forhim to hit a home run if the ballwere moving slower when struck.Does this belief have any physi-cal basis?
14, p. 274.
impulse elasticitycollisions
caution should be exercised in com-
2.10Karate punch
In karate classes I was taught toterminate a punch, kick, or edge-of-hand chop several centimetersinside my opponent's body. Thisis different from normal streetfighting where there is muchfollow through. Which techniquewill produce more damage?Through a rough calculation, canyou show the feasibility of a karatefighter breaking a wooden board,a brick, or a human bone with apunch?
1632.2.11
Hammers
Should a sculptor use a heavyhammer or a light one on hischisel? Which hammer should beused to drive a nail? When wouldan elastic collision (that is, onewith a full rebound of the hammer)be more desirable than an inelasticcollision? Consider something ona grander scale, a piledriver, forexample: should the piledriver beheavy or light compared to thepile? A guess is easy to make, buta calculation should back it up.
15' 16, pp. 396-399.
2.12Softballs and hardballs
Should you hit a hardball and asoftball differently? in particular,should there be more followthrough for one than for the other?
4.
2.13Heavy bats
Why do home—run hitters preferheavy bats? It seems it wouldbe harder to give the heavy bat alarge final speed and hence harderto hit the ball very far. Should youuse the heavy bat for a bunt? Con-sidering the range of weight normal-ly used, does the bar's weightreally make much difference?
4.
center of mass motion
2.14Jerking chair
A body's center of mass movesonly if an external force is applied,but you can get to the other sideof the room in a chair withoutletting your feet touch the floor.If all your twistings and contor-tions are internal forces, whatprovides the external force?
The walrus speaks of classical mechanics 25
DOVVBl’ pressureBRBIQY force
2.15Click beetle‘: somersault
if you poke a click beetle lying onits back, it throws itself into theair, as high as 25 cm, with a notice-able click. That in itself is trifling,you say? But the beetle, withoutusing his legs, hurls himself up-ward with an initial accelerationof 400 g and then rotates his bodyto land on his legs. 400 gl Even
more surprising is that the powerneeded for this is I00 times thedirect power output of anymuscle. How does the beetleproduce such an enormous poweroutput? How frequently can heperform this amazing feat, andwhat physically determines thefrequency?
21,’ 1485' 1531.
weightl momentum transfer
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Balanced hourglasses.Sand in bottom of each.
ll you tip over an hourglass,does it weigh less?
Figure 2.16The weight of an hourglass
2.16The weight of time
Does the weight of an hourglassdepend on whether the sand isflowing (Figure 2.16)? Ifsomeof the sand is in free fall, won't
the weight of the hourglass beless?
17.
2.17Pressure regulator
Have you ever used a pressurecooker? Mine has a solid cylinderon top of the lid that somehowregulates the pressure. There arethree different size holes drilledinto the side of the cylinder, and lpick the pressure by placing the ap-propriate hole over the hollow stemextending from the pan (Figure2.17). How does it work? Thepan's steam must lift the samecylinder no matter which hole lpick. Why do I get different pres-sures by using different holes?
' -'51’.
Figure 2.1 7Pressure regulator.
26 The flying circus of physics
elasticity
2.18The superball as a deadly weapon
If a small superball,* which is avery elastic rubber ball, is droppedimmediately after a large one asshown in Figure 2.180, the smallball will be shot back up into theair after the two balls strike thefloor. If the mass of the smallball is appropriately chosen, theother ball will completely stop atthe floor and the smaller ball willrebound to about nine times itsoriginal height.
'I\'y this as well: drop a largesuperball, a small superball, and aping-pong ball as shown in Figure2.18b. If the balls are appropriate-ly chosen, the ping-pong mayreach almost 50 times its originalheight.
18 through 20.
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'® Wham-O Manufacturing Company, Figure 2.18San Gabriel, California; similar balls are Rebounds ofseveral superballssold under other brand names. dropped simultaneously.
Friction2.19 through 2.22
2.19Locking brakes
If you must stop your car in ahurry, should you slam on thebrakes and lock them?
2.20Wide slicks on cars
If you had to decide betweenregular-width tires with no treadsand wide tires with no treads (bothare called slicks), which would youchoose for better braking ability?
In drag racing wide slicks arepreferred for the rear tires. Why?
workDOWOF
2.21Friction in drag racing
In drag races there are two mea-surements of interest: the finalspeed and the total elapsed timeon a quarter-mile course. Tohelp gain traction, a sticky fluidis poured under the rear wheelsbefore the “go" light, but ap-parently the track's friction reallyaffects only the elapsed time andhas little influence on the finalspeed. Why?
22.
The walrus speaks of ciassical mechanics 27
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Figure 2.22Sliding your index fingers under a yardstick
2.22Sliding stick acro fingers
Hold a yardstick horizontally on first on one finger and then on theyour index fingers and slide your other, and so on. Why does thefingers together smoothly (Figure sliding change back and forth?2.22). Does the stick slide smoothly _over your fingers? No, it slides 2'3 24' pp' 83.84
Rational kinematics frictionand dynamics torques2.23 through 2.66
angular motion angular momentumtorque rotational energy starting 3 carmoment of inertia
'I'here is much debate about how tostart a stick-shift car on a slipperyroad. Some claim you should havethe car in low gear; others swearyou must put it in high. Why doesthe gear you use matter at all?What is needed to get the car mov-ing? Why must the initial speed besmall? What advantages wouldany one gear have over the others?You'll have to explain how thetorque applied to the wheel de-pends on the gear and decide
2.23 IAccelerating and braking in a turn
Why is it unwise for you to do anysignificant braking when your caris in a turn? For example, supposethat while in the curve you decideyou are taking it a bit too fast.What happens if you apply thebrakes too hard?
Race drivers accelerate as theyare leaving a curve, not whilethey are in it. Why?
29,‘ 30, p. 8.28.
when you need more or less torque.
2.25Left on the ice
For a mean trick, your friendsdesert you in the middle of a
rge frozen pond. The ice is sovery slippery that you can't walk
a small one How can you getthe ice?
Now lat us suppose you were
off in a big huff, or even crawl offin .off
first placed on your back. Afterlying there for a while, your backisto
frozen to the bone and you wantturn over. How do you do it on
such slippery ice?They could have been meaner.
They could have stood you up endtied you to e pole fixed in the ice(Flgure 2.25). How could you turnyourself ebout that pole if they
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28 The flying circus of physics
had left your hands free? The poleis too slippery to use, and the iceis too slick to turn with your feet.How then do you turn around toface the other way?
9, p. 238.
collisionimpulseslinear kinematics
2.27Pool shots
precesion (the cue ball follows after the bal
center of gravity with which it has collided) or a
2.26Turning a car, bike, and train
I-low do you tum a bicycle? I-low,exactly, do you initiate the turn?On a motorcycle you turn byleaning the bike and not by tum-ing the handle bars. Why the dif-ference?
When a train goes around a curveit leans because the roadbed isbanked to prevent the centrifugalforce from detailing the train. Willthe leaning also affect the turningas in the motorcycle case? Try arough, back-of-the-envelope cal-culation to see. Whether or notthe effect is significant or even rea
elevated.Finally, do you have a similar
consideration in turning high speedcars, such as the Formula 1 racecats?
16, pp. 535-536; 24, pp. 156-157; 3E 36, pp. 43-44; 37, pp.146-147; 38, PP. 89-93; 1612
1.the outside rail on a curve is often
the collision). l thought thet if a
iect of the same mass, the firstobiect stops.
A masse shot is one in which thecue ball describes a parabolic peth(Figure 2.27.9). (These shots areusually outlawed in most poolhalls for a missed masse shot willrip up the teble cover.) Howmust the cue ball be hit to bringthis about and why, in detail, doesit happen?
Why is the cushion higher thanthe center of the balls (Figure2.27b)? Wouldn't you get betterrebounds if the cushion were atthe center's height?
How can English be used in acushion shot?
14, pp. 143- 146; 24, pp. 158-161, 250-251; 25' 26, PP. 183-186; 27, PP» 139- 143, 268-274,290-301.
How do you set up a "fo|Iow shot"l
"draw shot" (cue ball returns efter
moving obiect hits e stationary ob-
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The walrus speaks ol classical mechanics 29
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One of the most significant Figure out how you set up eachadvances made by our technolog- trick and explain how they work.ical society is the Superball *.. . . . . 37; 32-Because of its high elasticity it can , ._ _ ® Wham-O Manufacturing Company,perform some rather amazing mck$- San Gabriel, California; similar balls areSeveral are shown in Figure 223- sold under other brand names.
stability
mechanical efficiency
2.29Bike design
the way it is? In the past therehas been a great variety of designs(Figure 2.29al. Some forexample, had radically differentwheel sizes, and some had thepedals attached to the front wheel.ls the modern bike more efficientor more stable than its predeces-sors?
Why does the modern bike have signs shown in Figure 2.29b?a curved front wheel fork? Wouldthe bike be more or less stable 439'41' 42’ vol‘ H‘ Chapterwith the other possible fork de- ' '
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30 The flying circus of physics
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2.30Hula-Hoop
that can be kept rotating aboutyour waist by an appropriate cir-
2.30). The toy was first popularin the 19505, but similar hoops
been used for toys and in dancesfor a long time. The AmericanIndians, for example, used themin some types of hoop dances.
Think about what it takes tokeep a Hula-Hoop up and going.You throw it around your waist
hula motion. Should the initialspeed you give it be more than thspeed at which you are going totrap it? How do you drive itaround? Is the hoop’s motion inphase with yours? What is theminimum speed you can use?
34.
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Figure 2.30Hu la-Hoop.'® Wham-O Manufacturing CompanySen Gabriel, California.
The l-lula-l-loop* is a plastic hoop
cular motion of your hips (Figure
rotated about the arm or leg have
and then trap it with your driving
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Figure 2.31“Nobody likes to fall, Rocco—butthis is ruining our image. " TheSo turday Evening Post.
driven rotational motion
stabilitylOl’QLlBS
2.3 1Keeping a bike upright
l-low do you keep your balance ona bicycle? When you sense a fall,do you steer into the fall and there-by right the bike? Or does thebike itself do most of the stabiliz-ing? lt must at least contributesome stability because if it ispushed oft‘ riderless it will stay upfor almost 20 seconds.
How do you balance and steerthe bike when you ride withoutusing your hands? Suppose youstand next to the bike and youlean the bike to the right. Whichway does the front wheel tum andwhy?
24, pp. 156-157,‘ 35' 36, pp. 43-44,‘ 37, pp. 146-147; 38, pp. 8.9-93; 42, Vol. II, Chapter 6; 43,‘ 44,pp. 122- 123.
2.32Cowboy rope tricks
How does a cowboy keep his lassoup and spinning? What minimumspeed must he maintain in order tokeep the lasso horizontal? Vertical?
33.’ 120.
moment of inertiastability
2.33Spinning a book
If you hold it closed with a rubberband, you can toss this book intothe air spinning about any of thethree axes shown in Figure 2.33.'I‘he motion about two of the axesis a simple, stable rotation. Therotation about the third axis,however, is much more complicated,no matter how carefully you throwthe book. (See Figure 2.33.) Tryit. What causes that uncontrollablewobbling about the third axis?
44, p. 115.
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The walrus speaks of classical mechanics 31
energy conservation moment of inertiacollision stebllity
2.34FlddlesticksFiddlesticlts' is a remarkably simpleyet fascinating toy. It consists of aplastic ring (of relatively lerge innerdiameter) on a stick. Once thenng is sent spinning by a flick ofyour fingers, the stick is held ver-tically. The ring begins to drop(slower than you would expect),and as it comes down the stick,the ring spins faster and fallseven slower (Figure 2.34). By in-verting the stick iust before thering reaches the lower end of thestick, the process can be repeatedindefinitely. Why does the spin
increase as the ring falls? In fact,why doesn't the ring iust fallwith the full gravitational ac-celeration?
Now use two rings at once. Notonly is this more spectacular, buta curious thing often heppens.The top ring may be droppingfaster than the lower ring and thusmay run into the lower ring. Ifthis occurs, the rings bounceapart, the upper ring rising (Figure2.34). Why?'® Funfeir Products, lnc.. New York,N.Y. 10016.
2.37Car in icy skid
If your car starts to skid on anicy road, are you supposed tostraighten it out by turning thefront wheels in the direction lnwhich you want to move or in thedirection of the skid? Why?
46.
2.38Tire balancing
If your tire is balanced staticallywith a simple bubble leveler, willit still be balanced when it'sspinning? Can you get both staticand dynamic balancing with asingle balancing weight added tothe rim? How about two?
47.
torque
Figure 2. 84
moment of inertia
torquescenter of gravity
2.35Eskimo roll
l-low does a kayaker right anoverturned kayak without everleaving the cockpit?
45' 1563.
2.36Large diameter tires
Will large diameter tires reallymake your car go faster?
2.39Tearing toilet paper
Why, on some toilet paper dispens-ers, can l get a long piece of toiletpaper without tearing if the roll isfat, but when the roll has beennearly used up, the paper inevita-bly breaks too soon, giving onlyshort pieces? Why is iust the op-posite true for other dispensers?
32 The flying circus ofphysics
IOFQUBS
angular momentum
2.40Skipping rocks
How does a stone skip acros thewater? If you skip a stone acrosshard-packed, wet sand, the marksin the sand provide a record of thestone’s flight. You'll find thefirst bounce is short (several inches),the next is long (several feet), andthis sequence repeats itself over andover until the stone comes to rest(Figure 2.400). Why does it followthis pattern?
During World War H the skippingrock effect was used by the Britishin the bombing of German dams.lt isvery difficult to drop a bombon a dam, especially when you are
Figure 2 40a
being fired upon. So, the RAFdeveloped a bomb (cylindrical,with a length of about 5 feet anda slightly smaller diameter) whichwas given a backspin around itslength of about 500 rpm in theplane's bomb bay before it wasreleased over the target (Figure2.40b).
When it hit the water, thebomb skimmed like a stone,bouncing in shorter andshorter jumps until it hitthe dam itself. Then, in-stead of rebounding away,the back-spin forced it
against the wall and made itcrawl downwards until itexploded, on a hydro-static fuse set for 30 feetbelow surface, still clingingto the dam. lt was a beauti-fully simple idea for position-ing a bomb weighing almost10,000 lbs to within a fewfeet. 50*
48; 49; 1486.
' From The Royal Air Force in WorldWar II, edited by Gavin Lyell, copyright© 1968 by Gavin Lyell. Published byWilliam Morrow and Company, lnc.
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The walrus speaks of classical mechanics 88
torque orbits IOTQUBS
angular momentum IONIUBS angular momentum conservation
2.41Car differential
When your car takes a turn, theoutside wheels must move fastertitan the inside wheels. Sincethere is an inside and an outsidewheel on each axle, how is thisturning accomplished?
angular momentum
24, PP. 254-255' 52, pp. 500-501.
moment of inertia
2.42Racing car engine mount
Some of the European racing carshave their engines mounted in thecenters of the cars, rather than inthe fronts or rears. The racingcircuits in Europe are really juststreets and therefore have lotsof fast tums. Considering thetorque needed to tum a car,what advantages does acenter-mounted engine haveover the conventionally mountedengine in this situation?
2.44Carnival bottle swing
'I11ere’s an old carnival sideshowtrick involving hitting a bottlewith a pendulum suspendeddirectly above it (Figure 2.44).To show your skill, you muststart the pendulum so that itmisses the bottle on the forwardswing and then hits it on thereturn swing. The barker, ofcourse, won’t let you throw thependulum over the top. Still,this trick shouldn't be too hard,should it? With a few tries youshould find the arc needed to winthe prize. Well, try it, and thenworry about why it doesn't workand then about what would makeit work.
53, p. 184.
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2.45Falling cat
lt is common knowledge that ifyou drop a cat upside down it willland on its feet; even tailless catsshow this mysterious ability toright themselves. Now, if there isno external torque the cat's angularmomentum must be constant. Isthe angular momentum constantduring the fall? If so, how doesthe cat turn itself through a full180°? lf the angular momentumis not conserved then somewhere,somehow, there must be a torqueon the cat. But where? References36 and 54 contain photographsof a cat turning over, and they areclear enough to provide an explana-tion.
9, p. 238; 36, pp. 56-57; 54;55.
2.46Ski turns
Askiturncanbeasetofrathercomplicated twists and gyrationsbut consider the several simpleelements of such a turn.
The Austrian turn requires a
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2.43Tightrope walk
How does a tightrope walker keephis balance? Why does along barhelp?
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sinking of the whole body, followedby a powerful upward thrust and arotation of the upper part of thebody. The lower part, and hencethe skis, rotate the opposite way
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Figure 2.44Swing the ball so as to hit thebottle on the return swing.
as a result. Why? For a givenupper-body rotation, how muchdoes the lower body tum?
34 The flying circus of physics
The normal skiing stance gives astraight skiing path, but a shift ofone’s body either forward or back-ward on the skis will force a turn.Why and which direction ofshifting gives which sense of tum?
If the skis are edged (the ski'suphill edge is held into the snow sothat the ski is at an angle to thesnow’: surface), turns are alsocaused by a shifting of weight, butthe sense of tum is opposite tothat in the normal-stance case.Why is that, and again, what forcesthe tum?
55 1525
2.47Yo-yo
Can you tell me why a yo-yo comesback up? How about the sleepingyo-yo in which the yo-yo is throwndown and spins at the end of thestring until it returns when yougive the string a slight jerk. If thesleeping yo-yo touches the floor,it will walk along the floor- this is"walking the dog."
As an even better trick, put theyo-yo to sleep, take the string offyour finger and hold it betweenyour thumb and index finger. Nowgive that hand a slap. As soon asthe yo-yo starts to climb back up,let go of the string. The yo-yowill charge up the loose string,neatly winding it up. Dazzle yourfriends by catching the yo-yo inyour coat pocket when the stringis wound up.
24, pp. 246-247,‘ 56.
2.48Slapping the mat in iudo
When you've been thrown in judo,slapping the floor with your armat the moment of impact will pre-vent iniury in the fall. How doesit work? The effect is probablypartly psychological, but I knowthat for the most part it is real.When I was taking lessons, l wasalways hurt when I missed theslap or when my timing was off.When I slapped the mat properly,my discomfort was only mild.
center of gravity
iOFQUBS
stability
angular momentum
%-2.1;. 11-4..;=;;v,>
LIOFQUBS
stability
2'49
Bullet spin and drift
Why are bullets given a spin asthey travel down the rifle barrel?The rifle, in fact, derives its namefrom the riiling—the spiral groovesin the bore-that impart this spin.
If the bullet is given a counter-clockwise spin as seen from therear, it will drift to the left of thetarget. A clockwise spin will causea drift to the right. Why? Can youcalculate, roughly, the amount ofdrift for small and large guns?
16, pp. 536-537," 26, pp. 154-155‘ 36, pp. 53, 140- 144,‘ 37,pp. 148 ff, 274 ff,‘ 38, pp. 117-1 19,‘ 40, pp. 440-441; 64, PP.393-394.
iii <‘>_£ '\Figure 2. 50Leaving a leaning tower for alibrarian.
2.50The leaning tower of books
If you want to construct a stack ofbooks leaning to the side as muchas possible (Figure 2.50), what isthe best way to stack them?Would you put the edge of onehook over the center of the lowerbook?
57 through 59,’ 1559.
The walrus speaks of dassical mechanics 85
tOfqUBS forces in a rotating frameangular momentum
center of gravitystress and strain 7
2.51Falling chimneys
When a tall chimney falls, itusually breaks in two at some pointalong its length. Why doesn’t itfall in one piece? Where do youthink the break will occur? Willthe chimney bend towards or awayfrom the ground after the break(Figure 2.510)? You can checkyour answer by toppling a tall stackof children's blocks and seeing
which way the stack curves as itfalls.
If the chimney does not break,something even stranger may occur:the base of the chimney may hopinto the air during the fall (Figure2.51b). How can it do this,seemingly against gravity?
9, pp. 124- 125' 60 through 63.
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(a) Which way will a chimney break?Figure 2.51
(bl ll it doesn't break. it may hop up.
forces in a rotating frame
2.52The Falkland Islands battle and BigBertha
During World War I, there was afamous British-German naval fightnear Falkland Islands (about s0°slatitude) in which the British shots,while well aimed, were mysteriouslylanding about a hundred yards tothe lefrof the German ships. The
British gun sights were not faulty,for they had been set very preciselyback in England. During theGerman shelling of Paris in thesame war, a huge artillery piececalled Big Bertha would pumpshells into the city from 70 milesaway. If normal aiming procedurehas been employed, Big Bertha'sshots would have missed theirmark by almost a mile. What washappening to the shells?
68 through 72," 1488
2.53Beer's law of river erosion
Why does the right bank of a riverin the northem hemisphere suffermore erosion, on the average, thanthe left bank?
24, p. 164; 72; 73.
2.54A new twist on the twirling iceskater
The twirling ice skater has longbeen used as an example of theconservation of angular momentumWhen she pulls her arms in, shespins faster due to the conserva-tlon of angular momentum (thereare no extemal torques).
'l"hls is all true, of course, but Iwould like to explain the speedingup in terms of forces becauseforce arguments are more acces-sible to the imagination thanangular momentum arguments.What is the force that speeds upher spinning?
74.
36 The flying circus of physics
airfoil theory
angular motion
2.55Boomerangs
Returning boomerangs are designedto be thrown great distances and toreturn to the thrower. Australiannatives have thrown them as far as100 yards and to heights of 150feet with five complete circles.The nonreturning type, which ismore practical for hunting, can bethrown as far as 180 yards.
The ordinary boomerang isshaped like a bent banana. lsit essential that the boomeranghave this particular shape? Can onemake a returning boomerang
boomerangs are designed to bethrown with the right hand. Whatis the difference between left-and right—handed boomerangs?Why does a boomerang (of anyshape) return? Why does it looparound in its path (see Figure2.55)? Finally, how does thepath depend on the boomerang'sorientation as it leaves thethrower's hand?
26. PP- 153- 154,‘ 37, pp. 291-in 296; 65 through 67,‘ 1564.
the shape of an X or a Y? Most
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Periodic motion(2.56 through 2.68)angular momentum
IOFQUBS
potential and kinetic energy
center of gravity
2.56Swinging
When you swing, you must pumpfirst to gain height and then iustto keep going. How does pump-ing work? How do you pump ifyou want to start to swing fromrest? Do you pump differentlywhen you are sitting and standing?ls it possible to turn a completecircle on a well-oiled swing, or isthere some limit to the height youcan reach? You might want toconsider a swing hung on rigidbars as well as on chain or rope.How much work do you do inpumping from rest to some maxi-mum height?
9, p. 239,‘ 25, PP. 245-246; 42,Vol. /, PP. 179-181; 75through 80.
oscillationsYGSO l'l3l'lC9
2.57Soldiers marching across footbridge
In 1831 cavalry troops were travelsing a suspension bridge nearManchester, England, by marchingin time to the bridge’s swing. Thebridge collapsed. Ever since then,
The walrus speaks of classical mechanics 37
troops have been ordered to breakstep when crossing such bridges.What is the common explanationfor the danger, and is the dangerreal? Make rough calculations ifyou can.
81, pp. 59-60,‘ 82, pp. 1.93-1.94,’1571.
resonant oscillations
2.59Road corrugation
A road that is initially flat maydevelop a bump, and soon there-after ripples appear down theroad. In fact, the ripple itselfseems to propagate slowly alongthe pavement. Thus many un-paved roads and even some black-tops and concrete roads look likewashboards, especially after a
rain leaves the depressions filledwith water.
A similar pattem has been ob-served on trolley car and railroadtracks. A train passing over suchconugation makes so much noisethat the tracks are called “roaringrails." Skiers may also find a washboard surface on their ski trails.What causes such corrugation?What determines its periodicity?Can you predict the periodicityby simulating the effect in a sand-box with a hand-held wheel?
89.
torques, angular momentumenergy change, resonant oscillations
2.58Incense swing*Pilgrims to Santiago de Campostella, pumped by about six men (see meter each time it passes throughSpain, visit the shrine of St. James Figure 2.58) until it is swinging the vertical; they release the sameto burn incense. The incense and through 180°. The swinging makes amount of rope when the containercharcoal are held in a large silver the charcoal burn energetically for reaches its maximum height. I-lowbrazier hung from the ceiling. the pilgrims. The pumping is the does this shortening and lengtheningThe brazier is set swinging with a interesting part: they do it by of the rope increase the amplitude?small amplitude, and then it is shortening thB rope by about 8 ‘H. Pomerance, personal communication
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38 The flying circus of physics
coupled harmonic motion pendulum motion coupled harmonic motion
2.60A ship's antiroll tank
unsettling, but if the waves strikethe ship at its resonant frequen ,the rolling can be very dangerous.Consequently, some ships havecarried tanks partially filled withwater to diminish the danger(Figure 2.60). Such a tank hadcarefully chosen dimensions sothat the resonant frequency ofthe water it held matched that ofthe ship. But isn't there some-thing wrong? Since the resonantconditions were matched, howcould the tank have managed tostop the resonant buildup ofthe ship's rolling?
44, p. 270,‘ 88, pp. 202-203.
A ship's rolling is normally just
W
Figure 2. 60The antiroll water tank in a ship,as shown in cross section.
stability
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Figure 2.6 IIf the plate is oscillated verticallyfast enough, the pendulm won'tfall over.
2.61Inverted pendulum, unicycle riders
Suppose you inverted a pendulumand tried to stand it on its end. Itwould be unstable and would fallover at the slightest disturbance.But if the pendulum were madeto oscillate up and down fastenough (Figure 2.61). it would bestable even egainst small distur-bances. A unicycle rider accom-plishes the same thing, except thathe uses a horizontal oscillation tostabilize himself. Why is theremore stability in the oscillatingcases? What determines theoscilletion frequencies needed togain such stability? Rather thanuse equations entirely, can youexplain the inverted pendulumphysically?
83 through 87,‘ 795.
2.62Spring pendulumYou are already familiar withsprings and pendulums, but haveyou considered putting themtogether by suspending the pen-dulum bob on a spring? If youchoose the spring and the bobappropriately you will have aremarkable example of sym-pathetic oscillation. Just asyou would expect, a verticalpull sets up vertical oscillations;but soon the vertical motiondies away, and the bob beginsto swing like a pendulum (Figure2.62). After a short time it isagain oscillating vertically. Some-how the energy of the systemmoves back and forth betweenthe two oscillatory modes andcontinues to do so as long as thereis energy left in the system. Howmust you choose the bob's massand the spring's mass and lengthto obtain this oscillation exchange?Why does the exchange take placeat all? With what beat frequencydoes the bob switch from mode tomode?
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The walru speaks of ciassical mechanics 39
coupled pendulum motion
2.63The bell that wouldn't ring
There's no sense in putting up abell refusing to ring, but that's whatwas done at the Cathedral ofCologne. The pendulum frequencieof the bell and its clapper were sounfortunately chosen that the belland clapper swung in phase, and ofcourse the bell won't ring that way.Under what conditions will thependulum motions be so matched?And when it does happen, whatcan you do about it, short ofthrowing the bell out of the belfry?
16, pp. 409-413,‘ 37, p. 148.
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though they keep very good timeif fastened down securely. If hungfree on a chain by its stem (Figure2.64), the watch will graduallybegin to swing and may gain orlose up to 10 or 15 minutes a day.Why does it swing, and why doesthe timekeeping get messed up?Finally, why do some watches gain
s time while others lose time?16, PP. 420-424; 24, pp. 114-117; 42, Vol. II, pp. 85-87,190,‘ 90.
shorter the waterfall. In fact, theproduct of the frequency and theheight of the waterfall is alwaysone fourth the speed of sound inwater. Why should the frequencyhave anything to do with the water-fall‘: height, and why in the worldshould their product be one-fourththe speed of sound?
91.
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Figure 2. 64Swinging pocket watch.vibration
2.66Stinging hands from hitting the ball
Sometimes when you're batting aball, your hands may get a good,healthy sting. The sting is relatedto what part of the bat hits theball. Not only can such a collisioncause a sting, but also it makes itmuch more likely the bat will breakWhy are there such points on thebat, and where are they?
4.
I’9$Ol'l3l‘IC9Figure 2. 63 ~ vibration
Standing waves
coupled harmonic motion
2.64Swinging watches
Once hung on a chain, free toswing, should a pocket watch
Many pocket watches do, even
2.65Earth vibrations near waterfalls
Waterfalls pound the earth so hardthat you can feel the vibration inthe ground from a considerabledistance. For most waterfalls one
change its timekeeping rate? frequency of vibration is dominant,and the frequency is higher, the
2.67The archer's paradox
No matter how well an arrow isaimed, when it is loosed and thefeathered end is passing the bowgrip, it will deviate considerablyfrom the line to the target, perhapsas much as 7° (Figure 2.67). Thearcher's paradox is that a well-aimed arrow will still strike the
40 The flying circus of physics
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Figure 2.6 7Once the arrow is loosed, itdoesn't point toward the target.
target. How can this be? Firstof all, why is there a deviationand second, given the fact of thedeviation, why does the arrowthen hit the target?
High-speed photographs of thearrow show that the last timethe arrow touches the bow‘s stockis when it is first loosed. ltdoes not touch the stock even asthe feathered end passes. if that'strue, how does the arrow find itsway to the target?
92.
vibrationsdriven rotation phase
2.68Magic windmill
A fascinating toy which you caneasily build yourself is the rotoron a notched stick (Figure 2.680).One stick has notches along itslength and a small propeller on theend (on a straight pin jammed intothe stick). The second stick isused to stroke the notches. Hold-ing your forefinger on the far sideof the notched stick and yourthumb on the near side, run thestroking the stick back and forthnotches, as shown. As you arestroking, let your forefinger pressagainst the notched stick (Figure2.680). The propeller will tumin one direction. Now loosenyour forefinger and let yourthumb press against the stick,stroking the stick back and forthall the while. The propeller willtum in the opposite direction.
When you're showing this tothe uninitiated, you can slylyshift from the forefinger to thethumb and make a great mystery
direction.
spin. The number of lies you canfeed someone about why the rotorreverses is almost unlimited—l liketo attribute it to a variation incosmic ray intensity.
The first question you should askyourself is why the rotor tums atall. Next comes the bigger mysteryof why the spin sense depends onwhich side of the stick you pres.
lf you want something flashier,put four rotors on the stick (Figure2.68 b). All four will turn in thesame direction, so there's nothingessentially different about this.Another design, which is more dif-ficult to explain, has two rotorsmounted one behind the other(Figure 2.68c). Something strangedoes happen in this case. You canmake both rotors turn to the leftor both to the right or, best of all,you can make one go in one direc-tion and the other in the opposite
of the change of direction of the 93 through 96" 7487'
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The walrins speaks of classical mechanics 41
Gyroscopic motion<(2. 69 through 2. 73)torque precessionangular momentum
2.69Personalities of tops
Why does a spinning top stay up?Can you explain it using onlyforce arguments, without invokingtorque and angular momentum?The top stays up against gravity;hence, there must be a verticalforce. What produces that force?
ities of individual tops? Some“sIeep,“ that is, remain vertical;others precess (Figure 2.69) likemad. Some are always steady intheir motion; others are worri-some before finally settling downto a steady motion. Some die long,lingering deaths; others departrapidly. How do you account forthese varied temperaments?
36; 37, Chapter 1.’________ .
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Figure 2.69In precessing, the top’s axisitself rotates about the vertical.
Can you also explain the personal-
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2.70Diabolos
The diabolo, an ancient toy, is aspool made of two cones stucktogether, which is spun'by meansof a string whose ends are tied tosticks (Figure 2.70). Spinning isinitiated by first lowering the righthand, smoothly drawing it backup and thus spinning the diabolo,then quickly dropping that handagain and repeating the processuntil sufficient spin has beengiven the diabolo.
Why is the diabolo so muchmore stable when spinning? Eventhen, you may have to make cor-rections. For instance, supposethe near end begins to dip. Whatshould be done with the sticks tomake the spool horizontal again?Or suppose that you want thespool to turn to your left. Whatmust you do with the sticks?
36, pp. 40-4 1, 120- 121,’37, PP. 458-459.
2.71Spinning eggs
In times of doubt, you candistinguish a hard-boiled egg froma raw one by spinning them. Thecooked egg will stand on end andthe raw one will not. Why?Another way to tell if an egg is rawor cooked is to spin it, stop it withyour finger, and quickly release it(Figure 2.71). A cooked egg willsit still, but a raw one will beginto turn again. Again, why?
36, pp. 5-6, 51, 155337, pp.16-77, 264-272,‘ 108,‘ 109,pp. 39, 57,’ 110, p. 123.
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Figure 2. 71Testing for a fresh egg.
2.72The rebellious celts
Some of the stone instrumentsmade by primitive men in Englanddisplay curious personalities whenthey are spun on a table. Thesestones, called celts, are generallyellipsoidal in shape. When youspin them about the vertical axissome behave as you would guess,but others act normally onlywhen spun in one direction aboutthe vertical (Figure 2.72a). If youspin them in the other sense, the
42 The flying circus of physics
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' "
andthen spin in their preferred direc-tion. Some stones demand onedirection, others demand the op-posite.
If you tap one of these stoneon an end, say at point A inFigure 2.72 b, it will rock for awhile. But soon the rockingceases, and the stone begins torotate about the vertical axis.
Try to make some wooden celtsdisplaying this rebellious nature.What causes such personalities?
26, pp. 204-205' 36, pp. 7,54,‘ 37, PP. 363-366.
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2.73Tippv wasThere is a kind of top that reallyknocks me out-it is part of asphere with a stem in place of themissing section (Figure 2. 73).Given a spin on its sphericalside, it will quickly tum over andspin on the stem, the heavier sidethus rising against gravity. Whydoes it rise? What forces the topup? Isn't it completely contraryto your intuition that the spin-ning top is so unstable in the ini-
Initial orientation
tial orientation and so much stablerin the final one?
The same behavior can be seenwith high school and college ringshaving a smooth stone. Foot-balls and hard-boiled eggs willalso raise themselves up on theirpoints when spun in similarfashion.
36, pp. 5-6, 51, 155 97dirough 108; 109.PP. 39-57.
Final orientation
Figure 2. 73
Top turns upside down
Gravitationl2.74 through 2.79)gravilv kinetic and potential energy
orbitsIOFQUBS
moment of inertia
Figure 2. 72b.Celt initially set rocking atA begins to spin.
2.74Seeing only one side of moon
Why do we see only one side ofthe moon? Because the moonturns on its own axis at such arate that as it orbits the earth italways presents the same face tous. But is this pure chance?
26, pp. 369 ff.‘ 11 1.
2.75Spy satellites over Moscow
The United States would like to seewhat Russia is up to, so we put upspy satellites with long-rangecameras. We would really like tohave a permanent satellite staydirectly over Moscow 24 hoursa day. Why don't we? Why, in-stead, do we put up a series ofsatellites whose times over Moscowoverlap?
The walnss speaks of classical mechanics 43
2.76Moon trip figure 8
When the astronauts go to themoon, why is their path (earth-moon-earth) essentially a figure
8 (Figure 2.76) instead of an el-lipse? In particular, does thefigure-8 path require less energy?
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2.77Earth and sun pull on moon
How large do you think the sun'spull on the moon is, compared tothe earth's pull? Well, after all,the sun doesn't steal our moonaway, so the earth must bepulling harder, right? That'ssatisfying, but unfortunately itisn't true. The sun pulls morethan twice as hard as the earth.So why don't we lose the moon?
177.
2.78Making a map of India
l have read it is difficult to surveyIndia because the plumb line oneuses in surveying is pulled north-ward to the Himalayas and thusdoes not hang toward the earth'scenter. ls this true? I-low large doyou think the effect is, and is itlarge enough to influence large-scale surveying?
13,‘ 118,’ 119.
2.79Air drag speeds up satellite
Artificial satellites don't orbit theearth forever. Eventually theearth's atmosphere, thin as it maybe up there, will bring them down.But did you know the linear speedof a satellite in a nearly circularorbit will increase because of theair drag? The satellite will experi-ence an acceleration forward alongits path, and the accelerations‘s mag-nitude will be the same as if the airdrag were turned around and werepushing the satellite along. l-lowcan that be?
112 through 116.
44 The flying circus of physics
3Heat fantasies andother cheap thrills
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Boyle's law partial pressu I8
atmospheric and water pl’BSS.ll'B
3.1The well-built stewardess
LOS ANGELES (AP)-Whathappens to a stewardess wearingan inflatable bra when the cabinof her jet plane is depressurized?
Just what you're thinking,I-lerman. Inflation.
. .As Los Angeles Tunes colda
set of potentially explosivecumstances occurred recently
Matt Weinstock told it Fri y, thisci
H
St
fa
onaLos Angeles-bound flight. e
tyofgirl and airline
“When she had, ahem, exto about size 46," Weinstock“she frantically sought a solu
gallantly withheld the identi
pan
passenger who had a small
dedwrote,tion.
Somehow she found a womanhatpin
and stabbed herself strategically.“However, another passenger,
understood. l-le thought she W35trying to commit hara-km thehard way. l-le grappled withtrying to prevent her frompunching the hatpin in her
“Order was quickly restorlaughter still is echoing alongthe airlines."
a man of foreign descent, mis-
ched
Weinstock says it really happened.
her
est.,but
the
Exceptionally good reference: Chem-ical Principles Exemplified,” edited andwritten by R. C. Plumb, monthlyChem. Ed.
in J.
Good thing they don't makethese bras puncture-proof.
. . Associated PressCan you calculate the stewardess'spectoral measurements as a func-tion of altitude?
3.2Making cakes at high altitudes
Why does the recipe for a cakechange when you do the bakingabove 3500 feet? The side of thecake mix box calls for more flour,more water, and a higher bakingtemperature when the mix isused at altitudes greater than3500 feet.
316, pp. 184-186.
3.4Wells and storms
My grandmother claims that duringstorms her water well is easier topump but the water may be unfitto drink because of an increase insuspended matter. This happens,she says, whether the storm bringsrain or not. Others have noticedthat artesian wells generally in-crease in strength dun'ng stomus,again regardless of the rain. Whywould these wells respond tostorms? Might there be an op-posite effect in which a normallyfreely flowing well is stopped?
318, p. 143.
elasticitysurface tension
pressurehumldlty
3.3The Swiss cottage barometer
One of my grandmother's mostfascinating possessions is her Swisscottage barometer. She explainsthat when the pressure falls, a littleman comes out of the cottage towarn of a coming storm. Duringfair weather a little womancomes out instead. How does thiscottage barometer work, and doesit actually measure the barometricpressure? I notice that when Iplace it in the bathroom it pre-dicts bad weather far more often.Why the increase in frequency?
317, p. 201,‘ 318, p. 209.
3.5One balloon blowing up anotherballoon
Blow up two identical balloons,one more than the other. Takecare that air doesn't leak untilyou've joined the two balloons by ashort length of tubing as shown inFigure 3.5. What will they dowhen they are ioined? Does thesmaller balloon expand at the ex-pense of the larger one? Intuition
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46 The flying circus of phys
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Emergency ascent
expands. Why? The same phenom- suppose that while scuba divingenon occurs with soap bubbles. at some great depth, say 100 feet,See Boys's soap bubble book (322). you had to make an emergency
321,‘ 322, pp. 56-57. ascent without additional air. One
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lungful has to be enough for you to
Boy le’s law
partial pressure
3.6Champagne recompression
When a tunnel under London’sThames River had been completedand the two shafts had been joined,the local politicians celebratedthe event at the tunnel’s bottom.ln the tunnel they unfortunatelyfound the champagne flat and life-less. When they returned to thesurface, however, “the wine popped
Thames Tunn., .., iii ml Q%a
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in their stomachs, distended theirvests, and all but frothed fromtheir ears [Figure 3.6]. One digni-tary had to be rushed back intothe depths to undergo champagnerecompression ” (314). Whathappened to the politicians?
314,‘ 315.
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Figure 3.6The danger of subterranean chnmpn
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really just an academic question, forsubmarine crews are trained to makesuch emergency escapes.) Wouldyou continuously release air as youascend, or keep it all in? Well,although it may seem unreasonable,you had better release air or youwon't make it. In fact, novicescuba divers practicing in swimmingpools are occasionally killed becausethey neglect to exhale when prac-ticing emergency ascents. Why?It is said the urge to take another
breath stems from the partial pres-sure of the CO2 in your lungs, notthe volume of the C02. Researchersconclude from this that the mostdangerous and crucial point in yourascent will be at some intermediatepoint and not near the surface.Once you pass the crucial point,the urge to take another breath willrelax considerably. Why is this?What is the crucial depth? Howfast should you swim to the sur-face? Can you swim too fast?If you can, then what’s a reason-able rate?
325 through 328.
3I8
Blow-holes
You'd probably imagine that cavesare full of stagnant air. Some are,but at the entrances of some, called“blow-holes" by spelunkers, a ifierce wind blows constantly. Whyis that? Even stranger are thebreathing caves where the air blowsin for a moment and then out al-ternately. What drives the air backand forth?
318, pp. 143- 144,’ 319.‘ 320.8
Heat fantasies and other cheap thrills of the night 47
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In deep-sea-diving ascents thereis always the serious threat of“bends,” in which bubbles formfrom the nitrogen dissolved inthe tissue during the dive. Thiscan be not only painful butalso paralyzing and even fatal.Consequently, the ascent ismade slowly enough that thenitrogen is disposed of withoutbubble formation. You have seenthis in movies: the diver stops atvarious depths in his ascent.Where do you think the longest
stop is: near the surtace wherethe diver is almost at atmosphericpressire, near the bottom, or atsome intermediate point‘? Iwould have eliminated the firstchoice immediately, but thedecompression schedule inFigure 3.9 contradicts me: thelongest stops are near the sur-face. Why should that be? Whatis the deepest dive you can takewithout having to wait aroundon the way up‘?
323,’ 324.
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Figure 3.9Decompression schedule as recommended by the U.S. Navy for 35'36' 339'a one-hour dive at 200 feet. Dashed line indicates the sen-levelpressure. (After!-l. Schenck, Jr., Amer. J. Phys, 21, 277 (1953).)
Thermal expansion8: contraction3.10 through 3.15
3.10Hot water turning itself off
When I tum on the hot water inmy sink, the water's flow rateslowly decreases and the flow mayeven stop. The cold water won'tdo that, so why does the hotwater behave so badly? Why doesit do that only when I've firstturned it on and not the secondtime, after I've tumed it up?
thermal expansion
3.11Bursting pipes
Why do water pipes burst in winter?It‘ the only thing that occurs is thefreezing of water next to the pipewalls, then there shouldn't be anygreat strain on the pipe and hencethe pipe shouldn't burst. Besides,the bursting usually occurs awayfrom the point where the wateris frozen. So, again, what causesthe burst? Is there any real ad-vantage in letting outside tapsdrip all winter as some peopledo? Finally, is there anytruth to the common ideathat hot water pipes burst farmore often than cold water pipes?
253. PP- 136- 137,‘ 338, pp.
48 The flying circus of physics
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3.12Fever thermometer
When you take your temperature,the heat of your mouth makes themercury expand. Why doesn't themercury level fall as soon as youremove the thermometer fromyour mouth? lt doesn't, becausea constriction in the tube preventsit from falling (Figure 3.12). Butwhy? After all, during the expan-sion the mercury passed throughthe constriction. Why won't it
do the same during the contrac-tion?
Why does the reading drop fora moment if you stick thethermometer into hot water?(Don't overheat the thermometerso that it breaks.)
160, p. 114,‘ 317, pp. 117-118,129; 329, p. 50,‘ 330, p. 41,‘ 331,p.6.
3.14Watch speed
Since metal expands when it'sheated and a watch spring is metal-lic, wouldn't you think that awatch would run at different speedsin cold and in warm weather?
9, p. 82,‘ 160, p. 125' 317, p.129; 329, p. 43,- 330, p. 90;331, p. 23.
bu oyancy
nonlinear oscillations
3.15U-tube oscillations
If a U-tube of water is heated andcooled as shown in Figure 3.15,the water will begin to oscillatefrom one side to the other. (Theremust be open reserviors with the
3.13Heating a rubber band
Stretch an uninflated balloon andthen touch it to your face. Itfeels warm. Now let it contract toits normal size. it feels cool. Why?if you heat a rubber band it con-
tracts. Why is its behavior preciselyopposite that of metal? What's
3.13 shows a rubber-band enginebased on this property. The spokesof the wheel are rubber and hencewill shrink when heated. The wheelturns because of the shift in thecenter of gravity.
different about its structure? Figure
155, p. 244,- 332, Vol. 1, p. 44-333 through 337.
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‘Figure 3.15The water will oscillate from sidelo side if the tube is heated andcooled as shown. [After P.Welander, Tellus, 9, 419 (1957).)
Heat fantasies and other cheap thrills oi the night 49
air-water surface area larger than acritical size.) The change in waterlevels can be a millimeter or so, andthe period of the oscillations canrange from about 20 seconds to 4hours depending, in part, on thecross-sectional area of the U-tube.Doesn't the symmetry of the situa-tion make it seem curious thatthe water oscillates? What firststarts the oscillation and whatparameters determine its period?
340.
adiabatic processes
adiabatic process
3.16Bike pump heating up
Why does the valve on a bicyclepump get hot when you'repumping up a tire? Is it becauseof friction from the air beingforced through the valve? Well,perhaps, but if you use a gasstation's compressed air supply,the valve usually doesn't get hot.
341.
condensation
3.17West-slope hill growth
Why is it that in the United Statesthere is often more vegetation onthe westward slopes of hills andmountains than on the eastwardslopes? You may even find extremecases where the east side is bar-ren though the west side has thickgrowth.
360, PP. 162- 165
3.18The Chinook and going mad
The Chinook is a warm, dry windthat blows down from theRockies into such places as Denver(Figure 3.18). It can be up to50°F above the ambient tempera-ture and may reach speeds ashigh as 80 mph. The mystery ishow a warm wind could comedown off a cold mountain. Be-sides, warm air should rise,shouldn't it? Legend says thewarmth comes from the ghostsof lndians buried in the moun-tains.
Chinook-like winds are by nomeans confined to the Denverarea. In Switzerland this windis called the foehn; in Ceylon,the kachchan; in South Africa,the berg wind; in Southern Califor-nia, the Santa Ana; and in other
places, other names. They allshare the properties of being dryand warm.
They also share a very con-troversial feature, namely, it issaid that they drive men andanimals mad. When these windsblow, crime rates increase, rapeand murder are more frequent,there are more traffic accidents,and people iust act generally moreirrational. This could be an oldwives tale, or there could besome truth in it. How could dry,warm winds affect a man physio-logically? ls there any physicalreason for the irrational behavior?
164, PP- 217-218,‘ 343, p. 348,‘344, pp. 94-98; 345 through358.
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Figure 3. I8The Chinook wind blowing down off the Rockies.
50 The flying circus of physics
adiabatic process adiabatic process condensation
3.19Coke fog
I-lave you ever noticed the thin fogthat gathers at the mouth of achilled champagne or soda bottlejust after it's been opened (Figure3.19)? What causes the fog?
r(¢‘I.‘342.
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Figure 3.19Fog at mouth of freshly opened,chilled champagne bottle.
3.20Convertible cooling effect
On a hot day you're in luck if you'vegot a friend with a convertible.Driving down the road with a goodbreeze always does the trick againstthe heat. You feel cooler but athermometer should read thesame with or without a breeze,shouldn't it? Try it. With a ther-mometer in the back seat, measurethe temperature when the car isparked and when it is moving.You'll probably find that thethermometer reads about 112°Clower when the car is moving. Why?
359.
radiation absorption buoyancy
3.21Death Valley
Death Valley is both the lowestpoint on the American continentand the hottest place in theworld. Temperatures there maybe as high as 120° F for severaldays straight, and once a tempera-ture of 134°F was recorded.isn't there something physicallywrong in its being so hot if it isso low? Since hot air rises andcold air sinks, and since thevalley is surrounded by mountainswith cold air on their tops,shouldn't the valley be a relativelycool place?
223, p. 200.
adiabatic process
adiabatic process
3.23Holding a cloud together
What holds a cloud together? Or,on partially cloudy days why aresome parts of the sky cloudy andothers not? Wouldn't you expecta more uniform distribution of theclouds over the sky?
363, pp. 44-67; 365.
3 Q
Mushroom clouds
Why do ground-level nuclear andother large explosions leave mush-room clouds?
371, pp. 202-203' 372; 373.
condensation cloud genesis
latent heat stability
radiation buoyancy
3.22Mountain top coldness
Why are mountain tops cold? Isn'tthe solar heat per unit area on amountain about the same as at sealevel? And shouldn't cold air sink?
3.25Holes in the clouds
Mysterious circular holes have oc-casionally been observed in other-wise uniform cloud banks. Thefeeling is that these holes, whichare usually quite large, are not justrandom arrangements of the clouds.Suggestions as to their cause haveranged from burning meteors toaccidental or intentional cloudseeding. How exactly could anyof these explanations account forsuch holes?
362, p. 91; 374 through 379.
Heat fantasies and other cheap thrills of the night 51
cloud genesiscondensation
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3.26Mountain clouds
in Figure 3.26a. What causes these ¢l0\ld5'?formations? The wavelike series of
Figure 3.260 Figure 3-2617Two types of mountain peak clouds Wauelike clouds associated with a mountain peak
If you have ever lived near moun- clouds that sometimes occurs near 164, pp. 301-303; 360, pp. 86-tains you may have noticed the a peak is even more intriguing 88," 361, pp. 14-21, 39; 362,stationary clouds often found over (Figure 3-255} What determines pp. 64-73; 363, pp. 75-82; 364,mountain peaks. Two are shown the spatial periodicity of these pp. 229 ff; 365 through 370.
shock wave ab5°"ptl°"
condensation b"°Vi"°V
Spherical cloud of A-bomb blast
spherical cloud (Figure 3.27)
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condensation3.27 evaporation
3.28In some circumstances, a nuclear significantly reduce the radiation Burning off cloudsblast is accompanied by a thin, produced by the explosion?
- _ . When there were low-hanging cloudsWhat causes these clouds? How 219' pp’ 3” 312’ 371' pp' on an early summer morning, myfast do they expand? Will they 34 ff’ grandmother would often say .
the sun would “burn them off" andthe day would be sunny. Since theydid often disappear later in themoming, I figured she was right andthat the sunlight absorbed by theclouds indeed “burned them off."Was I correct?
Figure 3.27363, p. 76,’ 364, pp. 273-274.
52 'l1'|e flying circus of physics
cloud genesis
stability
buoyancy
3.29Mamma
What causes the breastlike cloudstructure called mamma (Figure3.29)? In particular, why are theresometimes bright gaps betweenthe mammae?
362, pp. 54-56.
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3.31Breath condensation
Why does your breath condenseon the window pane on a coldday? More specifically, whatactually causes the water mole-cules to form into a drop? Whydid those water drops condensein those particular places on theglass. . .what was so special aboutthose places?
Why does a hot piece oi toastleave moisture on a plate?
388, pp. 428 ft} 389.
bubble nucleation
3.33Salt water bubbles
Why are more bubbles producedwhen salt water is poured intosalt water than when fresh wateris poured into fresh water?
390.condensationadiabatic process
vort ices
buoya ncy
condensation
3.30Cause of fog
London's fogs have diminished inintensity in the last decade partial-ly because there was a reduction inthe use of open coal burning.What has open coal burning got todo with fogs? In general, whatcauses fogs?
388, pp. 480-510.
3.32Contrails and distrails
Why do contrails often form behindairplanes? Why aren't they alwaysproduced? If you look closely youmay see that a contrail actually con-sists of two or more streams thateventually diffuse and become in-distinguishable. Why is there morethan one stream at first? Why isthere a clear gap between the air-plane and the leading edge of thecontrail? What's responsible forthe bursting and blooming ofcontrails that makes them look
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Figure 3. 32
like strung popcorn (Figure 3.32).You may be fortunate enough
to see both a contrail and itsshadow on underlying clouds. Butthe distrail, a dark line left by anairplane flying through a cloud, iseven more interesting. How doesan airplane make that kind oftrail?
362, pp. 120- 129," 364, pp. 73-74,‘ 380 through 387,‘ 1537.
___ ._ . .._ w
Side view of contrail that has burs! to a popcorn appearance.
Heat fantasies and other cheap thrills of the night 53
ir
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bu oyancy
Bernoulli's principle
3.34Fireplace draft
In a good fireplace the smoke goesup the chimney rather than outinto the room, even if the fire isnot directly beneath the hole. Whatcauses this draft, and why is itbetter the taller the chimney?Why is the draft better on a windyday? Finally, why do somechimneys puff (Figure 3.34)‘?44, p. 188; 318, pp. 225-230,‘364, pp. 216-217,‘ 391. PP. 111-
392, pp. 108- 1 12,‘ 393; 394.1 12,‘_..___|_. Ha ___~i;_H5,;_--_.~_,.‘:_g;§fi
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3.35Open-air fires
Many communities that still allowopen-air fires forbid them duringthe daylight hours. Why would itmatter whether the fires are duringthe day or evening?
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54 The flying circus of physics
buoyancy supercooling
stability free energy
lapse rate
3.37Stack plumes
You would think an indus-trial stack plume would risevertically or, if there is a wlnd,would rise at some angle. Yetthe plume shapes shown inFigure 3.37.9 are often seen ina uniform horizontal wind. Whatcauses these shapes? The lastone with the peculiar periodicityis especially interesting. Why dosome bent-over plumes splitsideways downwind from thestack (Figure 3.37bl?
364, pp. 207-212; 395through 398.
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3.39Freezing water
Why does water normallyfreeze at 0°C? What is so specialabout that particular tempera-ture? Under some circumstancesliquid water can exist at subzerotemperatures; for example, waterdrops at temperatures as low as—30°C have been found in clouds.What must be done to make suchsupercooled water?
Can ice be heated above 0°Cwithout melting?
338,’ 389,’ 402 through 404.
freez inglatent heat
’} evaporation
Figure 3.370[After Bierly and Hewson, J.Appl Meteorology, I, 383 (1962),permission gran ted by authorsand the American MeteorologicalSociety.]
ice crystal growthcapillarityradiation absorption
3.38Shades of ice coverings
If you observe a distant ioecovering on a North Alaskanlake or river when it begins tomelt in the late spring, largeparts of the ioe will look darkand other parts will look white.
(and painfully) teach you thatthe dark ice is weaker and shouldbe avoided. Why is the ice lightand dark, and why are the darkareas weaker?
338 pp 120-126',’ 376
3.40Freezing hot and cold water
In cold regions like Canada orIceland, it is common knowledgethat water left outside will freezefaster if it is originally hot. Whilethis may seem completely wrongto you, it is not just an old wives’tale, for even Francis Baconnoticed it. Try putting warm andcool water in various containerseither outside on a freezing nightor in your freezer. If in any ofyour tests the warm water freezesfirst, then you'll have to explainwhy.
A walk across the ice can quickly ' ' ' 405 m’°”9h 47 7-
I-leat fantasies and other cheap thrills of the night 55
thunderstorm thermodynamics ‘density change with temperature
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3.41Worldwide thunderstorm activity
H. I th Id .de um deb the greatestamount of thunder-
EZZ:myzggguigfggfiitfle dence plausible? Is there anythat has a maximu;n at 7 RM. physical basis for this particular
London time and a minimum at dependence?4 A.M. London time (Figure 3.41). 219, pp. 123-124; 300, pp.In other words, when it is 7 P.M. 109-111; 332, Vol. II, Chapterin London, the earth is experiencing 9; 388, p. 445' 401.
convectioninsulation
you P at 8 wot M n storm activity. Is any time depen-
heat conduction may result in very painful injury.Why does your finger stick to
the trey? How cold must themetal be for this sticking tohappen?
3.42Getting stuck by the cold
If you touch a cold piece of metal
3.44Pond freeze
Why does the top of a pond freezebefore the middle and long beforethe bottom? (There's more thanone reason.) If this weren't so,there would be virtually no fresh-water fish outside the tropics.
In areas where water transporta-tion is nacessary, the formationof ice can be prevented by bubblingair up from pipes laid on the bot-tom of the lake or river. If ice isalready present, the bubbles willeven melt the ice although it maytake four or five days to do it.How do the bubbles clear a riveror lake in this way?
158, p. 288; 403,’ 412, pp. 495-496,‘ 413, p. 139; 414. PP. 4-6,58-6 1.
conductionphase change
such as a metal ice tray fresh from |mm hemthe freezer, your hend may stickto the metal. Be careful if youactuelly try this experiment, foryou can lose the skin that sticks tothe metal. Have water running inyour sink and, immediately aftertouching the ice tray, dunk yourfinger and the tray under the water.Do not lick the tray, es someunknowing children do, for that
3.43Wrapping ice
Why does ice keep frozen longerif it is wrapped in a wet piece ofpaper?
160, p. 166.
3.45SkiingWhat allows skis to glide oversnow? ls it the same as the mech-anism involved in ice skating?Could you ski on other frozensubstances or is snow (water)unique? Can it get too cold toski? Why are skis waxed? Finally,why do ebonite skis slide muchbetter than metal ones?
421, p. 393; 422 through 424.
56 The flying circus of physics
adiabatic compression\ pressures and phase change
3.46Ice skating
When you ere ice skating, why doyour skates slide along the icesurface? If you can, explain thephysics involved with precticalnumbers. Obviously it can get toowarm to skate. Can it get too cold?
ls the ice that is found in very coldpleces, such es Greenland, slippery?Could you skate in a similar weyon other frozen materiels such escarbon dioxide (dry ice)? Supposeyou had to walk across ice end youcould choose between a patch ofsmooth ice and e patch of roughice. Would you find one moreslippery than the other?
166,’ 321, p. 274; 414, pp. 111-1 13,‘ 4 18, p. 129,‘ 4 19,’ 420.
conduction
phase change
3.48Making a snowball
Why can't you make a snowball ifthe temperature is very low? Whatholds a snowball together, anyway?Approximately what is the lowesttemperature at which you can stillmake a reasonably good snowball?
166.
adiabatic compressionpressure and phase change
3.47Snow avalancheHow can sudden warmings andmechanical vibrations triggersnow avalanches? Why do manyavalanches occur at sunset whenthere is a general cooling ratherthan a warming? There areeven claims that a skier’s shadowmay be enough to set off anavalanche. Why would this happen?
In a dry snow avalanche a huge
cloud of snow particles precedesthe slide, crashing down themountain side at speeds up to 200miles per hour with enough forceto destroy large trees and movesteel bridges. According to onestory about a skier caught inone of these snow slides (Figure3.47), the skier and the slidereached the opposite slope with
such speed that the trapped airwas compressed and warmed andthus partially melted the snow.Within several minutes, how-ever, the snow had refrozen,and when the rescue team reachedthe still-living skier, they had tosaw him out.
415 through 417.
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Heat fantasies and other cheap thrills of the night 57
conduction freezing pointphase change
3.49Snow tires and sand for ice
Sand and studded snow tires areboth commonly used in winterdriving on icy streets. Why isit that neither does you muchgood if the temperature is belowzero? For that matter, why dothey help for temperatures abovezero?
I66.
freezing point
3.50Salting ice
made ice cream, she packs icearound the ice cream container,
she add the salt? In a similar vein,why is salt put on icy roads? Toboth these questions you'll proba-bly answer, "to lower the freezingpoint." Yes, but how does saltlower the freezing point? If theday is very cold, the salt won't im-prove the road contions. What is
12- 15, 47-48.
3.51Antifreeze coolant
Why does a mixture of antifreezeand water freeze at a lower tem-perature than pure water? Howdoes the antifreeze also provideprotection against overheatingin the summer? If antifreeze isso good in these respects, thenwhy don't you completely fillthe radiator with it and forgetabout the water? (Most anti-freeze manufacturers suggestthe mixture should not exceedabout 50% antifreeze.)
330, PP. 227-228.
latent heat
When my grandmother makes home-
and then she salts the ice. Why does
3.52Feeling cool while wet
Why do you feel cool when youfirst step out of a shower or a
pool? Try to estimate your rateof heat loss. (One parameter nowused to measure such a cooling ef-fect in a wind is the windchill fac-tor.)
Why are hosptial patients some-times given methyl alchohol rub-downs to soothe them? Why notiust use water?
When I was young and on vaca-tion with my family, we kept acanvas water bag on our car's frontfender. Though the day may havebeen hot, the water in the bag wasalways cool. Why was that? Canyou calculate the temperature ofthe water for some given situation(air temperature, humidity, carspeed)?
I58, p. 324; 427, p. 64,‘ 428;429.
freezing point
3.53Carburetor icing
On some days, even when the tem-perature outside is as high as 40° F,
How cold would it have to, be for
i
_ ~._. '-~ /fi\the lowest temperature at which / _it will still do some good? 7“ ,
a body of salt water to freeze ,-(‘fig _ , .over? i ‘U-". I '
413, pp. 187-188; 414, pp. 3-4, J? /\@fl—f§ €*- 7 ‘
5 Jl2.e
58 The flying circus of physics
my carburetor will ice up and ceusemy car to stall. Figure 3.53 showthe throttle plate being frozen inplace, thereby stopping the airflow to the engine. What causesthis icing? ls this more likely one dry or on a humid day? Can itheppen when the outside tem-perature is below freezing?
426.
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Figure 3. 53Carburetor icing.
5
fl
latent heat
diffusion
3.54Eating polar ice
Eskimos know that newly frozensea ice is much too salty to eator to melt for drinking but seaice several years old is fine. Theyhave also found that if the ice
is pulled up onto shore and outof the water, the desalting isspeeded up, especially if thisis done during the warm springand summer months. Why doesthe salinity decrease with timeand, in perticular, why does itdecrease faster in the warm monthswhen there should be more evapora-tion and a resulting increase insalinity?
338, pp. 95-97; 414, pp. 26-28; 425.
if she opens the oven door wideand then closes it just before shetums on the heat. If this is true,then explain it.
160, p. 174.
latent heat
latent heat
3.55A pan top for boiling water
if you boil a pan of water forspaghetti, why does the boilcome much faster if the lid isleft on? Well, there is less heatloss, right’? But what doesthat really mean? Is there lessconvection or less infrared radia-tion? When the lid is on, isn't thelid itself nearly at the boiling tem-
nearly as much radiation and conperature? Hence, won't there be
P9vection above it as above an opan? If so, why does the waterboil faster in a covered pan?
ll
3.57Water tub saving the vegetables
My grandmother puts a large potof water in the cellar near hervegetables to protect them fromfrost. Why would the presence ofthe water help protect thevegetables?
150, p. 161; 329, p. 70,‘ 438.
latent heat
convection|8l8f‘lI heat
3.56Briefly opening oven
My grandmother claims that onhumid days her oven heats up ter
3.58lcehouse orientation
Before the refrigerator was in-vented, people in northern climateswould store winter ice in icehousesfor use in the summer. Among thefeetures required of a good lcehousewas proper orientation: its door-way had to face towards the eastso the morning sun would eli-minate the damp air. But this alsmeant the sun would warm thelcehouse more than if it facednorth or south, and so the damp-
O
ness must have been far more un-desirable than the extra warming.Why was that?
439.
fas
Heat fantasies and other cheap thrills of the night 59
heat conductionheat pipes
latent heat
3.59Heating meat with a “Sizzle Stik"
l-low can you get a roast to cookfaster? Well, you can stick ametal rod into it as is commonlydone in baking potatoes. Sinceheat is then conducted into themeat's interior quicker thandirectly through the meat, themeat cooks much faster. There isa device called the “Sizzle Stik"*,however, which abandons the metalrod in favor of a hollow metaltube containing a wick from end toend and some water (Figure 3.59).It is claimed that heat conductionis 1000 times better than withthe solid tube, and indeed, cookingtimes may be cut in half. Buthow? Why would a hollow tubelike this be better than a solidone? And why is there water anda wick in the hollow tube?
430 through 432.
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latent heat
3.60The highest mountain
On the earth why aren't thereany mountains significantly higherthan Mt. Everest, say, ten timeshigher? (Nix Olympica on Mars isover twice as high as Mt. Everest.)If there is some limit to mountainheights, then what determines it,and approximately what is thelimit?
440.
Yubana, or boiling water ordeal,of the Japanese Shinto following.
In the Yubana, the performerapproached a huge caldronfilled with boiling water andsuddenly thrust two clumpsof bamboo twigs into theliquid, flinging it high andshowering it all about hishead, shoulders and arms.As the water reached thefire below the caldron, itproduced great clouds ofsteam, which subsidedonly when the caldronwas almost empty. Theperformer was then seenquite unharmed by theordeal, proving themighty power of Shinto.*
Boiling water would have bumedthe performer’s skin, of course, sothere must have been some trick.Hence, you should not try thisexperiment yourself. Would ithave helped if the Shintoist timedhis ritual so that his feat came soonafter boiling commenced? Whatwas the water temperature then?
449.‘From Master Magicians by WalterGibson, Copyright © 1966 by WalterGibson, Reprinted by permission oiDoubleday 8| Company, Inc,
phase changelatent heat
bubble formationconduction
3.61The boiling water ordeal
One of the most fascinatingexamples of Oriental magic is the
3.62Boiling point of water
What does it really mean to say thata pan of water is boiling? One
60 The flying circus of physics
hundred degrees centigrade is thecommonly accepted boiling pointof water at an atmospheric pres-sure of one atmosphere. How canany one temperature like this becalled the boiling point? Why canwater sometimes be heated above1oo°c without boiling (still at apressure of one atmosphere)?Finally, why is it claimed thatonce water has reached 100°C anyadditional heat input will not raisethe water’s temperature but willonly increase the evaporation rate?Why can't the water beneath thesurface get hotter than 100°C withan additional heat input?
441.
ideal gas law
VBDOY fll'9SSUf9
latent heatphase change
evaporation rate
3.63A puddle's salt ring
When salt has been used to deiee asidewalk, why is it left behind inrings around the puddles as thepuddles evaporate? The same thingcan be seen on a larger scale inthe white edges around lakes indry areas. You can even see itin your own kitchen by saturatinga glass of hot water with selt andthan letting the solution set for amonth. Afterwards, both theinside and outside surfaces ofthe glass will be coated with salt.Why is salt left on the outside ofthe glass?
360, pp. 21-23,‘ 458.
3.64Dunking bird
The dunking bird, which isprobably the most popular of allphysics toys, is a glass bird thatrocks back and forth and “drinks”from a glass of water (Figure3.640). You start the motion bywetting the head, after which thebird slowly begins to oscillate andeventually dunks its head into thewater. The bird then rights itselfand repeats the cycle withoutfurther assistance. As long as itkeeps getting its head wet, it willcontinue to bob up and down.What makes it go?
Perhaps the dunking bird is asolution to next century's powerneeds. Just imagine—we erect ahuge bird just off Califomia, andas it continuously dunks its headinto the ocean, it provides theentire West Coast with energy.
Felt orleatherson head
a/'1
L\Figure 3. 640Dunking bird.
This might lead to a dunking-birdcult, however, and we would allend up paying tribute by dunkingin unison three times to the westeach morning (Figure 3.64b), somaybe we'd better just forget it.
433 through 437; I457.'—.. . ’
Figure 3. 64bThe dunking-bird cull.
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Heat fantasies and other cheap thrills of the night 61
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3.65
if water drops are sprinkled ontoa dry, hot skillet, the drops willdance and skim along the skillet'ssurface. Why don't the dropsevaporate immediately? Whatmakes them skim along? Sur-prisingly enough, the drops willdisappear faster if the skillet iscooler. Why is that?
Examine a skimming dropclosely and you will find itassumes a variety of odd shapes.
Dancing drops on hot skillet
The drop is actually vibratingbut since your eye cannot followthe motion that quickly, you seea composite shape. To catch itin various vibrating states, use astrobosoope or a high-speedcamera. In Figure 3.65 some ofthe fundamental shapes are sketch-ed. Why do the drops vibrate?
155, p. 234; 160, pp. 171-172;330, p. 254; 442 through 446.
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Figure 3.66Artificialgeyser. (E. Taylor afterF. I. Boley.)
3.66Geysers
What causes the eruptions ofgeysers and, in Old Faithful'scase, what is responsible for theperiodicity of the eruptions?Could their energy souroe besimple heat conduction throughthe surrounding rock, or is afaster heat supply needed?
Suppose you were to make anartificial geyser with a continuousheat source as shown in Figure 3.6How deep should you make the
provide for the heating, how oftenwould it erupt, and how high woulthe water jump?
450 through 452.
6.
tube, how much power should you
d
62 The flying circus of physics
vapor pressure vapor, conduction, radiation
3.67Percola tor
How does my plain old, non-electric coffee percola tor work?For example, must the centralstem be relatively small? And, isall of the water at boiling tempera-ture when the pot begins to perk?
253, PP. 1 10-1 11,‘ 1533.
latent heat
3.68Single-pipe radiators
While most steam radiators havetwo pipes (one inlet and one outlet),there is one system in which thereis only a single pipe (Figure 3.68).As if that were not strange enough,it is said that the steam and retum-ing water in that single pipe are atthe same temperature. How couldthey be at the same temperatureit‘ the radiator is heating the room?Where does the radiated heat comefrom?
318, pp. 6-8; 418, p. 143.
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Figure 3. 68
W3.69
Licking a red-hot steel bar
Though fire walking has long beenassociated with Far East mysticism,there have recently been somescientific investigations into thefeat and even a fire-walking dis-play before thousands of peopleat a soccer match halftime. Evenmore amazing than the fire walkers,however, are those people whocan briefly plunge their hands intomolten metal and touch and lick (I)red-hot steel bars without theslightest iniury. You may suspectdeceit is involved, but the feat canactually be explained with gOOdphysics. Although I have dippedmy fingers into molten lead with-out harm, you should not try these
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experiments yourself, for they aredangerous and can result in a verybad burn. Figure 3.69 shows thateven good physics won't save anoverconfident scientist.
Suppose a professional showmanwere to lick a red-hot steel bar.What might guard his tongue notonly from a very serious burn, butindeed from any burn at all? Whyshould he use only extremely hotmetal? ls there any danger in lesshot metal? In fire walking is thereany optimum speed with which towalk? In particular, can a firewalker walk too fast?
330, pp. 254-255' 447,‘ 448.
I-leat fantasies and other cheap thrills of the night 63
steam flashconvection
3.70Banging radiator pipes
What causes the hammerllkepounding of steam radiators?
253, p. 15$ 318, pp. 9, 15;p. 319.
453,
thermal absorptionradiation
3.71Wrapping food with aluminumfoil
Ordinary kitchen aluminum fo'l
Does it really matter which finishis on the outside when the foil iswrapped around something to becooked, as a baked potato forexample? Which finish should beoutside when the wrapped materialis to be frozen, and again does itreally make a difference?
Ihas one shiny side and one dull side.
3.72Old incandescent bulb
Why does an incandescent bulb be- ,\ ‘ 4 Icome gray as it becomes old? Doesit become uniformly gray, or isone side preferred?
3.73How hot is red hot?
Probably you know that en ob-iect sufficiently heated will becomeincandescent. A red-hot pokerin the fire is a common example.Can you estimate the temperatureat which an obiect, let's say, thepoker, first becomes visibly in-candescent? Does it matter if thepoker is black iron or shiny steel?
1583.
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mgFigure 3. 74Refrigerator as an airconditioner.
3.74Cool room with refrigerator
Once, on a very hot day, I tried tocool my dorm room by leaving myrefrigerator door open (Figure3.74). l-low much did I cool myroom that way?
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64 The flying circus of physics
Q
thermal absorption DYOSSU Y8
and transmission nonlinear oscillation
3.75Black pie pans
Why are the bottoms of somefrozen pie pans painted black?
if you make a pie yourself andyou want the bottom crustbrowned, why should you use athermal glass pan rather than ametal one? If you have to use ametal one, why should it have adull finish, instead of a nice shinyone? You may very well alreadyknow why in principle, but doesit really matter in fact? Try somesimple experiments to see.
radiation
3.76Archimedes’: death rey
During the Roman attack of Syra-cuse about 214 B.C., the Greekscientist Archimedes supposedlysaved his town by burning theRoman fleet with sunlight directedby mirrors located on the shore.Presumably, many soldiers simul-taneously reflected the sun'simage onto each ship in turn, andeach ship was set on fire.
Considering that Archimedes,did not have very large mirrors,would such a feat be possible? Canyou estimate how many mirrors,
3.77Toy putt-putt boatThe putt-putt boat (Figure 3.77)has an unbelievable means of pro-pulsion. Two pipes join a top sec-tion, the boiler, to the boat's rear.When the water-filled boiler isheated by a candle, the steam thatis produced forces water out of thepipes and thus drives the boat for-ward. The boat should stop whenthe boiler runs out of water, but
actually more water is sucked intothe boiler through the pipes, andthe process repeats itself. Thus,the boat putt-putts its way along.Why is water sucked up? Whenit is sucked up, why doesn't theboat move backward as far as ithad previously moved forward?
454 through 457.
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Figure 3. 77
Amer. J. Phys, 31, 289 (1963).)Cutaway view ofputt-putt boat. [After I. Finnie and R. L. Curl,
let's say, one meter square, would
100 meters away within less thana minute? Should those mirrorsbe curved or flat if the target dis-tance is variable? lf they are flat,how large is the image of the sunon the wood? Finally, couldArchimedes have destroyed theRoman fleet in this manner?
conduction
be needed to set aflame dark wood specific heat
1574 through 1580,‘ 1615' 1616.
3.78Feeling cold objects
Shouldn't all objects at the sametemperature feel like they are atthe same temperature? You aren'treluctant to put your clothes onwhen they are at a room tempera-ture of about 70° F, but how aboutsitting down naked in a dry bathtubat the same temperature? What'sthe difference?
462, p. 76.
Heat fantasies and other cheap thrills of the night 65
/=1;'9
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J’ ;_ l‘f[,i;i itFigure 3.79“It's not the heat or the humidity,it's this damn 100% wool, fullylined burnoose."
:\ eéfgi
thermal <=°"d"<=Il°" pots and pans as opposed to steelones. Cooks, from the gourmet tothe occasional, swear there is lesssticking and better, more uniformcooking with the cast iron pot.Is there any physical basis to thatclaim?
and absorption
3.80Cast-iron cookery
There is an ancient kitchen mys-tique about cooking in cast-iron
radiationheatingiluxthermal conductivity
radiationconvectionphase change
3.79White clothes in the tropics
Why do people wear white clothesin the tropics (if, in fact, they do)?Supposedly it keeps them cooler.Is that a real and measurable effect?If they have light skin, does whiteclothing make any difference?Does the sun heat you primarilywith ultraviolet, visible, or in-frared light? How does whiteclothing respond to each of thesefrequency ranges? How much ofthe heating is from direct sun-light, and how much is from theenvironment? Finally, it you'retraversing a desert, should youwear white clothing or go'nude?
344, pp. 58-59,’ 459 through46 1.
3.81The season lag
Why exactly is it cold in winter andwarm in summer? ls it because theearth is closest to the sun in sum-mer and furthest away in winter?No, actually just the opposite istrue (Figure 3.81).
Predict which months should bethe coldest and which should be thewarmest. You will probably pick,if your explanation is the commonone, the months of November,December, and January for thecoldest and May, June, and July
for the warmest. However, theweather records and your ownexperience tell you that thecoldest months are December,January, and February and thewarmest are June, July, andAugust. As my grandmothersays, “When the days get longer,the cold gets stronger." Whydoes the weather lag yourprediction by one month?
388, p. 7.
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66 ‘file flying circus of physics
temperature
kinetic theoryradiation
3.82Temperature of space walk
What is the temperature of the spacewhere an astronaut is space walking?If he held up a thermometer, whatwould it read?
Fred l-loyle's excellent sciencefiction book, The Black Cloud(470).
219, pp. 153- 154,‘ 388, p. 22,‘466, pp. 33-34,‘ 467 through469,‘ 1544; 1545.
conductionconvectionradiation
radiation
3.83Greenhouse
A greenhouse is somehow de-signed to keep plants in a warmenvironment. How docs it dothis? Does it have special glass orwill any glass material do?
A controversial application ofthe greenhouse principle is inpredicting the results of ouratmospheric pollution. For ex-ample, a catastrophic warmingof the earth might be caused bya high altitude, supersonic trans-port system. Why is this feared,and how could the more generalpollution of the atmosphere leadto a runaway greenhouse effect?The subject is, of course, verycomplicated. In fact, some claimthat the pollution will not bringa warming, but instead will leadto a cooling of the earth andpossibly even another ice age.An intriguing account of theeffects of clouds on the solarlight input to the earth is in
3.84Why do you feel cold?
lf you stood naked out in a fieldon a cold winter day, why wouldyou feel cold? For instance, isyour body heat escaping to theair by heat conduction? Whywould a fur coat make you feelwarmer? Wouldn't it conductheat too?
While indoors on a cold day,stand facing a large window andthen turn the opposite way. Most
likely your face will feel cooler inthe first position. Why is that?After all, the air temperaturedoesn't change suddenly as youturn around.
ln the movie 2001: A SpaceOdessey an astronaut spacewalked without a spacesuit for afew seconds. (The author, ArthurC. Clarke, believes this could bedone without harm to the astro-naut.) During such a walk in deepspace, would the man have a sensa-tion of cold?
How is it that some people canadapt to very cold working condi-tions? Some people, in fact, courtan adverse, cold environment forreligious reasons or to prove theirstoic nature. An extreme case ofadaptation was discovered byCharles Darwin when he found theYahgan Indians of South Americaliving in temperatures near 0°Cwith little more than a fur capedraped over their shoulders. Whatphysically changes in the body's
Figure 3.84"He was streaking. "
Heat fantasies and other cheap thrills of the night 67
response to the cold to allow suchadaptation?
Finally, when you do get verycold, why do you shiver?
253, pp. 140- 142; 344, Chapter4, 5' 412, p. 498; 428; 459; 460;463 through 465
heat loss
3.85Wrapping steam pipes
Exposed steam pipes are oftencovered with asbestos to minimizeheat loss, and so we might concludethat asbestos is a poorer conductorof heat than the room air. Other-wise why would anyone pay forasbestos insulation? But, as a mat-ter of fact, asbestos is a betterheat conductor than air. Why thenis it used to cover pipes, if thatseems precisely the wrong thing todo?
253, p. 74.
convection
3.86Thunderstorm wind direction
"You don't need a weather-manTo know which way the windblows"
. ---Bob Dylan,Subterranean Homesick Blues.‘
When a thunderstorm is a few milesaway and coming toward you, doesthe wind blow toward or away from
the storm? Most likely you'll findthat it changes direction as thestorm gets closer. Why should itdo that?
300, p. 4,’ 362, p. 47; 363, pp.105- 106.
‘© 1965 M. Witmark & Sons, all rightsresenred. Used by permission of WarnerBros, Music,
convection
3.88Insect plumes over trees
There have been many observa-tions of dark plumes formingover tree tops near sunset (Figure3.88). Though the plumes looklike smoke, closer inspection re-
convection
3.87Silvery waves from your finger
Sprinkle a small amount ofaluminum powder into a squatjar of wood alcohol, screw on thetop and put the jar in the refrigera-tor. Once it has cooled, remove it,and place your finger against theside of the jar. Silvery waves formand quickly spread away from your
{IF/
Figure 3.87
Inc. All rights reserved.)
finger (Figure 3.87). What gener-ates the waves? (The powderserves merely to make themvisible.) What would happen ifinstead you pressed an ice cubeto the jar’s side while the jar andalcohol are at room temperature?
472.
Waves spread from your finger across the alcohoL (From “The AmateurScientist" by C. L. Stong. Copyright © I967 by Scientific American,
68 The flying circus of physics
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isms; till:.»' .1 ‘
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Figure 3.88Insect plumes over trees.[After J. H. Wiersma, Science,152, 387 (April 15, 1966),Copyrighl I966 by the AmericanAssociation for the AdvancementofSc|'cnce).]
veals they are actually thickswarms of insects, usually mos-quitos, that have gathered abovethe trees. The columns are ver-tical and well defined and mayeven suggest a small fire in thetree. They have also been seenover TV antennas and churchsteeples. In fact, there is even astory about a fire departmentrushing out to fight a churchfire only to find that the plumeabove the steeple was insects andnot smoke. Why are these in-sect plumes formed‘?
473 through 480.
I\-
convection phase change
3.89Shrimp plumes and Ferris wheelridesShallow water brine shrimp as-cending in large numbers also takeon the appearance of a plume(Figure 3.89). These plumes, whichmay be as large as several cubicmeters, are always found overstones on the bottom. What's more,they are never found over shadystones, but only over those stonesthat enjoy some sunlight. In spiteof this, however, the shrimp plumesfrequently lean away from the sun.The questions to be asked aboutthis are obvious. Why do theshrimp ascend in such large con-centrations only over sunlit stones?If the sunlight is desirable, thenwhy do the plumes frequently leanaway from the sun?
A shrimp in the plume is carriedup to the surface of the water,where it separates itself from theplume and swims back to thebottom. Why are the shrimp thendrawn back to the plume to con-tinue their Ferris wheel ride?
481.
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Figure 3. 89
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latent heathurnan heat transfer
3.90Heat stroke
If you ever mowed the lawn in themiddle of summer as I used to doin Texas, you've probably wonder-ed how your body stays as coolas it does. A significant amountof thermal energy is generated in-side your body, up to 1400 kcalper hour during heavy physicalexercise, and if that heat is notdisposed of somehow, yourbody temperature could rise asmuch as 30°F per hour. orcourse, that would soon be fatal.How is the heat dissipated? Canyou trace the path by which it islost?
Mowing the lawn in the middayon a once-a-week basis wasmiserable, for I always got heatexhaustion, yet there are peoplewho do this daily without ill ef-fects. Somehow the body be-comes accustomed to workingin the heat. What exactly happens?The heat is generated at the samerate internally, so the dissipationmechanism must somehow change.
High temperatures in Texas wereusually bearable because thehumidity was so low. Why is it somuch more uncomfortable in placeswith high humidity?
344, pp. 57-59; 482.
Heat fantasies and other cheap thrills of the night 69
cooling convection
conduction conduction
thermal radiation radiation
3.91Cooling a coffee
Suppose you have iust made a hotcup of coffee, but you've still got5 minutes until class. If you wantto bring your coffee to class as hotas possible, should you put thecream in now or iust before class?When should you add the sugar?When should you stir it and forhow long? If you don't want tostir it, should you leave thespoon in? Does it matter whetherthe spoon is plastic or metal?Would your answer be differentif cream were black instead ofwhite? Does your answer dependon the color of your cup? Makenumbers for your arguments ifyou can.
latent heat
3.93Heat islands
Why is the temperature in a cityhigher than that in the surroundingcountryside by 5 or 10 degrees(Figure 3.93)? In addition to therebeing more heat producers in thecity, how ls the temperature dif-ference affected by a city's tall
perature distribution of a city,whether large or small, find a“heat island" concentrated nearthe city's center. Temperaturesare lower as one moves awayfrom the heat island, toward thesuburbs and countryside. One
buildings, expanses of rock and con- congequgnge of this is that spring.¢1’°te, quick "ii" drainage and SHOW time blooming of flowers shouldremoval, dust concentrations, fre- begin sggnef near the city’; cemel-_quency of smog and fog, etc.? 344, pp. 78-81; 483 through 493.Meteorologists who map the tem-
transport andlEI‘l1p8l’3lU Y8
3.92Polaroid color development
If you take a color Polaroid pictureon a cold day, you must developit in a metal plate previously warmed by your body. lf you don't,the colors will be off balance, be-cause when the dyes are cold, theywill not reach the positive in theproper amount of time. Why doesthe temperature affect the transittime of the dyes that way?
497.
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Figure 3.93Heat island of a city.kinetic theory iideal gas law
3.94Total kinetic energy in a heatedroom
A stove will warm the air in aroom. Will it also increase theair’s total thermal energy? (Thethermal energy is kinetic energy
of the air molecules.) Well, theair’s thermal energy certainlydepends on its temperature,and since the air is being warmed,the total thermal energy will beincreased. That sounds correct,but one discussion of this claimsthat the total energy will notchange. How can that be?
343, pp. 40-41; 494 through496‘.
70 'l11e flying circus of physics
P
radiation
3.95Smudge pots in the orchard
Why does a fruit grower putsmudge pots in his orchard over-night when he fears a frost?Since the pots are placed so farapart, they surely can't providemuch heat to warm the fruit.What's the point then? Doesthe grower ever use them duringthe day?
330, p. 398,' 471, p. 130.
conduction
convection
3.96A warm blanket of snow
Why is there less danger of cropdamage on a sudden cold day ifthere is a good snow cover on thecrops?
160, p. 183; 413, p. 205
may ignite clothing, paper,dry wood, and other simi-larly combustible materialsat distances up to 15 kilo-meters, and present capabil-ities make it necessary toscale this range upwardby an order of magnitude.The resulting lire stormwould in many populatedareas “escalate” untildestruction of life andproperty would be virtual-ly total (219).
But if you are more than severalkilometers from the blast site thereis sufficient time (up to 3 seconds)to fall behind an obstacle for pro-tection. First of all, how exactlydoes the blast cause fires severalkilometers from ground zero?Second, why does this fire dangercome at such a relatively longtime after the explosion begins?
219, PP. 307-310.
3.99Snowflake symmetry
Why are snowflakes six-sided (hexa-gons or six-pointed stars), and whyare the six arms exactly alike? Howdoes one arm know what its neigh-bors are doing as the snowflakeforms?
388, PP. 449-453; 404; 499through 506.
surface tensionwetting
crystal genesis
Wien’s law
atmospheric transmission
3.97Fires from A-bombs
Of the multiple dangers tolife which nuclear explosionspresent, . . . the resultingsetting of innumerable firesis perhaps the worst. Asingle one-megaton bomb
3.98Growing crystals
Why does it take small particles,perhaps impurities, to start crys-tals growing in a supersaturatedsolution?
498.
3.100Two attractive Cheerios
If two fresh Cheerios‘ are placednear each other while floating onmilk, they will rapidly pulltogether. What force causes thatattraction? ls it possible to getthe Cheerios to repel each otherfor a suitably chosen liquid onwhich they are floated?‘An O-shaped breakfast cereal fromGeneral Mills, Inc.
capillarity
3.101Cultivating farmland
Why are farmlands in semiaridregions frequently cultivated (thetop soil is plowed and broken upinto a loose texture)? If a foot-print is left undisturbed in cultivat-ed soil, the soil inside the fwtprintwill become hard and dry. Whyis that?
758, pp. 141-142.
Heat fantasies and other cheap thrills of the night 71
surface tensionwetting
3.102Wall curvatures of a liquid surface
Some liquids have surfaces thatturn up near a glass wall; othersturn down. Why do they do this?What force pulls them up ordown? What is the fundamentaldifference (on a microscopic oratomic scale) between thosethat slope up and those that slopedown? Can you calculate whatsurface shape is expected?
drops after being placed on a flatglass surface. What prevents thefrom spreading out? What is thefundamental difference betweensuch a nonwetting liquid and awetting one? Finally, what is thenonwetting drop’: shape when itis sitting on the surface?
Suppose a nonwetting liquid is
Some liquid drops will remain
H1
Figure 3.102Which way does the nonwettingliquid curve?
in a small trough as shown inFigure 3.102. Which shape doyou expect? Or is either pos-sible, depending on the trough'sangle? If the latter, at what angleis the liquid flat?
51, pp. 127- 128; 321; 507through 51 1.
osmotic pressureatmospheric pressurenegative pressure
3.103Rising sap in trees
How does sap rise in trees, especial-ly in very tall ones (some redwoodsare 360 feet high)? Certainly thereis a pressure difference betweencrown and roots, but why? Doesthe tree act like a suction pump?If so, then shouldn’t all treeheights be limited to 33 feet sincethat is supposedly the maximumheight of a suction pump? Someother mechanism must be involved.
512 through 519.
top of the columns. Strangelyenough, when the columns form,the ground itself is unfrozen andusually wet. What makes thesecolumns grow? lf the temperatureis low enough to cause freezing,shouldn’t there be ice on theground? Finally, what will limita column's height?
338, p. 133,‘ 521.
capillarity
osmotic pressurefreezing water
osmotic pressure
Vcapillarity
freezing
3.104Ice columns growing in ground
Have you ever seen columns ofice growing out of the ground,perhaps about 1'/2 inches high?Upon close inspection you mayfind bits of soil and pebbles on
3.105Growing stones in the garden
If you have ever taken care of agarden, you may be aware of theannual crop of stones that must becleared from the garden each spring.Though some regions don't havethis problem, others, New Englandfor example, have an abundantstone crop. Robert Frost's"Mending Wall" is about such acrop of stones.
The stones obviously migrate up-ward from the rock bed below thesoil, but why? The stones, afterall, are denser than soil and shouldgradually move down, not up.What's forcing those stones up?A simple simulation of this stonemigration, suitable for the class-room iab, is given in Bowley andBurghardt (522).
403; 522 through 526.
72 The flying circus of physics
osmotic pressure capillary and f
capillarity osmotic forces
freezing
3.106Winter buckling of roads
“Something there is thatdoesn’t love a wall,That sends the frozen-grouncl-swell under itAnd spills the upper bouldersin the sun"- - -Robert Frost, "MendingWall"*
If you have ever lived in the northyou might have seen pavementdevelop bumps (on blacktops)or cracks (in concrete) or evenbecome tilted during the winter(Figure 3.106). These bumpscan sometimes be as high as afoot. What could cause this?My first guess would be thatwater underneath the pavement
expanded in freezing, but itwould require so much waterto make these large bumpsthat such an explanation ishard to accept. So, what doescause the bumps?
338, pp. 137- 133,‘ 403; 520.
‘From "Mending Wall" from ThePoetry of Robert Frost edited byEdward Connery Lathem. Copyright1930,1939, © 1969 by Holt, Rinehartand Winston, Inc. Copyright © 1958by Robert Frost. Copyright © I967 byLesley Frost Ballantine. Reprinted bypermission of Holt, Rinehart andWinston. lnc.. the Estate of RobertFrost, and Jonathan Cape Limited.
Figure 3.106Buckling of road in the winler.
3.107Shorting out a masonry wall
Masonry walls usually becomedamp, especially near the ground.One way to prevent this is toground the wall electrically byrunning a wire from the wall toa metal stake in the ground(Figure 3.107). No batteries orother such power source are
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527.
surface tension
3.108Soap bubbles
What keeps a soap bubble together?ls it really spherical? What is thepressure inside the bubble? Doesa bubble go up or down in air?
Heat fantasies and other cheap thrills of the night 73
ls there any part of the surfacethat is most likely to burst first?
322; 528 through 532.‘ 533,pp. 139 ffl
surface tensionbuoyancy
3.109Inverted soap bubbles
Inverted soap bubbles—where thewater and air have traded places—can easily be made by carefullypouring soapy water into a dish ofwater from a height of a fewmillimeters. If you pour slowly,drops skim across the water surface.If you pour a bit faster, a drop maypenetrate the water and remainthere with a shell of air trappedaround it, thus forming an inversesoap bubble (Figure 3.109).
Will these soap bubbles showcolors as normal ones do? Will theyhave uniformly thick shells? Willthe bubbles go up or down in thewater dish? Finally, do you thinkthere will be continuous evapora-tion from the inner drop into theair shell, eventually leading to, acollapse?
534.‘ 1608.
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Figure 3.109
capillarity combustion
3.110A candle’s flickering death
Why do many candles, especiallysmall ones, flicker and pop in thelast moments before burning out?What determines the frequency ofthe flickering?
535.
combustion
3.111Dust explosion
One of my most delightful under-graduate tricks was to replace afriend’s overhead light bulb witha short wire and a bag with someflour ln it. The wire almost com-pleted the circuit so that therewas a spark when the lightswitch was thrown. Just beforethe victim appeared, I shook thebag to fill it with floating flourdust. Got the picture? Myfriend tumed on his light, therewas a spark, and the dust exploded,neatly covering his entire roomwith a layer oi‘ flour. Such dustexplosions are very serious prob-lems in some industries wherestatic electricity builds up in aroom full oi‘ dust. In either case,why does a spark cause an explo-sion of the floating dust?
536‘, pp. 383-384,‘ 537 through539.
thermal conduction
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Figure 3.112
3.112Davy mine lamps
The open flame miner's lamp isvery dangerous if the miner en-counters explosive gases. Thedanger can be avoided, however,if a fine mesh screen is placedover the flame holder as shownin Figure 3.112. The screen cer-tainly can't prevent the explosivegas from reaching the flame, but itnevertheless prevents the explosion.How?
110, p. 171; 155, p. 232' 413, p.205' 541, pp. 74-75‘ 542.
74 'l11e flying circus of physics
SUGSS SYFBSS
desiccation freezing
3.113Mud polygons and drying cracks
You have frequently seen cracksin dried mud, but have you everwondered why the cracks formor tried to explain their polygonalappearance? Sometimes the edgesof the polygon will curl up, per-haps even so far that a tubedevelops, separates from the sur-face, and rolls away.
Ever since airplanes and aerialphotography came into prom-inent use, giant polygons have beenseen in the dry desert basin bottomsthat have periodically had water.By giant I mean the widthsof the polygons can be up to 300meters and a fresh fissure may beas much as a meter wide and fivemeters deep.
Why do the cracks and tubesform? If the ground cracks intopolygons, is there any reason tobelieve, as some authors haveargued, that the polygons tend tobe pentagons or hexagons? ln otherwords, is there any preferentialangle at which two cracks willintersect?
543 through 551.
3.114Thermal ground cracks
Mud cracks are not the only typeof patterned ground you can find.For example, polygonal cracks arefound in the permanently frozenground of the arctic and subarcticregions. What causes the crackingin this case? ls there any pre-ferred angle between cracks atintersections?
438,‘ 552 through 556.
. -.. lulli<i1>W‘I\ _,W T391;
¢c_ . JnigmsFigure 3. I I 6“Now, in the second law ofthermodynamics. "
EHUODY
freezing
colloidal suspension
3.115Stone netsAs a final example of patterns inthe ground, stone nets—circ|esand polygons of sorted stones(Figure 3.1 l5)—should be men-tioned. What brings the stonesfrom a random distribution intosuch geometric shapes?
556 through 558.
‘.;_"I
'019'.I_%DQ i-"I'=
_
. . 0.Figure 3. I I 5Naturally occurring circles ofstones.
3.116Life and the Second Law
“As you stay in a givenplace, things and peoplego to pieces around you.”
- - -CelineIn thermodynamics one learns thatentropy, which is a measure ofdisorder in a system, always in-creases in an irreversible process(the so-called Second Law ofThermodynamics). What aboutbirth and life? lsn’t the creationand growth of a human being aviolation of this rule, for in thatprocess, doesn’t order increase?Isn't the rule also violated bythe evolution of all animals overmillions of years?*
559 through 562.
‘A similar problem. whether or notquantum mechanics can explain life, iscovered in Mehra (I569).
Heat fantasies and other cheap thrills of the night 75
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Hydrostatics
(4.1 through 4.i4l
fluid pressure buoyancyPascal's law Archimedes’ law
4.1
Holding back the North Sea
Remember the story of the Dutchboy who saved his town bythrusting his finger into a hole hediscovered in the dike? How didhe do it? How could one littleboy hold against the pressureof the whole North Sea?
418, p. 6'8.
4.2Breathing through air tube
To what depth can you breathethrough a simple air tube whileswimming under water? Whatdetermines the limiting depth?
sea.
4.3 ~Measuring blood pressure
Why do doctors always measureblood pressure on your arm at aheight about even with the heart?Couldn't they iust as well measureit on the leg?
412, p. 191.
Exceptionally good references: Craw-ford's Waves (I70) is the best exampleof real-world physics in a major text-book l have found. See also Tricker(399). Scorer (364), Lodge (923). andScliaefer (830).
4.4Last lock in Panama
A ship is waiting patiently in thelast lock of the Panama Canal asthe water level is lowered. Whenenough drainage has taken place,the gate begins to swing opentoward the ocean, and the lockdirector engages the machinery tofinish opening it. The ship thenbegins to move out to sea with-out the aid of a tugboat and with-out using its own power. Whatforces it seaward?
564.
4.5Panama Canal ocean levels
You may already know about thedifference in ocean levels at thetwo ends of the Panama Canal.During the dry season the dif-ference is small, but during therainy season it can be as muchas 30 centimeters. Why aren'tthe ocean levels the same?
565.
4.6Hourglass's bouyancy
If an hourglass is floating in anarrow tube of water as shown inFigure 4.6, will it float again ifthe tube is inverted? The sand thatwas initially in the lower part ofthe hourglass is now pouring downfrom the upper part. The weightand volume of the hourglass arethe same, however, so the hourglass
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Figure 4. 6When the lube of waler is turnedover, why doesn't the hourglassfloat up? (From “MathematicalGames" by Martin Gardner.Copyright © I966 by ScientificAmerican, Inc. All rights reserved.)
should float back up to the top.Instead, it stays at the bottom ofthe tube until the sand haspoured into the lower section.Why? Does the buoyancy of thehourglass really depend on whetherthe sand is in the lower or uppersection?
566‘.
4.7Boat sinking in pool
There is a famous problem aboutthrowing a stone from a boat intothe swimming pool where the
The madness of stirring tea 77
boat is floating. When the stoneis thrown from the boat, does thewater level rise, fall, or remainunchanged? This problem wasasked of George Gamow, RobertOppenheimer, and Felix Bloch,all excellent physicists, and totheir embarrassment, they allanswered incorrectly.
What happens to the waterlevel if a hole is made in thebottom of the boat and the boatsinks? If the water level changes,when does the change begin? Inparticular, does it begin to changewhen water first enters the boat?
557.4.8
Coiled water hoseIf you try to pour water into acoiled hose, as shown in Figure4.8 no water will come out the
Qtl'
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other end. Indeed, surprisinglylittle water will even enter thehose. Why?
566‘.
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4.9Floating ship in dry dock
When a ship is put into dry dock,the water is removed as the clockis made smaller (Figure 4.9). Whatis the minimum depth of waterunder, say, a two-ton ship thatwill still support the ship?
567; 568.
4.10Submarine stability
How does a submarine ascendand descend? How does it re-main submerged at a fixed depth?Shouldn't changes in the waterdensity at the submarine's depthmake the submarine unstable?Sure, small corrections for thechanges could be made, butsuch corrections are impractical.Besides, if quiet conditions areessential to avoid detection, thenconstant corrections are certainlyforbidden.
Fortunately, there are manydepths in the sea where a sub-marine is stable against the sea’sperturbations. What is peculiarabout those regions, which arecalled thermoclines?
570.4.11
Floating bar orientation
Does along, square bar float on aside or tilted over on an edge(Figure 4.11)? Even if you findthe answer obvious, try floatingseveral long square bars in a varietyof liquids and then classify yourresults according to the relativedensity of the bar and liquid.Is your intuition correct?
569. i _l l Y
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78 'l'he flying circus of physics
4.12Fish ascent, descent
Do fish ascend and descend thesame way as submarines? Do theycompress and expand their swimbladder to change depth? This mbe a common explanation, but itisn't correct because a fish has nomuscular control over its swimbladder. So how do they do it?
Although fish can't survive rapiddepth changes (in trawling, codand hake are dead when pulled tothe surface because of this), theycan live at tremendous depths.For example, fish at 15,000 feetWithstand a pressure of 7000pounds per square inch. Whatprovides the resistance to such psure?
571.
fly
res-
end. Whether the inverted ar-rangement is stable or not dependson how much water is in the tubebut probably not in any way youwould have guessed. If the tubeis nearly full or nearly empty, it isstable when inverted with thecardboard. But if it is about halffull, the water falls out every time.Why?
572.
4.14Floating bodies
Why do drowning victims firstsink and then, after a fewdays, float to the surface?
buoyancystabilitymolecular and thermal diffusion
gravity waves
Rayleigh-Taylor instability
air pressuresurface tension
4.13Inverted water glass
the mouth of a glass of water(The glass does not have to be f IL)Invert the glass, holding the card-board in place. Now remove yourhand from the cardboard—itstays in place and, therefore, thewater stays in the glass. Why?
Try the same thing with a longglass tube (about 60 centimeterslong and 3 or 4 centimeters indiameter) that is sealed at one
Place a piece of cardboard over
u
4.15Stability of an inverted glass ofwater
If the cardboard used in Problem4.13 were to disappear suddenlywith the water glass inverted, whywould the water fall out? Yes, Iknow gravity will pull the waterdown, but how does the fallingstart? Isn't the water surface ini~tially stable? Isn't it precisely thesame forces holding it up againstgravity? Once you decide why thefalling begins, can you figure outhow long it will take to emptythe glass?
574 through 579.
4.16The perpetual salt fountain
Tropical and subtropical oceanshave warm, salty water near thesurface and cooler, less saltywater below. A seemingly perpe-tual fountain may be made bydropping a tube to the bottom,and pumping water to the surface.The pump can then be removed,and the fountain will continueitself (Figure 4.16). What keepsthe fountain going? Is it trulyperpetual?
580, pp. 44-45; 581," 582,’ 1546.
= » -T II =T.T-?~T-».-21?-~.i.-I1-,?.3?I-I-=-.-.1‘ "Frgure 4. 1 6Perpetual salt fountain in theocean.
The madness of stirring tea 19
buoyancy buoyancy
stability nonlinear system
molecular and thermal diffusion Ravleieh i"5lBbi|ilv
4.17Salt fingers
You can see a phenomenonto the salt fountain in yourkitchen by half filling an aqu
adding (carefully, without
water on top. (The dye is on
water, making the boundarytranslucent (Figure 4.17).
pour e sugar water solution
the finger growth, and why athe fingers so stable?
582 through 590.
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related
ariumwith cold, fresh water and then
mixing]a solution of warm, dyed salt
Ivmeant to be a tracer.) Immediate-ly fingers of the upper solutionextend into the underlying fresh
areaYou
can see the fingers without thetemperature difference if you
overa selt water solution. (Again, usea dye for a tracer.) What initiates
IE
Warm,dyedsaltwater
Cold,freshwater
Salt fingers (exoggera ted scale).
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4.18Salt oscillator
If you take an ordinary tin can,punch a pinhole in the bottom, fillit with saturated salt water, andpartially immerse it in a container
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flow down through the hole, thenfresh water will flow up, and so on(Figure 4.18). This oscillationmay continue for as long as four
of fresh water, will the two solutions days. with an oscillation P911011eventually mix? Well, yes, they of about four seconds. Why iswill, but in a surprising way. (Color 111919 S\l¢h 811 08¢ll|fl¢0YY exchangeone of the solutions with a dye so of fluid, and what determines theyou can see which is which.) There P8l'i0d?will be an alternating exchange ofsolutions, that ls, salt water will
591.
Bernoulli Effect(4.19 through 4.40)
4.19Narrowing of falling water stream
Why does a smoothly flowingstream of water from your faucetnarrow as it falls? ls there someforce squeezing it together? Canyou calculate the change in thestream's diameter as a function ofthe distance from the faucet?
4.20Beachball in an air stream
To catch the attention of cus-tomers, vacuum cleaner salesmenwill sometimes reverse the air flowin a cleaner and then balance abeach ball in the exhaust jet (Figure4.20). The ball is quite stableand can be held in place withthe air jet at a considerable angle.Even a good slap will not beenough to release it from thejet. Why is it so stable? Will the
80 The flying circus of phy
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ball spin in any particular direc-tion?
27 7, p. 155‘ 399, PP. 102- 103,‘592, p. 6'0; 593.
4.21Toy with suspended ball
A toy, "5-Blow-Go"*, uses thissuspension trick also. Youbalance a light ball by blowingthrough a small side tube, asshown in Figure 4.21. With along, hard blow, the ball is lifteduntil it is pulled into the top of thetube and shot back to its originalposition. The point of the gameis to circulate the ball this wayas many times as possible withinone breath. (My record is five
ii ,;._> E
gm... 1Figure 4.21By blowing through the sidetube, you make the ball circulatethrough the main tube.
c
complete circuits.) What makesthe suspended ball stable, and whatmakes the ball enter the top tube?Norsfar Corp., Bronx, New York
momentum transferwetting
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Figure 4.22Boll suspended in water jet.
4.22Ball balanced on a water jet
In another similar trick, a ball isbalanced on a vertical water jet(Figure 4.22). Occasionally theball may sit still for several seconds,but usually it wavers and bobs.Why doesn't the wavering cause itto fly out of the jet? What holdsit in? Does this really involve thesame physics as the beach ballproblem?
To be honest, the ball does some-times escape the jet, but in thecourse of its fall, it reenters the jetand is returned to its former posi-tion. It will even do this in a
vacuum. What entices the ball backinto the stream like this?*
595.
‘For yet another suspension but withphotons instead of air or water, seeProb. 5.104.
4.23Egg pulled up by water
Let a faucet pour onto an eggfloating in a glass of water (Figure4.23). For flow rates above somecritical value, the egg will rise asif it were attracted to the fallingwater. Why, and what determinesthe critical flow rate?
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Egg pulled upward by water stream.
The madness of stirring tea 81
momentum transferwetting
4.24Spoon in a faucet stream
If you hold alight spoon roundside upward in a stream of wateras shown in Figure 4.24, the spoonseems to be glued to the stream.You can move your fingers severalinches away, putting the spoonat a considerable angle, and thespoon will still refuse to leavethe stream. The falling watershould, by all rights, push thespoon away, not attract it. Whatcauses this?
592, p. 60,’ 595 596.
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Figure 4.24The spoon is kept in place by thewater stream.
4.25Water tube spray guns
If you put one end of a tube intowater and blow across the open en(Figure 4.25), you can force waterup the tube. With a strong blow
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Figure 4.25Water is lifted up the tube by theair blown across the tube.
across a short tube, you can soakyour friends. The aerosol can is amore practical application: pres-surized air blows across a narrowcontainer of the material to besprayed. How do such sprayguns and cans work?
597.
4.26Passing trains
When high-speed trains pass eachother, they must slow down ortheir windows will be broken.Why? Will the windows be pushedinto the train or sucked out? Willthis happen if the trains are travel-ing in the same direction? If youstand near a high-speed train, will
you be pulled toward or pushedaway from the tracks . . . or both?
599 through 602.
4I27
Ventilator tops and prairie dogholes
Why is the draft through a ventila-tor pipe improved if the top of thepipe is surrounded with a cone(Figure 4.27a)? Similarly, why is
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Figure 4.270Ventilator pipe with cone top.
the ventilation inside a prairie dogtunnel improved if the entrances aresurrounded by high, conical mounds(Figure 4.27b)?
139, pp. 17.9-180,‘ 598.
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Figure 4.27bPrairie dog hole with highmound.
82 The flying circus of physics
pressure
4.28lnsects rupturing on windshields
Are insects squashed directly on muses the rupture? You may be stream carry the bugs safely overthe windshield of fast moving cars, tempted to blame the insect's the car? (Figure 4.28 shows oneor do they rupture in the air and fate on turbulence, but is there way to avoid the bugs.)then splatter on the windshield? really that much turbulence? Whylf the latter is the case, then what
no vbu want‘ musme B06 cease-N? * ,__<» /__ kw
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(By permission of John Hart. Field Enterprises.)
364, pp. 12-13.
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4.29Flapping flags
Why does wind, even a uniformwind, make flags flap? Whatdetermines the frequency of theflapping?
124, p. 115‘ 453, p. 51.
Bernoulli effectmomentum transfer
4.30Wings and fans on racing cars
Racing cars have gone through agreat many changes over the years,some obvious, some subtle. Oneof the best developments was the
the rear of the car. When a carwith such a wing entered a curve,the driver would tilt the wing for-ward. Upon leaving the curve, thewing was leveled again. This wingand its adjustments proved veryuseful in keeping a car on the roadin turns, hence allowing muchhigher speeds there. Were it notfor the danger of broken wingsresulting in uncontrollable carson the tracks, these movable wingswould still be in use. But safetyforced the racers to fix their wingsin place. In either case, movableor fixed wing, how would a winghelp in keeping the car on theroad?
One of the strangest versions ofa racing car has been the Chaparral2J, which was built by Jim Hallwho also pioneered the movable
wing. The Chaparral 2J had twolarge fans in its rear designed topull air beneath the car, throughthe fans, and out the rear. Skirtswere built along the bottom sidesof the car, hugging the road, so asto tunnel the air beneath the car.Again, Hall greatly increased thespeed of his cars by increasingthe traction. But how? Why wouldair tunneled beneath the car andout the rear increase traction?Can you estimate the resulting in-crease in traction and speed?
1581.
The madness of stirring tea 83
Bernoulli effectmomentum transfer
4.31Lifting an airplane“How does an airplane gain lift?”ls a standard physics question,and the standard answer involvesBemoulli’s principle, but is thatthe only, or even the major,factor? If the winm are shaped(as ls in Figure 4.31) to producea Bernoulli effect, then how doairplanes fly upside down?
The crucial point of the standardargument ls that the air movesfaster over the wing than underthe wing, and this means, becauseof Bernoulli's principle, therels greater air pressure beneath thewing. Hence there lslift. Whydoes the air move faster overthe top? Well, the two streamsof alr moving below and above thewing must cross the wing in thesame amount of time. The alrmoving above has a greater dis-tance to travel and thus movesfaster. Here the standard argumentstops. But why must the upper airtraverse the wing in the same timeas the lower air? This is rarelyexplained. As a matter of fact,the top and bottom streams haveunequal traversal times. So,why does the wing have lift?
593,’ 603 through 605.
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4.32Pulling out of nose dive
Suppose a plane stalls and goes ina nose dive. Why must the pilotwait until he reaches a high speedhigher than his normal cruisingspeed, before he attempts to pullout of the dive?
6'03.
4.33Salim‘' g into the wind
It's not difficult to see how a sailing
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611 through 6‘13.
4.34Frisbee
What keeps a Frisbee* aloft? Musit be spinning? It apparentlydoesn’t have to be a disc, becauseFrisbee rings work almost as well.
"® Wham-O Manufacturing Company,San Gabriel, California.
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84 The flying circus of physics
4.35Manpowered flight
ls it possible for a man to fly underhis own power (Figure 4.35)? Thequestion is an old one but far fromdead. It now seems that presentattempts to design manpoweredaircraft will eventually lead to aworking model.
Some of the problems in design-ing the aircraft are how muchpower can a man produce, andhow much is needed for flight?l-low large should the wings be?Should they flap? ls the liftimproved if you stay close tothe ground?
606 through 610,‘ 1518,‘ 1519.
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Figure 4.36Top spin on golf ball causes it to roll forward.
4.36Golf ball top spin
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4.37Flettner's strange ship
In 1925 a most unusual ship crossed cylinder to an airplane’s wing.the Atlantic propelled by two large, How would such a cylinder pro-vertical rotating cylinders (Figure vide lift for the airplane?4.37). How did those rotating cyl- "0 p 22, 155 p 11 7_ 399inders drive the ship forward? p. 105 453' pp_ 7142', 615;
In a more modern application, 6.23NASA has used the same principle 'by adding a horizontal rotating
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Figure 4. 35Man in glorious flight.
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The madness of stirring tea 85
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Figure 4.38Strong winds through building.
4.38Winds through a buildingIn one type of modern buildingdesign, the floors are hung likebridges between two solid wallsand the ground level area is leftopen (Figure 4.38). This is an at-tractive design, but inconvenient inwindy regions. For example, whenthe spring winds blew through onesuch building at MIT, wind speedsup to 100 miles per hour weremeasured, certainly much higherthan elsewhere on the campus.(Students and junior faculty alikewere bowled over by the wind;only full professors could with-stand the gale.) What causes thisenhancement of wind speed?
5 14.
4.39Curve, drop, and knuckle balls
Can baseball pitchers really throwcurve balls, drop balls, and knuckleballs? If they can, then explainhow each is thrown. Does a curveball break continuously or sud-denly? Does a drop ball suddenlydrop? And does a knuckle ballactually dance, as batters claim?How far will a major leaguepitcher’s curve ball deviate from astraight line by the time itcroses home plate?
36, pp. 53, 138- 13.9; 211, p.156,‘ 5.93; 615 through 622.
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4.40Curves with smooth bells
A smooth ball should not curvesince, unlike a baseball, it has norough surface with which to "grab"the air. You can nonetheless throwa curve with a smooth ball, but itwill curve in precisely the oppositedirection as will a baseball. Why?
593,‘ 519 through 522.
Waves(4.41 through 4.59)
wave speed (group and phase)superposition refractioninterference dispersionreflectionBernoulli effectflow around obstacledriven oscillator
4.4 1Building waves
How are periodic water wavesbuilt up by random gusts of windthat play along a water surface?Is the wind drag across the surfacemore important than vertical dis-turbances? ls there a minimumwind speed required to maintainthe water waves? Do the wavesprovide a feedback to the wlndflow to build up the waves evenfurther?
399, pp. 141-147; 580, PP. 133-135; 524,‘ 525
wave interference
4.42Monster ocean waves
There are many stories about shipsat sea suddenly encountering in-credibly large waves. For example,a wave 100 feet high was seen by acargo vessel captain in l 956 offCape Hatteras, and there werereports of 80 foot waves in theNorth Pacific in 1921. In 1933 a
86 The flying circus of physics
wave estimated at 112 feet high erevitv and capillary waveswas seen by the U.S.S. Ramapoin the North Pacific. Imaginestanding on the bridge beneath awave 112 feet high!
Why do these waves suddenly ap-pear and then disappear? If theyare somehow caused by storms,then shouldn't there be more thanone large wave? Could they becaused by a sudden underwaterearthquake? (Can such earth-quake waves be detected by a shipat sea?)
3.9.9, p. 138; 626, pp. 48-4.9;627; 628; 629, PP. 53-60.
4.45Whirligig beetle waves
When a whirligig beetle skimsquickly along the surface of thewater, why does it make pro-nounced waves in front of itself,but in back barely visible wavesor none at all (Figure 4.45 a)?lf it skims slowly, there are nowaves, front or back. Why? Aboat doesn't do this; it alwaysmakes waves to the rear. What isso different about a skimmingwater beetle?
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l//JpWhy exactly do whitecaps form on .1,/;_/;/{/,.the ocean and other bodies of water, A .and why are they white? In a ,,/* I .§moderate wind, why do they often H ,3; , ,iappear in succession, each forming 3' ldownwave of the previous one witha time interval of a few secondsbetween appearances? Fi9'_"'€ 4-45"
Whirligig beetle waves.390/ 530} 531.
4.43Whitecaps
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A similar asymmetry is presentin the wave pattern around anarrow obstacle in a movingstream: the waves upstream havea much smaller wavelength thanthose downstream (Figure 4.45 b).What causes the asymmetry, andwhat determines the wavelengthsin the two cases?
633.‘ 634.
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Figure 4. 45 bWaves around stick in movingstream. [Both figures after V. A.Tucker, Physics Teacher, 9, l0(1971).)
wakes other things larger than insects?Be,,,°,,||, em,“ lf the limitation is friction from
the water, then why does a4 44 longer boat generally have a
Bo t; d and h dm lam“ higher maximum speed? Wouldn't8 pee y p g a longer boat feel more friction
and hence have a lower maximumWhat determines the practical speed?speed limit of boats, ducks, and
Why can a hydroplane go muchfaster than a nonnal boat of similarlength? It is, as you know, partiallylifted out of the water. How is thelifting accomplished, and how doesit permit such high speeds?
632; 633.
The madness of stirring tea 87
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Figure 4.46Ship waves as seen fi-om above.Phys, 25, 466 (1957)).
4.46Ship waves
If you ever have a chance to fly
examine their wave patterns.Notice the disturbed areas arealways V-shaped with the sameangle (380 56'). As one writerput it, the V shape is present
duck or a battleship" (760).Why is that?
Inside the disturbed area, thepattem gets more complicated(Figure 4.46). Can you explain
[After H. D. Keith, Am. J.
origin of the two types of waveover ships moving in deep water, crests that are present? Are they
also the same for a duck and abattleship?
How does the pattern change inshallow water? First, can you ex-plain what "shallow" means? Shal-
whether the moving obiect is a lqw cgmpared m what?
51, pp. 200-203,‘ 399, Chapter17; 635, Chapter 8," 636through 640.
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4.47Edge waves
While investigating water waves,Faraday discovered a very curiousform of wave produced by a simple,horizontally oscillating plateslightly immersed in a water basin(Figure 4.47a). Ignoring wave re-flections from the basin’s sides,I would have guessed that only com-mon, plane waves would be made.However, when the oscillatingplate was immersed about 1/6 inch,he saw the following:
Elevations, waves or crispe-tions immediately formedbut of a peculiar character.Those passing from the sur-face of the plate over thewater to the sldes of thebasin were hardly [visible],but apparently permanentelevations formed, begin-ning at the plate and pro-jecting directly out fromit to the extent of 1/3 or
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Figure 4.47aPlate oscillating in water.
88 The flying circus of physics
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Bernoulli effect wave speed
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Figure 4. 4 7bEdge waves on the oscillatingplate, as seen from above.
1/2 an inch or more, likethe teeth of a very shortcoarse comb [Figure4.47 b] (643).
Faraday also noticed thesestrange waves had half the fre-quency of the vibrating plate.Now how can a vibrating platepossibly set up standing waveswhose crests are perpendicularto the plate?*
641 through 646.
‘To see the edge-wave theory used todiscuss rip currents on ocean beaches,see Refs. 647 through 651 and Ref.‘I618.
ref racti on
4.48Swing of waves to shore
4.49Surf skimmerYou can surf, in a sense, onwater only one or two inches deepby riding a wooden disc skimmingalong the shallow surf (Figure4.49). If you leap on it when ithas sufficient speed, you may becarried 20 feet or more. Whatholds you up during such a ride,and why does this support disap-pear when the disc slows down?Why do longer boards travelfarther? Shouldn't a longerboard provide more friction andhence stop sooner?
Q26,“pp. 152- 15§,' Q53.
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When ocean waves reach the shore, '\5“\~\°r5¥‘ O - ° MA“_ '\J\J\,~ F6why are they approximately parallel r'\/o~ r 3
to the shoreline? Surely the wav_es ° "’\-;’“., ° = ° ° ‘ "originally come from a variety ofdirections.
360, p. 28; 399, pp. 95-96; 628;635, PP. 133- 136.
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Figure 4.49
4.50Surfing
What rushes you to shore whenyou're surfing? Are you pushedby the wave, or are you continouslyfalling downhill? Why are thebest waves to ride those on theverge of breaking, and why ismost surfing done in waters overgently sloping beaches? Why isthe surfing position on the wavefront relatively stable? ls asurfer more stable on a long boardthan on a short board?
626,‘ 652, pp. 80-81.
buoyancywakes
4.51Bow-riding porpoises
Porpoises are often seen ridingmotionlessly a few feet beneaththe water surface near a ship bow.They make no swimming motionsat all, so they somehow gain theirpropulsion from the ship itself.The technique must be welldeveloped, for a porpoise can ridefor more than an hour with littleor no effort and can remain sta-tionary, flip over on a side, oreven slowly revolve around its bodyaxis. There may even be two orthree layers of the porpoises, all
The madness of stirring tea 89
carries the porpoises along?A similar case is related by
Jacques Cousteau in one of hisunderwater books (660). Sharksare often accompanied by small"pilot fish" that, according tolegend, guide the shark. Cousteausaw one such pilot fish, a verysmall one, directly in front ofthe shark's head, somehow beingpropelled along by the shark it-self. That was a precarious posi-tion indeed! l-low was the pilotfish pushed, and why was hisposition so stable?
654 through 660.
gravitynoninertial forcesstatic and harmonictheories of tldes
4.52Ocean tidesWhat causes the ocean tides? Youmay be satisfied in answering thatthe tides are driven by the gravita-tional attraction of the moon andsun, but let me ask a few morequestions.
Does the water bulge on themoon side of the earth becausethe moon pulls the water verticallyaway from the earth? If it does,that seems strange becauseisn't the water's attraction for theearth much, much greater than itsattraction for the moon?
If the earth's seas are pulledto the moon and the resultingbulge in the ocean is the high tide,
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Figure 4.52Two tides on the earth(exaggerated,of course).
then why are there two high tidesa day? The earth turns once a day,and hence each point on the earth'ssurface should face the moon onlyonce a day. Therefore, shouldn'tthere be iust one high tide a day?However, since there are two hightides a day, the water on theearth should have two bulges, oneof them being away from themoon (Figure 4.52). How do youexplain the second bulge?
Some seas, (the South ChinaSea, the Persian Gulf, the Gulf ofMexico, and the Gulf of Thailand,for example) have only one hightide a day. Why don't they havetwo? Still other places, such asthe Indian Ocean, have alternatingdiurnal and semidiurnal tides.Again, why?
Finally, why isn't there a hightide when the moon is directlyoverhead? For some reason, thereis always a lag.
1 11; 399, pp. 3-14; 661, Chapter5, pp. 149-181; 662, pp. 26-32,40 ff)‘ 663, Chapter 4, PP. 1 1-55‘664, pp. 177, 179, 188 ff; 665,pp. 195 ff; 667 through 669;1589.
4.53Tides: sun versus moon
Which provides the strongerdriving force on the tides, themoon or the am? If you makea rough calculation to see, wouldyou compare the direct gravita-tional pulls of the moon and sunon a piece of the earth's water?
aIf you do, you'll find th tthesun is the dominant body.
Why are there spring tiwhich are the larger thantides near the times of n
des,average
ew andfull moons, and neap tides, whichare the lower than average tidesnear the first and third quartersof the moon?
399. PP. 15-16.‘ 661 , P159; 662, pp. 32-33; 6623-24, 35 ff,‘ 664, pp. 189-192.’ 668.
p. 156-3: '
angular momentumconservation
4.54Tidal friction effects
As a tidal current flows acrossthe ocean bottom, energyto frictional heating. Onsequence of this energy Ithat the earth’: rotationand the day gets longer.
is loste con-oss isslows,
Does the energy loss have anymfurther effects? A syste
have a change in its totalmomentum unless there’side torque. There is no
cannotangular
s an out-such out-
side torque on the earth-moon
90 The flying circus of physics
system, but we've got an earth witha decreasing spin. How then is thetotal angular momentum to be con-served?
Will this go on forever? Willthe earth's day continue to getlonger? Will there be any changein the apparent motion of themoon? One prediction is thatsome day the moon may travelbackwards across the sky.
1 1 1; 661, Chapters 76, 17,"663, Chapter 1 1; 672; 673.
shock fronts
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wave speed
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4.55Seiches
Water in a lake often sloshes backand forth just as it does in a smallrectangular trough. The residentsaround Lake Geneva long agonoticed this sloshing (called aseiche), which can reach threefeet in amplitude, but they didn’tunderstand what determined itsperiodicity or even what causedit. What does determine thesloshing frequency in a rectangularbasin? What periodicity do youpredict for Lake Geneva (averagedepth about 150 meters andlength about 60 kilometers)?Finally, what makes the lake slosh?
170, pp. 45-46; 580, pp. 138-740,’ 635, pp. 423-425,‘ 661,Chapter 2,‘ 662, pp. 62-65,‘ 663,Pn- I-8.-664.». 272-273. l 5:??? -g __;;=;
4.56Tidal bores
In most rivers emptying intothe sea, the tidal rise is calm,perhaps even imperceptible.But in others the rise becomes sorapid that an almost vertical wallof water, a bore, races up theriver with great force (Figure4.56). The English rivers Severnand Trent and the Canadian riverPetitcodiac experience these waterwalls. The bore of the Amazonis an awesome sight, being a milewide at places and up to 16 feethigh, sweeping upstream at 12knots. The most striking of themall, however, is the bore of theChinese Tsien-Tang-Kiang,
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which has risen as high as 25feet. The Chinese skillfully usethe bore to float their junksupstream, ignoring the dangerand the helrer-skelter ride. Whydo these bores form, and whydon't all sea coast rivers havethem? Does their speed dependon their height or the depth ofthe river?
399, pp. 33-66; 635 pp. 320,326-333, 351 ff; 661,Chapter 3; 662, pp. 97-.98; 663,pp. 8, 120-125' 664, pp. 320-321; 674 through 676.
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Figure 4.56Tidal bore racing up river.
The madness of stin-ing tea 91
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4.57Bay of Fundy tide
Why does the Bay of Fundy inNova Scotia (Figure 4.57) have theworld's largest tidal range (thechange in water height due to thetides)? In some places the rangeis so large that men fish by erectinglarge nets during low tide andthen during the next low tide,simply collecting the fish caughtin the net during the high tide.At the mouth of the Bay, the
Figure 4.57Tidal range in the Bay of Fundy.
range is not too large, about 10feet during spring tides. Furtherup the Bay at St. John the rangeincreases to 25 feet, and at theend of Chignecto Bay it is 46 feet.The largest range, 51 feet, is foundat the end of the Minas Basin.(Winds can add as much as another6 feet to these figures.)
Cana bay have an especiallyfavorable length to enhance the
tidal range? What would such alength be for a bay whose depthis like that of Fundy (75 meters)?l-low does that compare withFundy's actual length?
399, pp. 27-29,‘ 663, pp. 113-115‘ 654. PP. 235-236,‘ 670;671.
92 The flying circus of physics
shock frontW8i8f WBVES
wave speed
4.58Sink hydraulic jump
When a stream of water falls intomy sink, the water spreads out ina relatively thin layer until itreaches a particular distance fromthe stream where the water sud-denly increases in depth. I-lence,a circular wall of water surroundsthe stream (Figure 4.58). Thesame type of wall is made if thestream falls onto a flat plate,though the depth change is not aspronounced. What causes thesejumps in water depth? Whatdetermines the radius at which ajump occurs? l-low high is thewall?
635.9/J. 324 ff; 677 through681.
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4.59Standing waves in falling stream
If you hold your finger or the flatof a knife in a thin water stream,a standing wave appears in thestream* (Figure 4.59). Why?What determines the spatial peri-odicity of this wave? Why doesthat periodicity depend on thedistance between the flat sur-face and the faucet?
‘Elizabeth Wood. personal communica-tion.
4.60Beach cusps
Why are cusplike formations,sometimes outlined on a side withsmall pebbles, very often found onsandy beaches (Figure 4.60)?Shouldn't the ocean waves strikingsmooth beaches be plane waves?Although some cusps are isolatedand can be dismissed as flukes,there are many long beaches
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whose entire length is embroideredwith periodically spaced cusps.What causes them?
629, pp. 386-389; 648, p. 5490;650; 682 through 691.
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Figure 4. 60Beach cusps.forces in rotating frame
friction
4.61Ekman spiral
Suppose there is a steady windblowing over the water somewherein the middle of the ocean. Inwhat direction is the net total masstransport of water by the resultantcurrent? In the direction of thewind? Slightly to the left? Well, Iunderstand that it is 90° to the righin the northern hemisphere and 90°to the left in the southern. Why90°? The current off the Californiacoast provides an example ofthis in shallower water. The windsthere usually blow southward andparallel to the coast, but the toplayer of the ocean moves towardthe west.
580, pp. 76—79,‘ 692.
The madness of stirring tea 93
t
vorticity secondary flow fluid flow around obstaclenoninertial forces centrifugal force pressure gradientfriction friction forces in rotating frame
4.62Stronger ocean currents in the west
Doesn't it strike you as odd that inboth northern and southernhemispheres there are strongerocean currents along the westernsides of the oceans?
North Atlantic: Gulf StreamSouth Atlantic: Brazil CurrentNorth Pacific: KuroshioIndian Ocean: Agulhas Current
(The one exception is in the SouthPacific, for there is no such largecurrent off Australia.) Why is thewest favored for strong currents?
666, p. 1025' 692 through 696.
secondary flowcentrifugal force
friction
4.63Tea leaves
Why do leaves in a cup of tea col-lect in the center of the cup whenyou stir it? Since the tea is rotating,you may want to class this as iustanother centrifuge example, butwait—in a centrifuge don't thedenser objects move outward?Hence, the centrifuge argumentwill only make the behavior of thetea leaves even more mysterious.
44, p. 189; 73; 700. PP. 84-85'716.
4.64River meander
Natural streams and rivers, especial-ly the older ones, are rarely straightfor any great length; they almostalways meander back and forth(Figure 4.64). In some cases theweaving is so extreme as to cutoff and abandon a loop, formingwhat is called an oxbow lake. Ofcourse, the local terrain may forcesome sinuosity, but even still,shouldn't there be many morestraight sections? What causes themeandering?
44, pp. 189- 190,‘ 73,‘ 360, pp.43-48; 364, pp. 78-79,‘ 453, p.146,‘ 697, pp. 82-85, Chapter9; 698, pp. 56-58; 699, pp.144- 145' 700, pp. 84-87,’ 701through 715.’rI_.-:- =-="* r-'-'-e*": " '
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Figure 4.65If the ball is released in the centerof the rotating water, if lakeslonger to rise.
4.65Rising ball in rota ting water
Adjust a small ball's density (bypartially filling it with water) sothat it takes about 2 seconds toascend through four inches of wa ter.If the water is on a rotating turn-table and the ball is on the centeraxis (Figure 4.65), the ascent timeshould be the same, shouldn't it?But as a matter of fact, if therotational speed is 33 1/3 rpm,a four-inch ascent will now takeabout 30 seconds. Why is theresuch a big difference in rise time?Indeed, why is there any differenceat all?
717 through 719.‘ 1482.
Figure 4. 64
94 The flying circus of physics
pressure gradients vorticescentrifugal force coriolis force
4.66Taylor's ink walls
If a drop of dyed water is placed ina glass of clear water, the dyed areawill be about half a centimeterlarge. But if the drop is placed offcenter in a glass of water that issitting on the center of a rotatingturntable, the dyed area will becompressed into a thin verticalsheet that spirals around the centerof the glass (Figure 4.66). Whatkeeps the dye in such a sheet andprevents it from mixing with theclear water?
717.‘ 720.
v
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angular momentum
4.67Bathtub vortex
Do northern hemisphere bathtubsreally drain in a counterclockwisesense, as is commonly believed?If bathtubs do drain in oppositesenses in the two hemispheres,does that mean the water doesn’trotate at all on the equator?
72; 721 through 736.
soda water on a turntable's centerand spin it at 78 rpm. Bubblesemerge from the soda water as youwould expect, but when you adda small amount of sugar or someother granular substance, a tornadolike structure develops. Whatcauses this vortex, and what pro-vides its energy?
751 dirough 754.
vorticity
4.68Tornadoes and waterspouts
Do tomadoes and waterspoutstum in any particular direction,as do hurricanes? What makesthem visible? Does water go upor down in waterspouts? Whydo some tomado funnels hopalong‘? Do adjacent funnels attractor repel each other? Finally, whydo some funnels appear to bedouble layered, as if they con-sisted of two concentric funnels?*
226; 737 through 746,‘ 1538.‘For more information on tornadoes,their cause and behavior, see Refs. 224,225, and 747 through 750.
4.69mu’ /7 WW 7" I N“ 7 S0113 Wflfif tornadoFigure 4.66Taylor's ink wall in a rotatingglass of ware,-, Place a recently opened bottle of
buoyancy
4.70Coffee cup vortex
Carefully stir a cup of hot coffeeuntil you have a uniform swirland then carefully pour a streamof cold milk into the center. Avortex will form in the center anda dimple may be noticeable. Butif hot milk is used, the vortex willnot develop. Why is there a vortexin the first case and not in thesecond.
755.
convection
vorticity
4.71Dust devils
What drives dust devils, thosewhirlwind vortices that are oftenseen in deserts or other placeswith loose sand debris? Does theirinternal air move up or down, andis there a preferred sense of rota-tion as in hurricanes? How can
The madness of stirring tea 95
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Figure 4. 7IDust devil
seemingly small, local changes inthe air trigger them? For instance,a jackrabbit tearing acros thedesert floor can leave a trail ofdust devils. Why do nearly all dustdevils die within only three orfour minutes? ls it because of tur-bulence, or is the energy sourceremoved? Finally, why are theyshaped like an uneven hourglass(Figure 4.71) and not like a tomadofunnel?
756 through 764,- 1539; 1540.4.72
Fire vortices
Why do tomadolike vortices fre-quently develop near volcanos,forest fires, and large bonfires?
765 through 772.
4.73Steam devil
There is yet another natural vortex,but it is rarely seen. In the dense
steam fog over some winter lakes,such as Lake Michigan, steam devilsappear. You can simulate this byallowing cold air to blow over abathtub full of warm water in amoist bath room. What drives thesteam devils?
773,- 774.
4.74Vortex rings from falling drops
If a drop of dyed water falls into aglass of clear water, you can see thevortex ring created by the splashand watch the ring as it expandsand descends (Figure 4.74). Canyou explain in simple terms whythe ring is formed and why itexpands? Which way does thefluid rotate in the ring? Finally,why are more (but less pro~nounced) rings also created bythe same splash?
155, p. 103; 77$ 776, pp.522-525,’ 777.
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Figure 4. 74Falling and expanding vortex
4.75Ghost wakes
If you quickly move a verticalpiece of cardboard horizontallyacross a pool of water as shownin Figure 4.75a, two wakes willappear on the pool ‘s surface.Why? If the cardboard is movedto the side as shown in Figure4. 75b, only one wake appears.Again, why?
1481.
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Figure 4. 75aTop view of moving cardboardand vortices.
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Figure 4. 75bTop view of moving cardboardand vortex. [Both figures afterC. W. McCutchen, Weather, 27,
ring ofdyed water. 33 (l972).]
96 The flying circus of physics
vorticity d rag
adiabatic process eddies
friction
4.76Hot and cold air vortex tube
The Ranque-Hilsch vortex canmysteriously separate hot fromcold air without any moving parts.If compressed air (at room tem-perature, sayl is forced into thevortex tube through the sidenozzle (see Figure 4.76), air ashot as 200°C will emerge fromone arm of the vortex tube whileair as cold as —50°C escapes fromthe opposite arm. There are noheating-cooling mechanical de-
cular cavity with a center escapehole on one side and a valve atthe end of the arm on the otherside. How is the temperaturedifference created by this simplearrangement? Must we have alittle man stationed in the tube,feverishly sorting out cold andhot air from the room-temperatureair?
778 through 787.vices inside the tube, iust a cir-
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Figure 4. 76Compressed air blown into vortex tube separates into hot andcold air.
4.78Sinking coin
If a coin is dropped into a largecontainer of water, will it sink withits edge or flat side downward?Will the same thing happen in aviscous fluid such as oil or a sugarsolution? l-low will a cylindersink?
Common sense probably tells youa sinking obiect will always assumethe most streamlined orientation.However, for some parameters acoin and cylinder will sink inwater with whatever orientationyou initially give them. Making thedisc larger or the fluid moreviscous causes the disc to fall broad-face. What forces the disc to pre-sent its broadest side? Why aren'tsmaller coins and cylinders alsoforced into the broadside orienta-tion?
788 through 790.
wakes
eddies
aerodynamics
4.77Birds flying in V formation
Do you think there is any physicalreason for the V formation assumedby migrating birds? Or do youthink it is simply an interesting be-havioral response and serves no
real purpose? lf, perhaps, thereis some aerodynamical basis for theformation, is it important that theformation be symmetric? ls itnecessary that the birds synchron-ize the flapping of their wings?What advantage would the V for-mation have over any other forma-tion lline abreast or zigzag, forexample)? Why don't birds flyin schools like those of fish?
794.
4.79Tailgating race cars
In stock car races what advantageis there for one car to tailgateanother car (called drafting)? lsthe lead car affected at all? Whenthe trailing car suddenly pulls outto pass, why does it receive awhiplash acceleration around thelead car?
789.
The madness of stirring tea 97
wakes buoyancyeddies drag
4.80Several sinking objects interacting
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lFigure 4.80aT100 views of two cylinders fallingin a viscous fluid.
xfifi; fwd‘).:;€ia fi;;h?;d
ll:l. - .-
Several objects may interact instrange ways while sinking in vis-cous fluids such as oil or a sugarysolution. Here are three examples.
Into a viscous fluld, drop twocylinders, one closely followingthe other. For certain ranges ofviscosity and cylinder size andspeed, the trailing cylinder maycatch the leader and rotate aboutit until they are horizontally paral-lel, and then they will both rotatetogether and separate horizontallyas they sink (Figure 4.80a).
In a simpler interaction, twodiscs dropped after a leader discmay catch the leader, and thenthe three will take on a stablebutterfly configuration (Figure4.80b).
Also, a compact cluster of threeto six spheres will separate them-selves into a horizontal, regularpolygon, and this polygon willslowly expand as it falls.
Without getting into too muchdetail, can you roughly explainwhy each of these interactionstake place?
789 through 793.
Figure 4.80bButterfly configuration of threediscs falling in a fluid. [A fterK. O. L. F. Jayaweera and B. J.Mason, J. Fluid Mech., 22, 709(1965).)
wakes
vortices
4.81Strange air bubbles in water
Closely examine bubbles risingthrough a glass of water. The verytiny ones (with radii less than about0.7 millimeter) are spherical andrise to the surface in a straight linejust as you would guess. Slightlylarger bubbles (up to 3 millimetersin radius) are spherical but eitherzigzag or spiral upward. If theradius is even larger (more than3 millimeters), the path is againstraight, but for radii greater than1 centimeter, the bubbles look likespherical caps and resemble umbrel-las (Figure 4.81).
Why does a rising bubble’s shapedepend on its size? What forcesthe intermediate size bubble tozigzag and spiral, and what param-eters fix the frequency of thatmotion?
776. PP. 367-370, 474-477;796 through 801.
.___-____IiJZ>_--~._1f;;;21__-_~L__________-~____--____________.-____________-____-_-----_----______-____--___--.______-________________->____--_-____-_____T________-________~________-____-__---____--_-__--____________a___-____-_1::-__1r_1:-____-_-=,________;____-___JL___-__________________--~___-.____________,________--___. ______________-__-__-_____--_ ---_~_______-__L-'-:-:--:-"-"-"==-:-:~‘ '-I-:-:-:-:-:—:-:-:-:-:-:-:~__._----—-s-_—.-_--- ;._____-_-----4. _ _ _ _ ____. __. _ - ._ __ .______________________~-:-:---:-_-_~:- -:~‘3t-:-_ _-:-_—.—_-.-_—_-_-_-_-.-.—._ _ _ _ - - ... Q —_‘>_:- —;_- ~ —q_-:_-_-__:- - _ _ _-c______-__~-__ ___-___-____-________-,_______--_-___________-_______-_h_ ____-________________q_F_ ____________._____,_1:r 3::::____z________~- _1r______,__-__-__ z::_--__Jrrruugz ;::=:::r_______ »-_____>____-> ___________-~_ ___-_-__—_—-wk __-____._____~_ ~~_________::__ :;:-___
» L -___1r _____ _____>>_________ .__________________~________________________________-___-.____-.________--__-__-__q_-_—_—~_____________--_________,-_________-_________________________t________________________-____2
Figure 4.81A large bubble rising in waterresem bles a spherical cap.
98 The flying circus of physics
eddies eddiesdrag
4.82Fish schooling
The schooling of fish certainlymust have roots in social factors,but it must also offer a practicaladvantage to the fish, for whenswimming in such a school, afish's endurance is considerably in-creased, perhaps as much as six-fold. Why would there be an ad-vantage for fish of similar sizeand shape to swim in regulararrays and in synchronous motion?In particular, what determines thedistance between fish? Shouldone fish swim directly behindanother? Why don't fish swimin the V formation that birds use?
1095.
4.83Wind gusts on building
Why is the windward side of abuilding calmer than the rear in astrong and gusty wind? Shouldn'tjust the opposite be true?
453, pp. 138- 139.
driven resonance
harmonic oscillations
4.84Tacoma Narrows Bridge collapse
You may have heard of the failureof the Tacoma Narrows suspensionbridge, because physics depart-ments often have the spectacularfilm (1562) showing the bridgeoscillating and eventually col-lapsing.
The bridge began its oscillations
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Figure 4.82"It all started with an innocentgame of follow—the-leader!"
even when it was being built; infact, the structure's rippling motionmade the bridge workmen seasick.After it was opened to traffic, themotion was so pronounced thatmotorists came from miles awayjust for the thrill of being on thebridge. On days when the bridgeoscillated as much as five feet,motorists on the bridge actuallydisappeared from each other'sview.
Still, the bridge's collapse meas a complete surprise. Suddenly,on the morning of the collapse,the ripple ceased, and after a briefpause, the bridge went into afurious torsional oscillation. Twopeople on the bridge at the timecrawled on all fours to espe.After trying to rescue a dogabandoned on the bridge, a pro-fessor could retreat only along thenodal line of the torsional oscil-lation. (His retreat is seen in thefilm.)
After 30 minutes of torsionalmotion a floor panel fell from themain deck. Another 30 minutesbrought another 600 feet of deckdown. Though the twisting thenceased briefly, it began again, andit took only several additionalminutes to bring the remainingdeck down.
The bridge designer (who diedshortly after this tragic end to his
reer)could hardly be faulted, forat the time there was scant under-standing of the aerodynamic be-havior of suspension bridges. Therepercussions in bridge buildingwere enormous and long lasting.
The bridge failure is introducedin the physics classroom as an
The madness of stirring tea 99
example of driven resonance. Al-though the wind was not blowingunusually hard that day, thebridge's oscillations grew instrength to catastrophic pro-portions. But why and how ex-actly did the wind do this? Howwould a fairly steady wind causethe rippling, which soon led to thetorsional oscillations? Why wouldlongitudinal oscillations be created?Since driven resonance implies acertain frequency match betweenthe driving force and driven object,you must explain how the windproduced that frequency match.
How na bridge's aerodynamicinstability be minimized? Onenew feature resulting from thecollapse was the placement oflongitudinal gaps in the bridge'sroadway, say, between the op-posing lanes of traffic. Why wouldthis help stabilize the structure?
802 through 812.‘ 1556.
pilot lose control as a result.Often there are warning signs forthese various types of disturbances,but some turbulence can occur inclear weather, with no clouds, andat altitudes of several kilometers.This turbulence was unknownuntil jet airplanes of World War IIwere first able to reach the relative-ly high altitudes at which it takesplace. What is responsible forthe clear alr turbulence and theother types of disturbances? Whyis it experienced primarily athigher altitudes?
819 through e22.
4.86Watch speed on a mountain top
Why will a spring-driven watch runat a different speed on a mountaintop than at a sea shore?
9, pp. 80-82.
Kelvin-Helmholtz instability turbulenceconvection
4.85Air turbulence
What causes the bumps so fre-quently encountered by jet air-craft? Some disturbances aresingle jolts. Some force the air-plane up and down as if it werea ship at sea. Others quicklyheave the airplane to a differentaltitude, perhaps making the
4.87Wire mesh on faucet
Why is a wire mesh often placedover a faucet’s outlet? It will,of course, catch small stones in thewater supply, but people claim thewater is also “smoother” or"softer" with the mesh in place.Why would that be?
turbulence
_w _ave interference
4.88Fast swimming pools
Why are some swimming pools saidto be fast? Could different depths,different splash gutters, chemicaladditives, etc. noticeably influencea swimmer's speed?
edge oscillations
4I89
Nappe oscillationsWhen water is discharged over thespillway weirs of some dams, thefalling water curtain may go intosevere oscillations (Figure 4.89).The noise from the oscillations, inaddition to the normal noise fromwater impact at the dam's foot,may even make the vicinity un-bearable. What causes these oscilla-tions, and why is there so muchextra noise?
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Figure 4. 89
100 The flying circus of physics
eddies flow around obstacledriven pendulum particle transport
4.90Parachute holes
Why do parachutes often havecentral holes (Figure 4.900),especially the conventional para-trooper parachutes? Isn't a hole arather strange thing to have, forwouldn't you think it would becounter to the whole point of aparachute? If the hole is to reducedrag, why not just make the para-chute smaller?
Some of the unconventionalparachutes need even more ex-plaining. For instance, some onStock car racers resemble twocrossed-bandage strips (Figure
$§§§,$~\
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4.90b). Why would someone usesuch a drag chute? Wouldn't thedrag be quite low?
Even in the absence of gustywinds, men using conventionalparachutes swing to and froduring their descent. Since suchswinging can be very dangerousduring the landing, the men ob-viously are not doing it on purpose.What causes the swinging, and whatdetermines its period?
817,’ 818.
%Figure 4. 90aConventional parachute.
luh-"=.-‘-=s his 2~\- er F =,T<‘<*.-m \r~
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Figure 4 90bStock-car parachute.
eddies
4.92The gaps in snow fences
If you want to stop snow driftsnear a roadway, railroad track,or walkway, why do you put upa snow fence. . .why not a snowwall? Granted a fence may beless expensive, but wouldn't awall do a better job than a fencewith all its gaps?
453, p. 334; 600,’ 826.
flow around obstacleparticle transport
4.93
Snow drifts
Snow drifts are much more pro-nounced around posts and treesthan on the wind-facing sides ofhouses. Why is there such prefer-ential unloading of drifting snowaround the narrower obstacles?
364, pp. 12-13; 453, p. 333,’826.
drag
tu rbulence
momentum transferhydrostatic forces
4.91Speed of a drifting boat
A drifting boat is commonlythought to travel faster than
the stream. Indeed, since adrifting boat can be steered,doesn’t it have to? But howcan the boat, which supposedlyis just being pushed along by thestream, be moving faster?
453, p. 179; 824,‘ 825.
eddy formation
4.94Streamlined airplane wings
Why are the trailing edges of air-plane wings sharp? (To say thatit's just for streamlining is notenough.) Why do some planes haveswept-back wing and others not?
603; 605
The madness of stirring tea 101
air drag
4.95Skiing aerodynamics
Aerodynamically, what is the bestposition a skier can assume in adownhill race? Winners in theolympics and other world meetsare often determined by time dif-ferences between skiers ot‘ as littleas 0.01 second. Because of thecrucial need for sound knowledgeabout the stance as well as theequipment of a skier, the Frenchconducted wind tunnel experi-
Dla/\\
-C 11/(a) French egg position H“ _
ments and developed the “eggposition" (Figure 4. 95a). Al-though this in not the best posi-tion for drag reduction, it is apractical one to assume in astrenuous race.
How about the other two posi-tions shown? Before the testinga good many of the skiers had in-stinctively adopted the lowest pos-sible position, dropping the arms
alongside the legs (Figure 4. 95b).As it turned out, the high crouch(Figure 4. 95c) gives remarkablyless drag than the lower crouchwith lowered arms- but still notas little as the French egg position.Why?
823.
\6l . _ ‘
sl as‘I (b) ggérgtjgeagrgss (c)High crouch
L}<.':;;=~_,,\_ as-¢:'.\.,_ »§\,r~/‘via’-» ‘ we .- ‘r - ~~<~- f~- -'l.Q:re. ;;+“<' " A-‘ l ’~;r=¢-_'>.~.. .4. 4Q .~"~./1/~/\..*~:[email protected]‘_. _ ._i.\. ~\-4- .-
Figure 4.95Three skiing positions.air drag
4.96Dimpled golf balls
Why are golf balls dimpled? In thevery early days of golf, the ballswere smooth, and it was only ac-cidentally discovered that scarredballs traveled further than thesmooth, unsrred ones. If today'sdimpled ball is driven, say, 230yards, a smooth ball similarly struck
would travel only 50 yards. Doesthis make sense? Shouldn't thesmoother ball go further bemuseit will have less air drag?‘
593,‘ 827; 828.
‘I n the last lew years a newer golf balldesign—one with randomly spaced,hexagonal dimples rather than the old,regularly spaced, circular dimp|es—hasbeen sold with the claim of an addi-tional six yards in average flight distance.
air pressure
momentum transfer
4.97Flight of the plucked bird
How do birds fly? Yes, I knowthey flap their wings up and down,but how does that keep themaloft and moving forward? Well,maybe the bird flaps backwardson the downstroke, thereby pro-pelling itself forward. No, slowmotion movies show the wing
102 The flying circus of physics
moving forward not backward, onthe downstroke. Perhaps the bestclue to the bird's flight lies in theancient Greek myth of Icarus whoflew too close to the sun, lost thefeathers glued to his arms, andthen plunged to his death. Musta bird have feathers to gain liftand forward drive? Can a pluckedbird fly?
604.
’" I
ities;
,5»&
pressure
stability
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Figure 4.99Several bridling techniques for kites.
4.99KitesWhat keeps triangular and boxkites aloft, and which type ismore stable? Why do some kiteshave tails? Finally, what advan-
tages do the various bridling tech-niques shown in Figure 4.99 give?
829.
convection
vortices
lift and drag
4.98Bird soaring
What allows birds to soar soeffortlessly and so continuously?If they are riding on winds de-flected upward by trees and hills,for instance, then why can theysoar iust as well over flat land andwater? If they gain lift by glidinginto a wind whose strength in-
creases with height, then why dothey seem to soar so much betteron wind-free days? Finally, if theyride thermal currents upward, thenwhy can you sometimes see onegroup of birds soaring whileanother group, either below orabove the first group, must flaptheir wings to remain aloft? Be-sides, if the lift is produced bythermals originating on theground, shouldn't larger birds havean easier time soaring near theground? Actually, they can rarelysoar there.
Some birds stalk ocean linersacross long stretches of open water,somehow gaining their propulsionby gliding near the ship waves.How do they do this?
364, pp. 13- 15, 120-121,‘ 604,‘852, pp. 127- 131; 853 through862.
roll vorticesconvectioncondensation
4.100Cloud streets
Sometimes the sky is coveredwith long, straight rows of cumu-lus clouds lledcloud streets.What orders the clouds this way,and in particular what determinesthe spacing between rows? Whyaren't cloud streets made moreoften?
361, pp. 4- 13, 39, 43; 362,pp. 28-30," 364, pp. 154-155,175; 1456.
The madness of stirring tea 103
convection ‘row vortices ‘surface tension gravity wavesnonlinear fluid flow
stabilitycondensation
4.101Coffee laced with polygons
If you examine a hot cup of coffeeunder a strong light that is incidentnearly parallel to the surface of thecoffee, you will find the surfacelaced with polygonal cells (Figure4.101a). They disappear, however,
Figure 4.101.;Polygons on coffee surface. (AfterV. J. Schaefer, American Scientist,59 (Sept.-Oct. 1971).)as the coffee cools. You can alsodestroy the cellular appearanceby putting a charged rubber comb(charge it by running it throughyour hair) near the coffee.
Other liquids show surfacedesigns too. James Thomson, afamous Nineteenth-Century phys-icist, noticed the rapidly varyingsurface designs in a pail of hotsoapy water and in strong wines.Later, the Frenchman Bernard wasable to make regular patterns inoil surfaces when the oil was heatedfrom below. His regular polygonswould slowly evolve into a beauti-
.,, ...%
Figure 4. I 01 bHexagonal Bernard cells.fluids gave a roll-like appearance(Figure 4.101c). Recently, cellularsurface designs were attempted onboard spacecraft while under zerogravity.
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Figure 4. I 0 I cSurface with roll-like structure.
In these examples, why do rollsand polygons (especially honey-combs) form on the fluid surfaces?ls the same physics actually re-sponsible for all of the examples?Why do the coffee cells disappearwhen there is a charged body near-by? Finally, do these several typesof surface designs depend ongravity?
350. pp. 93-94; 453, pp. 418-
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4.102Longitudinal sand dune streets
Looking down on desert sand dunesfrom a high altitude airplane, onesees “curious long, narrow dunebelts running across the desert,roughly from north to south, inalmost straight lines [Figure4.102] ,” (863) as if one wereviewing well-designed parallelstreets. The dune belts are char-acteristic of virtually every majordesert in the world, and they allrun roughly north to south andhave spacing of about 1 to 3kilometers.
Leaves scattered over lake sur-faces and surface seaweed also col-lect into rows, though the scale issmaller, with the rows being only
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ture lFigure 4.101bl. Still other through 849. G high am-mac
104 The flying circus of physics
100-200 meters apart and up to500 meters long.
In these examples what deter-mines the direction the rows andbelts run? If it is the wind, thendo the rows and belts run parallelor perpendicular to it‘? Moreover,what determines the spacing be-tween them?
580, pp. 18-19, 1 19- 120; 862through 868.
eddies
saltation
4.104Sand ripples
Why are the sides of a sand dunecovered with sand ripples? Whatexactly determines the spacing ofthose ripples?
The sandy bottoms of streamsare also often covered with sand
ripples or waves. What causesthose, and again, what determinesthe periodicity of the waves? Ifyou watch them closely for a longtime, you may find them travelingupstream. Why do they do that?
144; 453, p. 334," 629. PP. 381-386; 687.‘ 688: 697, Pp. 55-59,"698, pp. 134-136," 869 through874.
vorticity
4.103Smoke ring tricks
To amuse me during the longslimmer days of a small countrytown, my grandfather would blowsmoke rings for hours on end.In one of his simpler tricks hewould send a ring toward a wall,and the ring would expand as itapproached the wall.
His best trick, however, wasblowing one smoke ring throughanother, larger one. After thespeedier trailing ring passedthrough the leading one, theformer leading ring contracted andspeeded up while the former
trailing one expanded and sloweddown (see Figure 4.103). Theirroles were exchanged, and thenew trailing ring than passedthrough the new leading ring.This game of leapfrog continueduntil the smoke rings became toodispersed for further play.
You can see the same thing bydropping a colored drop into a
pass through the first, and thegame of chase begins.
Exactly how are smoke ringsformed, and how do they retaintheir shape for so long? Whydoes a smoke ring expand as itapproaches a wall? Finally, whatcauses the chasing game of twosmoke or water rings?
beaker of water. Upon hitting the 36' 9- 7" 57- PP- 767467" 709-surface, the drop forrns a ring that P‘ 7" 453' p' 75- 7277 850" 857'both expands and descends.* Asecond, closely following dropwill produce another ring that will
‘See Prob. 4.74.
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itlFigure 4 1 03My grandfather's smoke-ring trick.
The madness of stirring tea 105
forces in liquids saltationcavitation flow around obstacleVBDOT Dl'8SSU F8 iriction
4.105Siphons '
How do siphons work? In parti-cular, if they depend on atmospher-ic pressure, then why can someliquids be siphoned in a vacuum?Do they depend on gravity? Whenthe siphon tube is first lowered intothe liquid, why doesn't the siphonstart itself? What force pulls theliquid up the first arm (denotedA-B in Figure 4.105) againstgravity? Finally, how is the heightof a siphon limited, especially whenthe siphon works in a vacuum?
875' 876.
B _,(-_..,:..._-..—;_.._:.»_
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Figure 4.106The march ofa sand dune over26 years. (Adapted from
4.106Marching sand dunes
I would have thought winds wouldtend to disperse a sand dune, butFigure 4.106 shows a typical casein which they marched a duneacross a desert floor. The dune’:character and identity remain
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Geology Illustrated by John S.Shelton. W. H. Freeman andCompany. Copyright © I966.)
intact even after 26 years oftravel. How, exactly, are dunesmoved by the wind?
144; 453, pp. 333-334.‘ 698,pp. 141-142; 699, p. 198.
siphon
entrainment*i
- -='I_= -;';-_;=;-,';. 1 ,;.;-:;;;;:-_;-.-:-'I':I I-. -5-" .
llU“
<3Figure 4.105 ASiphon.
4.107The Crapper
How does a flush toilet work?What forces the water, etc.(especially the etc.) to enter thepipes? When the water from thetank comes into the bowl, is itmerely falling from a water con-tainer above? Why do most toiletshave a second, smaller hole in thebowl?
I have come across in writing TheFlying Circus is Flushed with Pride:The Story of Thomas Crapper (878)It was Crapper who developed theflushing toilet. (Obviously he alsocontributed to the American lan-was-)
Now you may not appreciatethis, but it was tough workdeveloping the flush toilet, andserious research was conducted byCrapper and others. Of course intheir experiments these researchershad to simulate the actual materialtoilets normally handle. Toilettesting must have reached its
,F°r seven" curious types of siphuns one of the mos, interesting books zenith when in 1884 they achieveddevised by Hero of ancient Greece, seeRef. 877.
106 The flying circus of physics
“a super-flush which hadcompletely cleared away:10 apples averaging 1 3/4 ins.in diameter,l flat sponge 4% ins. indiameter,3 air vessels,P|umber’s “Smudge” coatedover the pan,4 pieces of paper adheringclosely to the soiled surface."*
A truly remarkable feat oftechnology!
253, pp. 334-335' 317, pp. 95-97,‘ 318, PP- 108-1 13; 878,‘ 879,pp. 260-261.
‘From the book, Flushed with Pride byWallace Fleyburn. Copyright © 1969 byWallace Fteyburn. Published by Prentice-Hall, lnc., Englewood Cliffs, N. J. Per-mission also granted by Wallace Fleyburnand Macdonald & Co.
drop aerodynamics
4.108Street oil stains
On some roads on which the trafficspeed is sufficiently high, oil stainsare annular with an unstained sec-
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| ‘ l ||| ll I.'-i1‘=E=’:IIiiI§%:IiEE=:;~rEi-i=2::iI?:5E§":!:5'=IlE§f=‘i=iili .l-El-|'1Figure 4.108Street oil stain.
tion of road in the center of eachstain (Figure 4.108). With slowertraffic the stains are iust splotches.Why do the annular stains appear,and how fast must the cars betraveling for them to be formed?
887, p. 187,’ 888.
surface films
boundary layers
4.109Lake surface lines
Here and there on the surfaces oflakes and streams you can see thin,almost invisible lines. They aremore noticeable if the water isflowing because then a small ridgef water builds up on one side ofline (Figure 4.109). What doou think these lines are, and whyre the ridges formed?Powder sprinkled on the ridge
will reveal a two dimensional flowpattern of streetlike channels onthe opposite side of the line(Figure 4.109). What causes sucha pattern?
893' 894.
D~<D°
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we
Figure 4. I 09The line and ride on a streamor lake water (overhead view).
surface film
4.110lVlilk’s clear band
The next time you're mullingover a glass of milk, examine themilk film at the edge of the milkas you tip the glass. Between thefilm left on the bottom of the glassand the milk there is a clear areaa few millimeters wide (Figure4.110). Why is the clear bandpresent?
458.
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8
, __ . 1- ,» ‘- _, .. .‘-_:.r-,-1_..._.._...........;‘.. ****._.._-;._'-...-..'._..._-..._.._._._. _a.'..,.l
Figure 4. I 10The clear band in a tilted glassof milk.
W818 Y WBVGS
surface tension
4.111Spreading olive oil on water
in Prospero ‘s Cell (889) LawrenceDurrell describes the nighttimespear fishing in the lagoons beneaththe Albanian hills. For spear fishingthe water must. be clear and calmbecause even a slight breeze severelydistorts the image of the fish andruins the aim. The fisherman can
The madness of stirring tea 1 07
cope with a small breeze, however,by sprinkling a few drops of oliveoil onto the water. Why do thesefew drops calm the water?
890, pp. 6'3 1-6'32; 891; 892.
internal waves
wave damping
4.112Marine organic streaks
Biologically active regions of the ‘oceans are often covered withlong, wide streaks where therippling of the water is suppressedby a film of organic material. Whenthe illumination is iust right, thesight can be beautiful. The organicstreaks apparently do not dependon the wind like the seaweed streetsdiscussed in Problem 4.102, for theyare best seen in a light breeze, nota strong one. (The breeze reallydoes nothing but heighten the con~trast between the size of the rippleson the free water and on the streak.)What cause the film to form intostreaks this way?
895 through 898.
Initialdrop
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does the central jet form and thenpinch off drops? The pinchingitself especially needs explaining.
Suppose the milk drop experi-ment is done in outer space (withno gravity). -Will the same type ofsplash mcur? In fact, will therebe any splash at all?
880 through 886.
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4.113Splashing milk drops
When a milk drop splashes on aliquid surface, a crater is thrownup, eventually breaking into acrownlike structure (Figure 4.113).As this crown subsides, a liquidjet (the “Rayleigh jet") leaps up
fc
Figure 4. 1 I3After P. V. Hobbs and A. J.Kezweeny, Science, I55 (8766),I I12-I114 (I967). CopyrightI 967 by the American Associationf A fSor the duancemento cience.
rom the center of the formerrater, which then pinches off and'ects one or more small dropseg .
Why does the craterlrlm break intothe crownlike formation, and why
surface tensionpressure
centrifugal foroe
4.114Water bells
If a water stream falls onto thecenter of a disc, the water willspread over the disc and form atransparent sheet as it flows off.The sheet may even close back ontothe center support of the disc,forming a beautiful bell shape(Figure 4.1 14). What forces thesheet back in like this, and whatdetermines the actual shape ofthe bell?
899 through 904.l ‘
Falling water stream
r‘ /Q¢\\Hf
in-,;-\
/Figure 4. I I4
108 The flying circus of physics
surface tensionmomentum conservation
W8ter WBVES
4.115Water sheets
If two identical water jets aredirected toward each other,beautiful thin sheets of water canbe produced (Figure 4.115). Whydo the streams form sheets ratherthan just break up? Why do thesheets eventually disintegrate atsome particular distance fromthe impact point?
The shape of the edge and thestability of the sheet fall intothree main types which depend on,among other things, the rate ofwater llow. For low speeds, thesheet ls stable with circular edges.
two things can happen: the edgemay be cusp shaped or waves maybe set up on the sheet. In thethird type, for even higher speeds,the sheet will flap like a flag inthe wind. Roughly, what causesthese differences?
904 through 910.
/' "\\\‘
§’/%
K2! /Q/*6.~ i ‘ Csfiri-=—-if \
’/‘“\\\\\Q“\‘*_--
;—*
ll lllllFigure 4. I I5Water sheet formed by collisionof upward and downward waterjets. [After G. I. Taylor, Proc.Royal Soc., A 209, I (I960).]
For the next type, at higher speeds,
4.116Gluing water streams
Punch several adjacent holes in theside of a can, parallel to the bottom.Fill the can with water and run yourfinger through the leaking streams.For some reason, the streams nowconverge and remain together evenafter you've removed your finger(Figure 4.116). What keeps themtogether?
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Figure 4. I I 6Three water streams seeminglyglued together.
surface tension
4.117Pepper and soap
if you dip a small piece of soapinto a bowl of water sprinkled withpepper, the pepper will immediatelyrace away from the soap. Why?How fast do you think the peppergrains are moving?
321,’ 592, p. 40.
Bernoulli effect
boundary layer
pressure differential
4.118Pouring from a can
When I pour my beer, why doesit insist on running down the sideof the can instead of fallingstraight down from the lip (Figure4.118)? What determines how fardown it adheres to the can? Howfast must I pour the beer toprevent any such “sticking”?
Your first impulse will mostlikely be to attribute the pheno-menon to surface tension or ad-herence of the liquid to the con-tainer. However, neither isresponsible for the spilt beer.What ls, then?
917,‘ 912.
Figure 4. I I 8Fluid stream is forced back alongthe can.
The madness of stirring tea 109
surface tensionfilm creep
4.119Tears of whiskey
After pouring a shot of whiskeyinto an open glass, you will see afluid sheet that first creeps up theside of the glass and then formstear drops around the side. Whatcauses that upward creeping tosuch surprising heights?
822,- 848,- 849,- 1530.
4.120Aquaplaning cars
If you lock the brakes on your carwhile moving at high speed on awet road, the car will act like anaquaplane. That is, the tires willskim along on a thin sheet of waterand will not actually touch theroad. Why does this happen, andwhy doesn't it always happen onwet roads even when the brakesare not applied? ls there anytread design that will minimizethis effect?
9 13.
almost miraculously escapingconsumption by the surface. Whatdelays the death of these drops?
534,‘ 914 through 916',‘ 1608,‘I609.
Non-NewtonianFluids
(4.122 through 4.13ll
4.122Soup swirl reversal
The next time you fix tomato soup,give the soup a good swirl in thepan and then lift your spoon out.The swirl in the soup dies out, asyou would expect, but during thelast few seconds the soup turns inthe opposite direction. What makesit do that?
977.
elastic fluids
surface tension
4.121Floating water drops
Water drops can often be seenskimming across a water surface,
4.123A leaping liquid
Some hair shampoos* (andseveral other liquids) display acurious leaping tendency whenbeing poured into a partially filleddish. If the falling stream is thinenough, the liquid will form asmall hump near the stream'sentrance point. Then the streamwill seemingly leap back upfrom the surface as shown inFigure 4.123). Each time this
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Figure 4. 123[After A. Kaye, Nature, I9 7,I001 (March 9, (1963).)happens the hump disappears andmust be rebuilt before anotherleap occurs. What causes the humpand the leaping stream, and whatis so unique about the liquidsdisplaying this property?
917,‘ 921; 922; 923, pp. 249-251.
‘A. A. Collyer, personal communication.
Weissenberg effect
viscosity
511855
4. 124Rod-climbing egg whites
When a glass of water is placed onthe center of a rotating turntable,the surface of the water curves uptowards the outside of the glassbecause of centrifugal force. Thesame shape is also obtained if theglass is held fixed and a rotatingrod is inserted along the centralaxis of the glass.
Not all fluids, however, behave
I 10 The flying circus of physics
in this common-sense way. Eggwhites, for instance, will have theproper curved surface on a rotatingturntable but will behave strangelywith the rotating rod. Rather thancurve up toward the outside, theegg white will climb the rod(Figure 4.124). Gelatin dissolvedin hot water will show normal be-havior at first, but as the mixturecools, it will begin to display thisstrange urge to climb the rod.Since the centrifugal force iscertainly still present becauseof the rotation there must be aneven stronger force pulling thefluid inward and up the rod. Whatis this force?
917," 921; 923, pp. 23 1-236,’924, p. 375,‘ 925, p. 121 ff,"926, PP. 52-53,’ 927, p. 6'71,‘928, pp. 522-524,‘ 929through 934; 1820.
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a reasonable height, the stream willbegin to wind itself up a short dis-tance above the plate (Figure4.125). Why does this coilingoccur, and what affects the dia-meter and height of the ooil andthe rate at which if forms?
918 through 920.r l
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being sheared by the knife. Thixo-tropy is just as important inpainting with one-coat paints.The paint must be viscous enoughto give a smooth coat withoutrunning, so the viscosity mustbe low when the paint issheared by the brush. But itmust increase quickly enoughafter brushing to prevent running.There are many other thixotropicfluids: ketchup, gelatin solutions,mayonnaise, mustard, honey, andshaving cream. What effect mustshearing forces have on the struc-ture of these liquids to cause thedecrease in viscosity?
1 10, pp. 185- 186; 921,- 923, pp.246-248; 924, p. 374; 925, pp.144-149; 930; 934; 935, pp.405-407.’ 936 through 938,’ 1547.
Figure 4.125Liquid rope coil. [After G.Barnes and R. Woodcock, Amer.J. Phys, 26 (4), 205 (l958).]
dilatancySIFGSS
viscosity
shearing
sol-gel change
viscous fluid flow
4.125Liquid rope coils
if you pour thick oil, honey, orchocolate syrup onto a plate from
4.126Thixotropic margarine
Many common, household fluidswould be useless if they were notthixotropic, that ls. if their vis~cosity did not decrease when thefluids were subjected to shearingforces. For example, margarinewould not spread very well atroom temperature were it notfor its decrease in viscosity when
4.127Die-swelling Silly Putty‘
Do you expect a fluid to changeits volume as it emerges from apipe through which it is beingpushed? Most fluids don't, theirdiameters upon emerging beingthe same as the pipe's insidediameter. An exception, however,is Silly Putty, a silicone puttysold in toy stores. Pack a smalltube full of Silly Putty, let itstand for a while to settle, andthen push it through the tube.As soon as it emerges, it expandsnoticeably (Figure 4.127). Suchan effect, called die swell, ob-
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Figure 4. I 2 7The Silly Putty expands whenpushed from the tube (die swell).viously stems from a peculiarproperty of this fluid, the SillyPutty, but what exactlycauses it to swell, what otherfluids respond similarly, and whydon't all fluids behave this way?
9 17; 92 1; 923, pp. 242-244;935, pp. 405-407; 1620.
'® Silly Putty Marketing, Box 741, NewHaven, Conn., U.S.A.
4.128Bouncing putty
Silicone putty also displays severalseemingly incompatible properties.Hit it with a hammer, and it shat-ters. Bounce a ball of it, and itbounces better than a rubber ball.Leave a ball of it undisturbed, andit will gradually flatten. Ap-parently it behaves like a liquidbut demands certain responsetimes to extemal forces. Accord-ingly it will shatter if struckquickly or will bounce elasticallyif hit a bit slower. Gravity actingfor a long time will cause it to
response times?917,- 923. PP. 236 ff: 939.
flow. What is it in the putty's hvdwsralic oreswrestructure that determines such yiscggity
siphoning
elasticity
4.129Self-siphoning fluids
Some fluids, such as polyethylenein water,* can siphon themselvesout of containers (Figure 4.129)if you will only initiate the siphon-ing by pouring out some of thefluid. What pulls such a liquidover the wall of the container,
917.’ 940.
and what holds the stream together?
4.130Quicksand
If you discover yourself stuck inquicksand, why is lying down onyour back the best thing to do?(Once you lie down and free yourlegs, you can then roll towardshore.) lf you should have to pullyourself, someone else, or ananimal out of quicksand, why isit best to pull slowly? Does theviscosity of the sand change whenyou pull more quickly? If so,why? Why do deeply entrenchedpeople and animals have bulgingeyes?
941.
fluid flow
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4.131Unmixing a dye solution
If a drop of dye is mixed into asolution by rotation, is thereany way to unmix it?
Between two coaxial glass cyl-inders of nearly the same diameter,pour some glycerol and then care-fully add several drops of dye(Figure 4.131). Rotating the innercylinder 10 times or so apparentlymixes the dye pretty well. How-ever, if you turn the cylinder backthe same number of turns, the
I 12 The flying circus of physics
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Figure 4.131The two cylinders for unmixinga dye solution. (The spacebetween the cylinders has beendrawn large for clarity.)
dye unmlxes itself back to ap~proximately its initial distribution.Why? If you wait too long to makethe reverse turns, this won't happenAgain, why?
942; 943.
The madness of stirring tea 1 13
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reflection
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5. 1Swimming goggles
Why is it that when you areswimming underwater you can seemuch better if you wear goggles?
A particular Central Americanfish, the Anableps, seems to havethe best, or the worst, of bothmedia, for it swims just beneaththe water surface with its largeeyeballs protruding above thesurface. Each eyeball is thus halfin and half out of the water.Considering your need of gogglesto see underwater, how can thefish see in both air and water thisway‘?
170, p. 534; 332, Vol. 1, p. 36-3,‘ 462, p. 1 16',‘ 944; 945' 1570.
5.2The invisible man
The invisible man in H. G. Wells’famous novel was invisible becausehe changed his body's index ofrefraction to an appropriately
Lxuvplirmully good rulcrcnces. Min-n.mri's book (954) is nlisulutely firstclass, his paper (99 ll updates the hook.O'Ctmnell's book (966) on the greenllush is iascinating. Also, Wood (360),l_.|rnmrtr and Hall (983), and Weather(ti |0urn.1ll.
Figure 5.2The invisible man.chosen value (Figure 5.2). Whatdo you think the value was? Noone was able to see the invisibleman. Could such an invisibleman, with that value of theindex of refraction, see any-thing at all himself?
5.3Playing with a pencil in the tub
If your bathtimes have becomedull and uneventful and you needsomething to spice them up,bring a pencil along and examineits shadow on the bottom of thetub. If you dangle the pencilhalf-submerged, you will findthat the shadow does not entirelyresemble a pencil. Rather, itlooks like two rounded rodsseparated by a white gap as
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shown in Figure 5.3. Why 1'8 "19"a gap, and what determines itswidth?
951,- 952.
5.4Coin’s image in water
If you place a coin in a trans-parent, open jar filled with waterand look down through the watersurface from the appropriate angle,you can see the coin’s image on thesurface of the water (Figure 5.4).Putting your hand on the far sideof the jar usually has no effect onthe image, but if your hand iswet, the image will disappear.Why?
950.
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If you look down at a fish in atank of water, you will see it at anapparent depth which is not asgreat as its actual depth. ls theapparent horizontal distance to thefish also distorted? The horizontaldistortion may depend on whetheryou use one eye or two. Try itout by placing some object in ashallow dish of water and lookingat it from a distance with your eyes
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nearly level with the surface of thewater (Figure 5.5). First judge theobject’s distance with your headupright and then with your headtilted 90°. If the distance seemsdifferent depending on the posi-tion of your head, can you ex-plain why?
946 through 949.
5.6
What causes the double image,ghosting, of distant obiects indouble-walled windows? Undercritical conditions, such as in airtraffic control et airports, theghosting can be not only annoying
Ghosting in double-walled windows but M50 dange,ous_ Assumingsome realistic situation, canyou calculate the angular separa-tion of a true image and its ghost?How will the separation vary withtime of day and weather conditions?
953.
5.7Mountain looming
There are places in the worldwhere, in late afternoon and earlyevening, mountains can be seenrising out of the horizon on theocean. The mountains are real,but they are too distant to be seennormally. First, in the earlyafternoon, a hazy patch peaksabove the horizon. Then, asthe afternoon wears on, the patchgrows, quickly sharpening intoobvious mountains near sunset.The individual peaks can even berecognized. How is this type ofmirage created?
164, p. 469,‘ 165, p. 164,’ 954, p.41; 957 through 960.
5.8Fata Morgana
Fata Morgana is the most beautifulof all mirages, and though it is veryrare in some areas, it is common inthe Straits of Messina between Italyand Sicily. When there is a layerof cold air over warmer water, onemay see fairy castles rising out ofthe sea, constantly changing,growing, collapsing. According tolegend, the castles were the crystalhome of Morgana the fairy. Thismirage is the most difficult of themirages to explain because thereare several competing effects in-vclved, but can you unravel theeffects?
164, pp. 474-475' 954, pp.52-53: 955 957,’ 953,’ 961.
I 16 The flying circus of physics
5.9Oasis mirage
What causes the water mirage com-monly seen on hot streets? Whatfeatures partially convince you thatthere is water in the street? Also,why do there seem to be palmtrees around oasis mirages (evenin areas where such trees cannotgrow)? To a thirsty man, of course,the palm trees are more thanenough to convince him of awater supply (Figure 5.9).
A pelican discovered on a hotasphalt highway in the midwestmight have almost met its endbecause of the water mirage.
The miserable bird hadobviously been flying,maybe for hours, across
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dry wheat stubble andhad suddenly spottedwhat he thought wasa long black river, thinbut wet, right in themidst of the prairie.He had put down fora cooling swim andknocked himselfunconscious.*Did the bird eee a mirage?165.PP. 164-165' 170,pp. 391-392,‘ 219, PP.295-295.’ 533, PP. 75-76;954. pp. 45-46; 955through 957.‘C. A. Goodrum, The New Yorker,38(8), 115 (1952l.
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5.10Wall mirage
Minnaert (954) describes amultiple image mirage that can beseen along a reasonably long wallfacing the sun. (He arggests alength of 10 yards or more.) Placeyour hand against the wall andwatch a bright metal object a friendbrings near the other end of thewall (Figure 5.10). When the objectis a few inches from the wall, it willappear distorted and you wlll see areflected image in the wall asthough the wall were a mirror. Ona very hot day you may even see asecond image as well. Why is therean image of the object inside thewall?
954' PP. 43-44.
She corneas in colors everywhere 1 17
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Paper doll mirage
A different type of mirage, the“superior mirage, " involves one ormore images of an object as shown
in Figure 5.11. What's responsiblefor those images?
164-PP. 470-473,‘ 165, p. 164,‘954, p. 51,’ 955' 958.
5.12One—way mirrors
One way mirrors are used a lotin spy movies, but are theyreally one-way? Try to devisea glass or a glass coating so thatroom scenes will pass in only onedirection. If this is impossible,then how do the so-called one~way mirrors work?
984.
5.13Red moon during lunar eclipse
Why is the moon red during alunar eclipse—that is, when themoon is in the earth's shadow?
954, pp. 295-296," 983, Pp.2 1-22.
5.14Ghost mirage
There are, or course, many curiousstories of strange mirages. Can youexplain the following one?
One hot August afternoona woman was pickingflowers from the wet groundwhen . . .she suddenly per-ceived a figure at the dis-tance of a few yards fromher. It was standing on awet spot where there wasa little thin mist (possiblysteam) rising, and wavereda little, never remainingstill, though she says,‘it had a great deal ofbulk.’ It was on a levelwith herself and formeda species of triangle, withherself and the sun. Shewas looking towards thesun, but not directly to it.
She thought at first thatthe figure might be a delu-sion: it stood exactlyfacing her and she firstdiscovered it to be herown image by perceivingthat like herself, it held. . .a bunch of flowers. Shemoved her hand with itsnosegay and the figuredid the same. The dressand flowers were preciselysimilar to her own and thecolours as vivid as thereality. She could see thecolouring and the flesh: it was
1 18 The flying circus of physics
a looking-glass (962)Needless to say, this soon unne edthe woman, and “she fled downthe steep hillside, often stumbling,to rejoin her friends, both ofwhom had seen the figure" (962).
962.
like looking at herself in
rv
///
How many "you's" do you see?
5.15Number of images in two mirrors
How many images of yourself doyou see while standing in front oftwo adjacent plane mirrors suchas you find at a clothing store(Figure 5.15)? How does thenumber of images depend on theangle between the mirrors? Doesit matter where you stand? If itdoes, where do you stand to seethe most images? Are youranswers the same for the numberof images you will see of a pack-age lying next to you?
985 through 989; 1524.
5. 16The green flash
Just as the top of the setting sundisappears beneath a clear, flathorizon, you may be able to see,for 10 seconds or so, a distinctgreen flash from the sun. Whydoes this happen? Could it bean optical illusion (say, anafterimage of the sun)? This wasthe common opinion for a longtime, until photographs weremade of the flash.’
In higher latitudes it can be seenfor longer times "Members ofByrd's expedition to the SouthPole are reported to have seen itfor 35 minutes while the sun, risingat the close of the long winternight was seen to be moving almostexactly along the horizon" (978).
Clear horizons, such as over thePacific, are a definite asset. "Ac-cording to Rear Admiral Kindell,strong and brilliant flashes wereseen by him and other membersof the U.S. Navy during theOkinawa campaign of 1945 atalmost every sunset on clear days"(978).
A similar effect, although veryrare, is the red flash that may ap-pear when the sun peaks outbeneath a cloud.
164, pp. 58-63; 165, p. 160;362, pp. 152- 153; 966through 981; 1614.
'O‘Connell's book (966) is lull oi greenflash [)l10lOg18phS.
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Figure 5. I 7Laser beam bouncing in a sugarsolution. [After W. M. Strouse,Am. J. Phys, 40, 913 (1912).)
5.1 7Bouncing a light beam
lf a narrow light beam (such as alaser beam) enters a container ofwater in which several lumps ofsugar have been added withoutstirring, the light beam will bendand then bounce off the bottomas shown in Figure 5.17. What
makes the beam bend down‘?What makes it bounce? And final-ly, once it is going up, what makesit bend down again?
963,’ 1551.
She comes in colors everywhere 1 19
5.18Flattened sun and moon
What causes the apparent flatteningof the sun and moon when they arenear the horizon? Can you roughlycalculate the amount of distortion?
164, p. 470,'219, pp. 297-298;954, pp. 39-40,‘ 964; 965.
reflectionpolarizationBrewster angle
5.19Blue ribbon on sea horizon
The horizon on the sea often ap-pears to be a much darker blue orgray than the sky or the rest ofthe sea. In fact, if you're standingon a beach, it almost appears thatsomeone has stretched out a brightblue ribbon to mark the horizon.The ribbon disappears, however,if you lie on the beach or if youclimb to a greater height. Oneclue about what causes the rib-bon might be that the light fromit is almost completely linearlypolarized. Can you explain theribbon and the polarization?
1500.
5.2030° reflection off the sea
If you look at the sea just belowthe horizon, you will see reflectionsof objects that are more than 30°
above the horizon. Objects lessthan 30° above the horizon are notreflected. Why? ls the minimumreflection angle determined by theaverage wave slope that, becauseof your observations, must beabout 15°? Actually, it is not.Can you think of any other reasonwhy the reflection is restricted inthis way?
954, pp. 23-2e sea
5.21Lunar light triangles
When the moon is reflected in thesea or a lake, why is there a lumin-ous triangle on the surface of thewater (Figure 5.21)? What deter-mines the shape and width of theluminous area? Why is there acorresponding dark triangle inthe sky above the water?
399, pp. 243-246; 954, pp.23-27, 138-139; 991; 992,pp. 74-80.
Figure 5.21Lunar light triangle in the waterand a dark triangle in the sky.
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5.22Shiny black cloth
Why do some types of clothglisten while others do not?Black felt has a shiny side anda dull side. Some wall paints areglossy black; others are flatblack. Since black absorbs visiblelight, how can a black surface beshiny?
253, pp. 278-279,’ 533, pp. 33-35.
120 The flying circus of physics
pinhole optics ray optics
5.23Inverted shadows
Punch a pinhole in an opaque sheetof paper, hold the paper a fewinches from one eye, close theother eye, and then carefully hold athin nail between the pinhole andyou (Figure 5.23a). Move the nailaround until a shadowy figure ap-pears in the circle of light from thepinhole (Figure 5.23b). What causesthat figure, and why is it invertedfrom the nail? Also, why does thefigure appear to be on the far sideof the pinhole?
533. PP. 49-51; 993.‘ 1582.
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5.24Pinhole camera
The simplest type of camera, andthe easiest to build, is the pinholecamera. Moreover, there are somedefinite advantages to using apinhole instead of a lens. Forexample, there is no linear dis-tortion, and there is tremendousdepth of field. Are there aber-rations of any significance? lnparticular, is there any chromaticdistortion in a simple pinholecamera? Finally, what is the besthole size, and what happens toyour pictures if the hole is largeror smaller than the best size?
994 mrough 998; 1501dvrough 1503; 1586.
5.25Eclipse leaf shadows
If you look at the shadows ofleaves during a solar eclipse, youwill see images of the eclipsingsun projected onto the ground.Why are these images made? Arethey present all the time or justduring an eclipse?
360, PP. 6'6-67; 533, pp. 29-31,’ 999.
5.26I-leiligenschein
Some morning when the grass issparkling with dew, look at theshadow of your head on thegrass. Around the shadow will bea bright light called the heiligens-chein. l-low, exactly, does thedew cause this brightening, andwhy isn't there heiligenscheinaround your entire shadow? Dothe blades of grass play any partin the effect besides holding upthe dewdrops? Can you alsoexplain the very bright helli-genschein that astronauts see whenwalking on the moon? (It certainlyisn’t due to dew-covered grass.)
164, p. 556; 165, p. 180;360,p. 68; 362.PP. 136-137; 380;954, pp. 230-234; 983, Chapter2; 1000 through 1008.
5.27Bike reflectors
If you shine light on a bike reflec-tor at virtually any angle, the lightwill be reflected back to the source.Why is the reflector so good atthis? An ordinary mirror will re-flect well, of course, but it willnot return the light to the sourceunless the incident light is per-pendicular to the surface. What,then, is different about the bikereflector? If a narrow beam oflight is reflected by a bikereflector, how wide will thereturn beam be?
170. P. 158,‘ 1011.
She comes in colors everywhere 121
5.28Brown spots on leaves
It is a bad idea to sprinkle water ontree leaves during the day, becausethe water drops leave brown spotson the leaves. What causes thespots?
5.29Rays around your head's shadow
I looked at the fine centri-fugal spokes round theshape of my head in thesunlit water. . . Diverge,fine spokes of light fromthe shape of my head, oranyone's head, in the sun-lit water! ---Walt Whitman,“Crossing Brooklyn Ferry",Leaves of GrassThese rays of light surround the
shadow of your head if the shadowis cast upon slightly turbulentwater. If the water is calm or hasregular waves, the rays do notappear. Why?
954, pp. 333-334,’ 1009.‘ 1010.
5.30Cats’ eyes in the dark
Why do a cat’s eyes shine sobrightly in the dark when youilluminate them with a flash-light? Why aren't they so notice-ably bright during the day? Doesthe amount of reflection dependon the angle between your line of
sight and the incident light beam?Why don’t our eyes shine as muchwhen illuminated at night orwith a flashbulb?
954, p. 350,’ 983, p. 36,’ 1012.
5.31Brightness of falling rain
Occasionally you can see distantrain falling, and in some case youmay notice that “when theseregions of falling precipitation areilluminated by direct sunlight, adistinct horizontal line can beseen, above which the precipita-tion appears much lighter thanbelow" (1013). What is responsiblefor the change in brightness?
1013.
5.32Rainbow colors
The color separation in theprimary rainbow is usually ex-plained as simple refraction andreflection of the light rays with-in raindrops. However, since thelight rays are incident on a drop'ssurface within a wide range ofangles to that surface (Figure5.32), shouldn't the emerginglight rays, even those of aparticular color, also leave thedrop in a wide range of angles?Why, then, do you see a parti-cular color subtending a par-ticular angle from the rainbow?
As a matter of fact, are rainbowcolors actually as pure as a prism's?If the simple refraction explanationis correct, shouldn't the rainbowhave pure colors?
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Figure 5.32Light rays from sun incident on awater d rop.
Why is the color sequence inthe secondary rainbow oppositethat in the primary rainbow, andwhy is the secondary rainbow soseldom seen? As a matter of fact,why can only two rainbows beseen in the sky? lf the primaryrainbow is due to a single reflectionof light rays inside the raindrops,and the secondary rainbow is dueto a double reflection, should notthere be more rainbows resultingfrom further internal reflections?
A double rainbow can also beseen in the beam of a searchlightduring a light rain at night. As thebeam sweeps through the sky, therainbows slide up and down thebeam and may even disappearbriefly. Can you account forsuch motion of the rainbows?
164, Chapter 3; 165, p. 177;380; 954, pp. 174-179; 983,Chapter 3; 1014, Chapter 13;1015 through 1021; 1499,"1627 dvrough 1631.
122 'l1|e flying circus of physics
5.33Pure reds in rainbows
Why can pure reds be found onlyin the vertical portions of rainbowswhen the sun is relatively low?*(The sun must be low so that thevertical portions of the rainbowscan be seen; if you are viewingthe rainbow from a high point,the sun will not have to be so low.)
1022.
‘Even the most commonplace featuresof the outside world still afford freshunderstandings and surprises. Fraser(1022) points out that this Simple teature of pure reds being restricted to
how esmped notice until his paper of1972. As another example of modernwork, it has only been recently thatphotographs of the infrared rainbowhave been taken (1023, 1024), thusallowing man to see for the first timewhat has periodically hung in the skyfor millions of years.
5.34Supernumerary bows
Sometimes several pink and greenbows can be seen below and adja-cent to the primary bow. Veryrarely they can also be foundabove the secondary bow. Whatcauses these additional bows?Don't they come as a surpriseif you draw too simple a pictureof the rainbow? Why aren't theyfound between the primary andsecondary bows?
164, pp. 477, 483," 954, p.178; 983, Chapter 6; 1014,pp. 241-242; 1019 through1021," 1025.
the vertical portions of the rainbow some-
535
Dark sky between bows
Why is the region of sky betweenthe primary and secondary rain-bows darker than the rest of thesky?
164, pp. 482-483,‘ 954, pp. 179-180.’ 983, p. 56,’ 1020.
5.36Rainbow polarization
ls the rainbow polarized? lf it is,can you explain its polarization?
361, pp. 8-9,‘ 954. PP- 181- 182,‘983.PP- 59 ff; 1014; 1020; 1630.
5.37Lunar ralnbows
Lunar rainbows are very rare. lsthis only because moonlight isso much dimmer than sunlight,or is there some other reason?
164, p. 476,‘ 954, p. 189.‘ 1020.’1026.‘ 1027.
5.38Rainbow distance
How far away from you are rain-bows formed? That is, how dis-tant are the water drops? Isit possible to have a rainbow afew yards away from you?
If you look at a rainbow in yourgarden sprinkler, you may very well
see two bows crossing over eachother (Figure 5.38). Why?
164, p. 496; 954, pp. 169, 174;1020.
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5.39Rainbow pillar
What causes the very rare pillarof light that has been seen at thefoot of some rainbows (Figure5.39)? [Minnaert (991) gives aphotograph of such a pillar, alongwith the comment that these pillarshave not yet been explained,]
991; 1028, plate 24; 1029.
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She comes in colors everywhere 123
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5.40Reflected rainbows
If you ever get a chance to seeboth a rainbow and its reflectionin water, you'll notice they aredifferent in shape and position.If a cloud is present, for example,you may see something resemblingFigure 5.40. Why is there a dif-terence in the cloud's position rela-tive to the rainbow?
164, pp. 497-499; 165, p. 175'954, pp. 186- 187,’ 983, p. 68;1020, pp. 272-275.
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(dewbowsl and on ponds withoily surfaces? In particular, canyou explain their shape (Figure5.41al? Why do dewbows formed
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Figure 5.41a Figure 6.4lbDewbow in grassy field. Dewbows as seen by someone
under a street light at night
beck, and B. Rystedt, Refi1030.)
5-41 (AfterJ. 0. Mattsson, s. Nord-
What causes the rainbows seen by streetlights have yet anotheron dew-covered grass fields shape (Figure 5.41bl?
5.42Sun dogs
Sun dogs (mock suns or parhelia)are bright images of the sunthat sit to one or both sides of thesun. They are normally outsidethe 22° halo (tr the halo is visible),as shown in Figure 5.43, beingfurther away the higher the sun isin the sky. When the sun is higherthan 60°, however, the sun dogsdisappear. Can you explainwhat produces the sun dogs andwhy their position and existencedepend on the sun's height? Also,why are they so much more color-ful than the 22° halo?
164, pp. 510 ff,’ 165, PP. 169-171; 36 1, PP- 24-25' 362,pp. 140 ff; 380; 954, pp. 196-
176,- 954, pp. 184-res; 1020; 9 ' ‘pp’ ' ’1030; 1031. 991; 1044 through 1051.
124 The flying circus of physics
5-43The 22° halo
Halos around the moon and sunare fairly common in most areas.The primary halo is 22° from thesun or moon (Figure 5.43) and iscolored red on the inside andwhite or blue on the outside.Except for the corona immediatelysurrounding the sun or moon,the sky inside the 22° halo isdark.
Certainly the halo is caused byscattering of the light somewherein the atmosphere, but what kindof scattering could give such a uni-form design? For example, would
you expect to get a 22° halo fromsunlight scattered by high altitudedust? Also, why is the area withinthe halo dark?
Almost universally the halo hasbeen thought to be a sign of im-minent rain. ls there any truthto that belief?
164, pp. 512-513; 165, pp. 169-174; 219, PP. 298-299; 360, pp.78-79; 361, PP- 24-25' 362, pp.140-143; 954, PP. 190-195'983, Chapter 4; 991.‘ 1033through 1050; 1610.
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Figure 5.45
5.45Sun pillars
Pillars of sunlight above and belowthe sun (Figure 5.45) can be seenfairly often near sunset or aftersunrise. The columns may bewhite, pale yellow, orange, or pink,so they are quite pretty. Undersome conditions they can evenbe seen above and below outdoorartificial lights such as streetlights.What causes these pillars?
164, pp. 543-544,‘ 165, pp. 169,172,‘ 361, PP. 32-33; 362, PP.148- 149,‘ 954, PP. 201-202,‘ 983,
$292310and sun dogs around the sun pp' 135 m 1028' p/are 23' p'245' 1033,‘ 1035' 106$ 1065;5.44 twice as wide as normal rainbows? 15g4_
Fogbows
Why are fogbows—rainbows formedin the fog—whitish bands withorange on the outside and blueon the inside? Why are they about
Can foqbows be produced bystreetlights? If so, what differencedo you expect from the fogbowsformed in sunlight?
165, p. 175' 380,‘ 954, p. 183,‘1020,‘ 1030,‘ 1032,‘ 1628.
She comes in colors everywhere 125
I ' “ “ " "'"'f{""'_¢n~'P‘ ' P
0l d
"j‘I,m m,, V. r T1 / l
i
¢ p > Zegith
d
h. if
C
/7 ‘ ' .r,.»o.-.“ ~-t... II
k~ _ J". Sun ” \-
e
Figure 5.46
P c
3 k
Some of the possible arcs, halos, and sun dogs around the sun.(Not all can be visible simultaneously.)
5.46Other arcs and halos
The full array of possible arcs and example, has apparently onlyhalos could be awesome if all ofthem were visible at once. (SeeFigure 5.46.) Usually, however,you will see only a few arcs orhalos. Some are so rare, in fact,that their existence is still con-troversial. The Lowitz arc, for
shapes tremendously as
watch as long as possibloccasional sketches. Secan explain the ones yo
recently been explained (1058).Several of the arcs can change
the sun
(a) 22° halo. (b) Sun dogs to22° halo. (c) 46° halo. (<1;Circumzenith arc. (0) Parheliccircle. (I) Sun dogs to 46° halo.(g) Parry arc. (h) §upraIateraltangent arcs to 46 halo. (i)Tangent arcs to 22° halo. (j)Lowitz arcs. (k) lnfralateraltangent arcs to 46° halo. (l)Paran thelia. (m) Paranthelic arcs(n) Narrow-angle oblique arcs toanthelion. (0) Anthelion. (p)Wide—angle oblique arcs of anthe-lion.
164, Chapters 4, 5' 165, pp. 169-174,‘ 361, pp. 28-29; 362, pp.140-149,‘ 380; 954, pp. 190-206,‘ 983, Chapter 4,‘ 991; 1034
¢ha"9°5 hei9hI. $0 ll Pills IO through 1038; 1044 throughe. making 1064; 1514; 1515- 1622.e if youu do find.
126 The flying circus of physics
electric fieldreflection
5.47Crown flash
Concurrent with a lightning strokein the main body of a storm cloud,there may be a brightening thatripples upward and outward throughthe top of the cloud. ls thisbrightening (called "crown flash"and "flachenblitz"l an unusualtype of discharge, or is it a peculiarreflection of light from the initiallightning stroke?
301, pp. 50-5 7,‘ 1067 through1069.
Polarizationl5.48 through 5.57)
5.48Polarization for car lights
Polarized plastic sheets were firstdeveloped to cover car headlightsso as to reduce the glare of an ap-preaching car at night. Howcould this be accomplished, andwhat would be the best orienta-tion of the polarized sheets?Don't forget that you still wantto see the oncoming car, so thelight shouldn't be entirelyblocked out. Will the tilt ofthe windshield matter? Couldyou obtain similar results withpolarized sunglasses?
1070, pp. 111-114; 1071through 1074.
5.49Polarized glasses and glare
Why do polarized sunglasses reduceglare? (Unpolarized sunglasses justdecrease the total amount of lightentering your eyes and do not pre-ferentially block the glare.) Whenwill polarized sunglasses improvea fisherman ’s ability to see beneaththe water?
1070, pp. 100-102.
5.50Sky polarization
clear sky polarized? Where shouldthe region oi maximum polariza-tion be? Can you verify yourprediction by using a pair ofpolarized sunglames? is light fromclouds polarized? Why areareas of the sky unpolarized?Why is the polarization in someparts oi‘ the sky perpendiculto that predicted by conventionaltheory? Can you also find theseneutral points and areas oi‘ per-pendicular polarization withyour sunglasses?
164, pp. 571-575; 165, pp.204,’ 170, pp. 413-414; 360, pp.62-63; 362, pp. 152- 153; 446,pp. 43-45' 533, pp. 193- 196;954, pp. 251-254; 1070, pp. 98-99; 1075, pp. 12- 17; 1076through 1079.
Why is the light coming from a
some
ar
194-
5.51Colored frost flowers
Some moming after a cold night,examine the thin, transparentfrost flowers on a window facingthe sun. if the flowers havestarted to melt and have formeda pool of water at the bottomof the window pane, look forreflections of the flowers in thepool (Figure 5.51). They willappear as patterns of coloredfringes. What causes the colorin these reflections?
1080.Window
glass
melted water
Figure 5.51Optics for seeing frost flowers.[After S. G. Cornford, Weather,23, 39 (I968).
5.52Cellophane between two polarizingfflters
Light will not pass through twopolarized sheets whose polariza-tion directions are perpendicular.But if clear cellophane is inserted
She comes in colors everywhere 127
between them, light is transmitted,the amount of transmission depend-ing on the cellophane's orientation.
If you replace the cellophane witha piece of plastic food wrap you willfind that very little light is trans-mitted. By stretching the foodwrap, however, you can onceagain get a large transmission. Whatis the fundamental differencebetween cellophane and un-stretched fwd wrap that ac-counts for the difference intransmission? How are the op~tical properties of the food wrapchanged by stretching?‘
170, pp. 420 fl? 360. PP- 14-16,‘ 1077; 1078,‘ 1081; 1082,pp. 79-93.
‘For a whole bagful of optical devicesand tricks that can be made with callo-phane, tape, etc., see Chapters 8 and 9of Crawford's excellent book Waves(170). Also see Refs. 1096 and 1097.
5.53Spots on rear window
if you wear polarized sun glasseswhile driving, you have probablynoticed the large spots, usuallyarranged in patterns, on therear windows of other cars. Whatare those spots, and why must
Figure 5. 54Detection of polarization change by syrup.
5.54Optical activity of Karo syrup
Although you probably haveused Karo corn syrup on yourpancakes, you most likely areunaware of the syrup’s mostfascinating property: its opticalactivity. Try this experiment;between two polarizing filters(they can be from polarizedsunglasses), put a glass of Karosyrup. Then place a white lightsource on one side of the glassand look at the light throughthe syrup (Figure 5.54). What isresponsible for the beautiful colorsyou see? By turning one of thefilters (while leaving the otherfixed), find the polarization of theemerging light and thus the
polarization change experiencedby the light in the syrup. By re-peating this procedure for severalthicknesses of syrup, you willdiscover that the polarizationchange depends on the distancethe light travels through the syrup.Why? l-low much rotation of thepolarization is there per centimeterof syrup, and is it clockwise orcounterclockwise? Why is the rota-tion in one direction instead ofthe other?
155 p. 425‘ I70, pp. 425-426,447,‘ 533, p. 198,’ 1070, pp.1 15- 118; 1082, pp. 136- 144;1083.‘ 1084.
you wear the polarized sunglassesto see them? Are the spotscolored?
360. PP. 14- 16.
5.55Animal navigation by polarizedlight
Honeybees, ants, and various othercreatures use the polarization ofthe sky‘ as an aid to navigation.How are they able to detect thepolarization angle of the light?
‘See Prob. 5.50.
And how can they use this abilityto navigate?
332, Vol. I, p. 36-7,’ 1070,P. 98,‘ 1085, Chapter 13,‘ 1066through 1089.‘ 1557.’ 1584.
128 ~ 11te flying circus of physics
5.56Magic sun stones
colors when under light of different polarizations. The crys
Dichroic crystals are different
tamay be clear with a faint yellowtinge under light of one polariztion, but dark blue when thepolarization is changed by 90°.
It is believed that the Vikingsused a dichroic crystal (cordlerite)to locate the sun when it was ndirectly visible. At least, accoring to the tales, they had somekind of magic “sun stone” bywhich they could find the suneven when it was behind theclouds or below the horizon.Since in the high latitudes thesun can be below the horizon
otd.
even at noon, such magic stoneswould have been a very valuablenavigational aid.
Why are different colorstransmitted through such crystalsfor different incident polarizations?Can the cyrstals really be usedfind the sun even if the sky iscloudy or the sun is below thehorizon?
170. PP. 448-449.
5.57Haidinger's brush
to
You may not realize it, but youare capable of detecting polarizedlight with your own eyes. Bylooking through a polarizing sh(polarized sunglasses, for examPat a bright light, you will momen-
utarily see a yellow hourglass figwith a blue cloud to each side
eetle)
1'8
. -:<'=:'=?s='<‘=;i;-. A
E Yellow\
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Figure 5. 5 7(Figure 5.57). Suddenly rotatingthe filter in its own plane mayhelp you to spot the hourglasseasier. This pattem is calledHaidinger's brush and is a directresult of the linear polarizationcaused by the filter. But why?What part of the eye is sensitiveto the polarization sense, andwhy is this particular pattemcreated? l-low does the orientationof the hourglass depend on thepolarization axis? Why does thepattern fade after a few seconds?I can see the brush fairly well,without a polarizing filter, inthe partially polarized light ofthe sky. Some people see it soclearly that it becomes irritating.
You can also detect circularlypolarized light with your eyes:left-circularly polarized lightgives a yellow brush tilted tothe right at about 45°, whereasthe opposite polarization givesa brush titlted to the left at about45°. Why?
954, pp. 254-257; 1070, pp.95-.97; 1090, pp. 300-304,-1091, Vol. 2, pp. 304-307;1092 through 10.94; 1621.
Scattering(5.58 through 5.90lRayleigh and Mie scattering
diffractiondispersion
5.58Sunset colors
All of us too often neglect sunsets,especially physicists who tend toshove the twilight colors under theheading of “Rayleigh scattering"and then forget them. Can youexplain the beautiful variety ofcolors in the twilight sky? (Thesetting sun may be red, but thesky is certainly not iust red.) Asthe sun sets, the western sky firstassumes yellow and orange tints.By the time the sun has turneda fiery red, the afterglow left inthe western sky varies upward fromthe horizon from a yellow-orangeto a green-azure. Eventually thearea about 25° above the westernhorizon turns rose-colored (the“purple light" discussed below).
Especially brilliant twilightcolors can be seen soon after maiorvolcanic eruptions. What causessuch color enhancements?
164, pp. 566-567.‘ I65, pp.184 ff; 380; 954, Chapter 11;983, pp. 234-244; 1075' 1102through 1109; 1526.
She comes in colors everywhere 129
5.59The blue sky
Probably the all-time standardphysics question is “Why is thesky blue?" Physicists often tossit aside with a few mutteringsabout “Rayleigh scattering.“Certainly the question deservesbetter treatment than that. Forexample, what part of the skyis bluest, and why isn't the entiresky a uniform color? Does thedaytime sky color actually followthe Rayleigh prediction? Whyisn't the sky blue on nights witha full moon? What is scatteringthe sunlight to produce the day-time sky color? Would you geta blue sky if the scatterers weremuch larger or much smaller?Finally, why is the sky on Marsblue only within a few degreesof the horizon, and black over-head?
164, Chapter 7; 165, pp. 192 ff;170, pp. 559-562,‘ 466‘,PP. 35 ff)‘954. PP- 238-251; 983, Chapter9; 1075, p. 10; 1079; 1098through 1102.‘ 150$ 1526.
5.60Twilight purple light
What causes the purple light (whichmay be more pink than purple)that first appeals in the westemsky as the sun sinks beneath thehorizon (Figure 5.60)? It is thebrightest about 15 to 40 minutesafter sunset.
ls the same physics responsiblefor the “second” purple light thatsometimes appears after the com-mon one has vanished and which
TwilightZenith purple
Belt of /' \ “gmVenus '1' \
I(7 -,. --'-1 .\l-.
" \\ '-‘-11;: '_'¢':;I:"
E8flh'S \I lshadow \ I
‘\ I
Hvrizon Sunbelow
horizonFigure 5. 60Sunset phenomena. (AfterH. Neuberger, Introduction toPhysical Meteorology, Pennsy-lvania State University.)may last up to two hours aftersunset? How could the sun stillprovide light to the sky afterhaving set an hour or so earlier?
154, p. 557,‘ 155, pp. 184-192,’954, pp. 270-280; 1075' 1102;1 104,’ 1 1 10.
5.61Zenith blue enhancement
I-lave you ever noticed the zenith(overhead sky) turns a deep blueduring sunset (Figure 5.60)? Isn' Ithat strange? Wouldn't you thinkthe zenith would be red, for thesame reason the setting sun is red
466, pp. 207-208,’ 1075,Chapter 4; I 102.
?
5.62Belt of Venus
What causes the twilight's rosypatch ("belt of Venus") thatborders the earth's shadow as theshadow rises out of the east(Figure 5.60)?
154, p. 555,‘ 155, pp. 184 ff}954, pp. 268 ff; 1075.
5.63Green street lights and redChristmas trees
While flying into a city you mayhave noticed that many streetsare lit by green lights. When youdrive through these streets, how-ever, the lights are not green at allbut white. Why is there a colordifference in the two situations?Similarly, why is the light from adistant Christmas tree primarilyred when in fact the tree iscovered with lights of manycolors?
1111, pp. 172- 173,‘ 1112.
5.64Brightness of daytime sky
Why is the daytime sky bright?Can you calculate roughly howbright it is?
164, pp. 563-565' 170.PP. 559-562; 465, PP. 35 ff; 954, pp.245-247,‘ 1075‘ 1100, P. 33.
130 The flying circus of physics
vision reflection
5.65Yellow ski goggles
Although skiers wear yellow-tinted goggles largely to befashionable, they often claimthat the goggles improve theirvision on hazy days. Supposedly,a sklier can better distinguish thesmall snow bumps in his path.Such a claim must have somevalidity, because the famous polarexplorer Vilhjalmur Stefansson alsorecommended amber glasses fortravel across snow and ice fields.Why might yellow glasses help?For example, is there a dominanceof yellow in snow-reflected sun-light on hazy days?
354; 1113. PP. 200-202.
5066 '
Stars seen through shafts
Ever since Aristotle men havebelieved that stars can be seenin the daytime if they areviewed through long shafts suchas chimneys. A shaft willdecrease the total skylight seen,thereby (supposedly) allowing thestars to be distinguished in thesmall patch of light at the top ofthe shaft. Your partial dark adap-tation (due to the smaller amountof skylight you see) may also aidin the distinction. Do you believesuch measures will actually makestars visible in the daytime? Canyou verify your belief by calcula-tions and by trying the experiment?
1114,‘ 1115.
absorptionscattering
5.67Colors of lakes and oceans
What is the color of a clear, cleanmountain lake? Does it matter ifthe sky is clear or cloudy? l-lowmuch do the material on the bot-tom and the depth of the watermatter? What is responsible forthe different colors of otherlakes? What color is the oceannear the shore and far at sea?What colors do you see in oceanwaves?
While swimming as deep as pos-sible, hold out a hand horizontallyand notice that the top is a differ-ent color than the bottom. Whyis there a color difference?
360, pp. 17- 19; 380; 466', pp.201-203; 954, pp. 308-335‘992, Chapter 13; 1116 through1 1 18.
absorptiontransmission
scattering
5.68Color of overcast sky
If you have ever lived in thecountry, you may have noticeda seasonal change in the color ofan overcast sky. Some peopleclaim that an overcast sky isslightly greener in the summer thanin the winter. Now l could make
the obvious guess about what causesthis color change, if it really doeshappen, but is there any validityto my guess?
1 119.
5.69Seeing the dark part of the moon
When the sun has iust set and thenew moon appears as a narrowcrescent, the "dark" part of themoon can be seen. How is thatpossible?
466, p. 199,‘ 954, p. 297.
5.70White clouds
Why are most clouds white? Whyaren’t they blue like the sky?Why are thunderclouds dark?
332, Vol. I, p. 32-8; 1123'1124.
5.71Sunlight scattered by clouds
Why does water scatter so muchmore sunlight after it has con-densed to form clouds than before,when it was just water vapor? Isn'tthe total number of atoms thesame, and shouldn't the scatteredlight thus be the same?
332, Vol. I, p. 32-8,‘ 1123.
She comes in colors everywhere 131
Figure 5. 72A kayaker finding his waythrough the ice field by the mapin the sky.
5.72Maps in the sky
Over the ice fields in the far north,large maps of the surrounding re-gion sometimes appear at thebase of overhanging clouds. Thesemaps, called “ice blink" and"cloud maps,“ allow the Eskimoto pick a route through the icefield if he is kayaking, or overthe ice if he is sledding (Figure5.72).
On approaching a pack,field, or other compactaggregation of ice, thephenomenon of the ice-blink is seen wheneverthe horizon is tolerablyfree from clouds, andin some cases evenunder a thick sky. The“ice-blink” consists in
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a stratum of a lucidwhiteness, which ap-pears over ice in thatpart of the atmosphereadjoining the horizon. . .when the ice-blink oc-curs under the mostfavorable circumstances,it affords to the eye abeautiful and perfect mapof the ice, twenty or thirtymiles beyond the limitof direct vision, but lessdistant in proportion asthe atmosphere is moredense and obscure. Theice-blink not only showsthe figure of the ice, butenables the experiencedobserver to judge
whether the ice thuspictured be field or packedice; if the latter, whetherit be compact or open,bay or heavy ice. Field-ice affords the most lucidblink, accompanied witha tinge of yellow; that ofpacks is more purelywhite; and of bay-ice,grayish. The land, onaccount of its snowy cover-ing, likewise occasions ablink, which is more yellowthan that produced by theice of fields (1120).
Can you explain these cloud maps?
1075, p. 8; 1113, p. 220; 1120through 1122.
132 The flying circus of physics
Mother-of-pearl clouds5.73
Not all clouds are white or dark.Mother-of-pearl clouds (nacreousclouds) may have very beautiful,delicate colors. Though they arerare and are usually seen only inthe high latitudes and only aftersunset, they can occasionallybe bright enough to color snowon the ground. What is differentabout these clouds so that theyshow such colors? Do the colorsarise from a fortuitous particlesize? Why are these clouds usuallyconfined to the high latitudes andto an altitude range of about 20to 30 kilometers?
361, pp. 20-21, 28-29; 362,pp. 74-75' 536, p. 170,‘ 954,pp. 229-230,‘ 1124 through1129.
illumination
scattering
intensity
interference
5.74Young's dusty mirror
When you look past a small lampdirectly into a dusty mirror,you will find that the reflectedimae of the lamp is surroundedby distinct colored frines. Avery clean mirror won't make thefringes; you must have a dustyor slightly dirty one. What causesthe fringes, and how many fringesof any one color are there?Most of all, why must the mirror bdusty or slightly dirty?
1 130,‘ 1 131.
B
Sudden end _tobeam , ~
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Il
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5.75Searchlight beams
1._‘[_ .IL’1 ' - __t.~_- In-0‘ ..~..-;-__:'.;.-.‘
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Why do searchlight beams (the kind do (Figure 5.75)? Wouldn't youused for airplane detection in expect a gradual fading of theWorld War ll but that have now been beam?demoted to siopenings) end as abruptly as they
5.76Zodiacal light and gegenschein
'I‘he next time you find yourselfaway from city lights on a clearmoonless night, search for thezodiacal light and gegenschein. Theformer is a milky triangle that maybe in the west for a few hoursafter sunset or in the east beforesunrise. The triangle is nearly asbright as the Milky Way and isoriented along the plane of the
g“°““g s“"°"""'k°‘ 954, pp. 252-253; 1147.
ecliptic.* The gegenschein is arather faint light seen at the an-tisolar point in the sky. What isresponsible for these lights in thenight sky?
t,1
954, PP. 290-295‘ 1143 through1146.
‘The ecliptic plane is the plane in whichthe earth orbits about the sun.
She comes in colors everywhere 133
reflect ion
Figure 5. 77
5.77Windshield light streaks
When driving through rain atnight you will find long streaksof light on your front windshielddue to the lights outside yourcar (Figure 5.77). Each streak ap-pears to run through the lightssource, and the smaller sources(such as streetllghts) give morepronounced streaks. As you move,
Streak of light in windshield from streetlight.
the light streaks move too. Ifyou step outside or look throughany of the car's other windows,however, you won't see them.What causes these streaks? Arethey as prevalent when it's notraining?
1 148.
538
Color of a city haze
If you've lived in a large city, youalmost certainly have spent part ofyour life in a haze. Why are suchhazes brown? ls it due to somekind of selective absorption of thelight? If so, by what? Or is it dueto dispersive scattering of thelight? Might it depend on whatyou're looking at through the haze?
1112; 1 163; 1164.
ull ‘ g
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*'*2'¥f'eil’l“l" ,\“You win a little and you losea little. Yesterday the air didn'tlook as good, but it smelledbetter. "
la;
5.79Glory
If you stand on a mountain withyour back to the sun and peerinto a thick mist below you,there may be a series of coloredrings around the shadow of yourhead. This set of colored rings,which may even be fuU circles,is called the glory (as well asthe anticorona or brocken bow).You may momentarily feeldivine when you notice thatthis beautiful and saintlydisplay is around your head butnot around a companion's. Whatcauses this seemingly divine selec-tion?
Glories are now most often seenfrom airplanes. Next time youfly, sit on the side away from thesun, and watch for the glory aroundthe plane's shadow on the cloudsor mist below. I have seen threefull spectrums at once, and as manyas five have been observed andphotographed.
What causes the glory? Why doesit surround the shadow of yourhead? What is the color sequencein each ring? l-low does the glorydepend on the size of the particlesin the mist?
164, p. 555' 165, pp. 180- 184;360, pp. 68-70; 361, PP. 4-5,"362, pp. 138-139; 380; 536,p. 131; 954, pp. 224-225; .983,Chapter 7,’ 1015,‘ 1017,’ 1019,‘1028, p. 130; 1149 through 1156;14.9.9; 1626.
134 The flying circus ol physics
5.80Corona
Why are the sun and moon some-times surrounded by bright bands,called coronas? Usually there isa single white band, but occasional-ly there will be blue, reen,andred bands outside the white one.If you're lucky, you may even seetwo such spectrums. What causes thebrightening, and why can you dis-tinguish colors only occasionally?What determines the corona's widthCan you predict the color arrange-ment?
164, pp. 547 ff; 165, pp. 178 ff;360, pp. 78-79; 536, pp. 130-131; 954. PP. 214-219; 983.Chapter 5
5.81Frosty glass corona
Walking past a frosty store windowon a cold winter niht, you mayfind the interior lights of the storesurrounded by colored rings. Atfirst thought, these colored ringsseem to be the same as in thesolar and lunar coronas. Inthe store window, though, theimage of the light is surroundedby a black band, not a whiteband as in the coronas discussedabove. Why is there a difference?And again, what is responsible forthe colored rings?
954, pp. 219-221,‘ 983, p.157 ff.
5.82Bishop's Ring
A different type of corona (anda much larger one, being about15° in angular radius) is the whiteand red-brown Bishop's Ring causedby volcanic dust spewed into theatmosphere. (After some volcaniceruptions the twilight sun turns abeautiful gold, the twilight skycolors take on a brilliant richness,and one can also see a secondpurple light* which lasts for hoursafter sunset.) What size particlesare responsible for the red-browncolor if that color is present? Willthe Bishop's Ring be colored ifthere is a large range of particlesizes?
164. p. 555' 165, pp. 178,191; 536‘, P- 130; 954, p. 282;983, pp. 167, 243; 1104 through1108; 1109, pp. 430-434, 441,-1110.
'See Prob. 5.60.
5.83Streetlight corona
On your nighttime walk you mayalso be struck by the colored ringsaround the streetlights you pass.Is the same physics responsible forthis corona as for the solar andlunar coronas and the store-lightcoronas? There is a simple test toshow that there is at least somedifference. If you screen off the
streetlight, a store's interior lights,and the moon or sun, do thecoronas in all three cases re-main? If any one disappears, thenyou should explain why it is dif-ferent from the others.
954, pp. 221-223,‘ 109 7. PP.224-225' 1157,‘ 1158.
5.84Blue moons
My grandmother is from Aledo,Texas, where the population isabout 100 people, dogs, andchickens. According to her, ex-citement comes to Aledo onlyonce in a blue moon. But howoften does a blue moon come?In fact, why would the moonever be blue? Can there be bluesuns too? ls either the moonor sun ever green?
536, p. 121,‘ 954. PP. 2.98-2.99,’983, p. 242; 991,‘ 1014, p. 421-423.‘ 1101; 1159 flrrough 1162.
5.85Yellow fog lights
Why are car fog lights yellow?Does it really help to have themyellow? Does it matter whetheryou're driving in the city or inthe countryside?
983, p. 244; 1 111, p. 40.
She comes in colors everywhere 135
5.86Blue hazes
There is a colorful but mysterioushaze that appears over vegetatedareas relatively free from man-made contamination. The BlueRidge Mountains of Tennessee andthe Blue Mountains of Australiaare both well known for theirbeautiful blue haze. What causesthis type of haze? Smoke? No,because the haze is found inrelatively uninhabited areas.Windswept dust? No, because thehaze has the deepest blue duringvery light winds. Finally, thehaze cannot be fog, because theblue is most common during warmsummers. What, then, causes thehaze, and why is it blue?
1112; 1165; 1166.
5.87Shadows in muddy water
Why can you see your shadowin slightly muddy water but not inclear water? Why can you seeshadows of other people only ifthe water is very muddy?
You might also notice thecolorsground shadows in slightlymuddy water. The edges closest toyou are colored differently fromthose farthest from you. Whatcauses this coloring? Does the colorof the edges depend on whetheryou are facing toward or away fromthe sun?
954. PP- 332-333,' 1565
5.88Color of milk in water
After adding a few drops of milkto a glass of water, look throughthe glass at a white light such as alight bulb. The source will appearto be red or pale orange. Next lookat the light reflected from the glass.The light will be blue. Why isthere such a remarkable change ofcolor?
aso, pp. so-61.
5.89Color of cigarette smoke
If you closely examine the smokerising directly from a cigarette,you'll find that the smoke isslightly blue. If the smoke is in-haled and then blown out, how-ever, the smoke ls white. Why isthere a change? (it is not due toremoval of tar and nicotine.)
155, p. 41 1; 360, p. 6'2; 533,p. 147; 536, p. 383; 954, p.236-237,’ 983, p. 235.
5.90Color of campfire smoke
A similar change of color is ap-parent in campfire smoke. Whenit is viewed against a dark back-ground (trees, for example), thesmoke appears to be blue. Higher
up, however, when it is seenagainst a light sky, the same smokeappears to be yellow. Why does itchange its color?
533, p. 147; 954. PP- 235-237,309.
5.91Oil slick and soap film colors
Why do oil slicks on the streetdisplay colors? How thick are theseslicks? Must the street be wet?Can you see them on overcastdays or only in direct sunlight? Ifyou can calculate the width of oneof the colored rings, compare yournumber with a measured width.Will the finite size of the sunchange the theoretical width of therings in any way?
Why do you see colors in soapfilms? How thin are the soap films,and in what thickness range willthey show colors? Why that range?Why are some parts of some filmsblack? Finally, why is there sucha sharp boundary between thecolored and black areas? Shouldn'tthere be a gradual change?
322; 528 through 531; 533,pp. 13.9 ff.
5.92Color effects after swimming
Why do you see colored ringsaround lights after you've beenswimming?
I36 The flying circus of physics
refraction diffractiondispersion
crystal structureSUGSS
5.93Liquid crystals
If a deformable container con-taining a liquid crystal issqueezed, colors appear aroundthe squeezed area. The particularcolors you see, however, will de-pend on your angle of view. l-lowdo the angle dependence and colorsequence compare with those ofan oil slick? If there is a difference,can you explain it?
1081; 1132 through 1137.
5.94Butterfly colors
Why are the wings of butterfliescolored? Are the colors due topigmentation? In some wings,yes, but in others, such as forthe Morpho butterfly, the colorsdo not arise from any pigmenta-tion. A possible clue to theirorigin may be found by look-ing at a wing from several differ-ent angles: the wing takes onslightly different colors for dif-ferent viewing angles. Why?
1128 through 1142,- 1625
5.95Dark lines in a fork
You have probably-seen the darkline which lies between yourfinger and thumb when they'realmost touching (Figure 5.95).You can see many such dark linesby looking through a fork‘sprongs as you rotate the fork.What's responsible for these darklines? Can you predict whetherthe spacing between the lines willdecrease or increase for a giventurn of the fork?
170, p. 487.
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Figure 5.95Dark line seen between twofingers.
5.96Eye floaters
What are the tiny, diffuse spotsyou often find floating in yourfield of view? Are they illusions?Are they bits of dust on the eye's
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surface? Or are they objects with-in the eye? By looking at a bright
light source through a pinhole insome opaque material, you'll finda beautiful array of floating con-centric circles and long chains(Figure 5.96). If the spots aremerely shadows, then why doyou see concentric circles andchains? Also, why does a pinholehelp you see the structure of thespots?
170, p. 530; 1091, Vol. 1, pp.204 ff; 1167; 1168;
Figure 5.96Structure of the floaters in youreyes.
5.97Points on a star
What causes the ocsional spikedappearance of car headlights? Thecause cannot be entirely physiological since photographs of the head-lights also show spikes. Similarly,what causes the spikes found instar photographs? ls it possible tofind any number of spikes on astar or a headlight photograph?In particular, can you find a starwith an odd number of points?
1 169, p. 3.
She comes in colors everywhere I37
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Figure 5.98Demonstration to show Poisson spot in the shadow of a small sphere.
5.98Poisson spotWhy is there a bright central spotin the shadow of a small disc orsphere (say, two millimeters indiameter), whereas larger objectsgive ordinary dark shadows? Byusing a cardboard tube and ascreen as shown in Figure 5.98,you'll find that not only is therea bright central spot in the shadowof the disc or sphere, but theshadow is actually composed ofmultiple dark and bright rings.What causes the central spot, whichis called the Poisson spot,* andthe rings? Why aren't they foundin your own shadow?
Opattem on Semen
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204; 1169, p. 200; 1170, pp.359-360.
‘When Fresnel defended his dissertationbefore his committee in the 18005, oneof the committee members, Poisson,remarked that if the dissertation werecorrect, there would be a bright spot ina spherical object's shadow. This resultclearly being ridiculous, he concludedthat the dissertation must be wrong.But as a matter of fact, the spot hadbeen seen some 50 years earlier and,soon after Poisson's conclusion, Aragorediscovered the central bright spot.ln spite of all this, in one of thosecurious twists in the history of physics,it is the objector‘s name that is associated with the spot.
refractioninterferenceturbulence
5.99Eclipse shadow bands
For several minutes before andseveral minutes after a total solareclipse, dark bands called shadowbands race across the ground. The
bands are separated by severalcentimeters and are about twocentimeters wide. What couldcause these bands? And why dothey appear during an eclipse? Arethey produced in our atmosphere,or are they made when the sunlightpasses the moon?
1171 through 1181,‘ 1561.
5.100Sunset shadow bands
Another set of shadow bands hasbeen seen during normal sunsets.Ronald Ives (1182) has reportedsix observations in 15 years, allof which were from high pointslooking down on flatlands. Thesebands were several miles wide andmoving at about 40 miles perhour. Are these bands anotherexample of shadow bands? In anycase, what causes them?
1182.
5.101Bands around a lake's reflection
As you fly toward a distant smalllake, eventually reaching theangle for optimum reflection ofthe sun, why are there alternatingdark and bright bands around theprincipal reflection from the lake?
360, p. 12.
refractionscintillation
turbulent cells
5.102Star twinkle
My mother taught me to say,“Twinkle, twinkle, little star. . ."Why does a star twinkle? Ap-proximately where is thetwinkling produced? Does a star
138 The flying circus of physics
change colors or move aroundbecause of the twinkling? Does ittwinkle more in the winter orsummer? Does a red star twinklemore than a white star? Do yousee twinkling when you use atelescope? Do the moon andplanets twinkle?
What causes the shimmer of anobject when you view it overheated surfaces such as, forexample, hot car tops or roadways?l-low high above the heated surfacewill your viewing be affected? Isit the air closest to you or farthestfrom you that dominates theshimmer?
164.PP. 462-466; 165, PP. 166-169,‘ 954. PP- 63-71; 983, PP.17-19; 1111, pp. 80-81; 1183through 1188.
radiation forces
photochemistry
refraction
5. 104Optical levitation
Earlier in this book we discussedlevitation of balls by air currentsand water jets* and in both casesthere was surprising stability.Light can also levitate and stabilizeballs, for light from a relativelypowerful laser has lifted and heldin suspension transparent glassspheres of about 20 microns indiameter (Figure 5.104). Howcan light lift such a sphere againstgravity? And how is stabilityagainst sideward motion provided?
1 189 through 1191.°Probs. 4.20 and 4.22.
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Figure 5. I04Glass sphere suspended in anupward directed, expandinglaser beam. [After A. Ashkinand J. M. Dziedzic, Appl. Phys.Let., I9 (8). 283 (1971).)
5.103Bleaching by light
How does sunlight fade coloredclothing? Does the rate of fadingdepend on the color? Why doessunlight or fluorescent light causeoil paintings to fade? Why aresome foods and beverages, such asbeer, shielded from sunlight? Isany particular light frequency mostdestructive?
466, pp. 2 14-215.
diffraction
5.105Lights through a screen
Car headlights viewed through ascreen look very different thanwhen they are viewed without
a screen (Figure 5.105). What,in detail, causes the difference?
533,p.16'3. in
1}’ ‘QFigure 5.105The change in the appearance of a light when viewed througha window screen.
She comes in colors everywhere 139
blackbody emissionatmospheric transmissionvision
5.106Star color
Some stars look red. Some lookwhite. Are there blue stars? Orgreen stars?
5.107Luminous tornado
There have been many reports,including published accounts,describing mysterious lights as-sociated with tornadoes. Thoughthey are generally dismissed asillusions, there has been at leastone published photograph (1192,1193) that apparently showsluminous columns in twonocturnal tornadoes. Eyewitnessaccounts of these particulartornadoes gave exciting descrip-tions of the light emission.
The beautiful electric bluelight that was around thetornado was something tosee, and balls of orange andlightning came from the conepoint of the tornado l1193l."
sewer saw the following:I was looking. . . up at theclouds when l saw some-thing that looked like asearchlight beam extendout of the cloud and reach
‘Copyright © 1966 by the AmericanAssociation for the Advancement ofScience.
to the skyline. It seemeda bit brighter than the cloudbackground. Edges werevery sharp, overall intensityeven, sides parallel. Widthabout a degree of arc. Nomovement or turbulenceevident. The phenomenonwas interesting enough soI took out my Polaroidglasses and observed this"ray" through them,twisting the lens to lookfor polarization. Nopolarization was noted.This ray was obvious enoughso that passersby on thestreet were staring at it.All this took, say, 60 to120 seconds (or more).Then abruptly the ray wasinstantly repleced by anormal tornado funnel.No transition stage wasnoted. The funnel didnot descend from thecloud layer. lt appearedover all, in situ (1193l."
Although these phenomena arepoorly understood, can you suggestcauses for them, perhaps makingsome rough numbers to supportyour suggestions?‘
224' 225' 1192,‘ 1193.I I
In another tornado occurence an ob- . PSee rob. 6.35 also.
triboluminescence
5.108Sugar glow
Late one night I was stirring somedry granulated sugar in a glass,which is kind of a late-at-nighttype of thing to do. Suddenly thelights went out. As I continuedto stir, I saw brief flashes oflight through the side of the glass.l-low did the mechanical stressand strain of my stirring cause thelight emission?
1194, pp. 121, 292, 378-387,‘1 195.
5.109Suntans and sunbums
What actually causes suntans andsunbums? is the same wave-length range of light responsiblefor both? Why is it more difficultto get sunbumed once you have atan? Can naturally dark skin be-come sunbumed as easily aslighter skin? What do suntain oils,lotions, and creams do to preventsunbum and promote suntan? Thepertinent point is, of course,whether they really do what theadvertising claims. If they inhibitwhatever causes sunburn, won’tthey inhibit suntan also?
Why are buming and tanningless likely when the sun is low orwhen you're behind glass? Whyare they more likely at the beachthan in a grassy backyard?
344, pp. 19-22; 466, p. 212;1203,’ 1512.
140 The flying circus of physics
photochemistry
5.110Fireflies
Catching fireflies at my grand-mother's house was one of themost enjoyable times of mychildhood (Figure 5.110). l haveread that the synchronous flashingof Asiatic fireflies is even morefascinating.
Imagine a tree thirty-fiveto forty feet high thicklycovered with small ovateleaves, apparently with afirefly on every leaf andall the fireflies flashingin perfect unison at therate of about three timesin two seconds, the treebeing in complete dark-ness between theflashes. . . . Imagine atenth of a mile of riverfront with an unbrokenline of. . .trees with fire-flies on every leaf flash-ing in unison, the in-sects on the trees at theends of the line actingin perfect unison withthose between. Then,if one’s imagination issufficiently vivid, hemay form some con-ception of this amazingspectacle (1 196).What mechanism produces the
light we see? That light is oftenreferred to as cold light, implyingthere is no energy lost to heating.
\.- ( /1
By permision of John Hart.Field Enterprises.
(An incandescent bulb, on theother hand, is a hot light.) ls thefirefly 100 percent efficient inconverting energy to the form oflight? What color is the light? Whythat color? Finally, how do theAsiatic fireflies lock themselvesinto a chorus of synchronousflashing?
1090, Chapter 4; 1194, pp. 538-554; 1196 through 1201; 1458;1585; 1624.
photochemistry
86
5.111Other luminescent organisms
Many other organisms producetheir own light, too. TheBrazilian railroad worm, forexample, has a red light on itshead and green lights down its side.Another type of luminescentorganism, the dinoflagellates, will“set the sea on fire" when disturbedduring the day (by a boat, say)but during the night they willrespond with a blue glow. One typeof crustacean, when dried, can bemade to glow by moistening. Sucha light source was used by WorldWar II Japanese soldiers when astronger light was too dangerous.Spitting on a bit of dried crustaceanwould give off enough light toread a map.
There have been many other,but less common, examples of
She comes in colors everywhere 141
natural luminescence. in onecase, cut potatoes glowed suf-ficiently that one could read bythem in an otherwise dark room.There has even been a case inwhich a corpse glowed in thedark. But the most disturbing,especially if one is relying ondarkness to conceal a slightindiscretion, have been the timesin which urine glowed in thedark.
In the case of the dlnoflagellates,why do they glow red during theday but blue during the night?In all these various examples, whatcauses the luminescence?
1194. pp. 457-492; 1200through 1202; 1458.
allow some soap manufacturers toclaim that their products get clothes“whiter than white”?
1205, p. 70.
fluorescence
photochemistrytransmission
5.112Photosensitive sunglasses
Some sunglasses are clear indoorsbut darken immediately uponexposure to sunlight. The changeis reversed soon after the sunlightis eliminated. What causes thisreversible change in the transmis-sion properties of the glass?
984,‘ 1204.
phosphorescence
5.114Fluorescent light conversion
How is ultraviolet light created andthen converted to visible light ina fluorescent lamp? How fastshould the conversion be? Youdon't want it so fast that the lamp’soutput shows the 60 cycles persecond of the line voltage used toexcite the tube. But then again,you don't want the lights to stayon long after you've turned offthe switch.
466, pp. 233-240; 1205, p. 76.
Vision(5.1 15 through 5.141)coherenceinterference
fluorescence
5.1 13Black-light posters
l-low does a black-light posterwork? Why does the same physics
5.115Speckle patterns
lf you look at a smooth, flat-blackpiece of paper at a 45° angle indirect sunlight, you will see a grainyspeckle pattern of various colorsdancing on the paper. Similar pat-terns are more commonly madewith laser light, but sunlight is cer-
tainly more convenient. ln eithercase, the pattern will move if youmove your head, but whether itmoves in the same or oppositedirection as your head will de-pend on whether you have normal,nearsighted, or farsighted vision.What causes these speckle patterns,and why are there colors in thesunlit patterns? Finally, can youexplain the movement of the pat’-tern and its dependence on yourvision?
1206 through 1209,’ 1560.
stroboscopic effect
5.116Humming and vision
If you hum while watching tele-vision from a distance, horizontallines will appear on the screen, andyou can make them migrate up ordown or remain stationary byhumming at the appropriate pitch.In a similar demonstration, a black-and-white—sectored disc is rotatedon a turntable. If you use a strobo-scope to illuminate the disc, youcan freeze the rotating sectors ormake them slowly migrate onedirection or the other by choosinga suitable flashing frequency. l-low-ever, you can also do this by merelyhumming at the proper pitch. Whydoes humming effect your visionin this way?
1210,‘ 1211.
142 The flying circus of physics
visual latency stroboscopic effect
light intensity
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Figure 5.1 I 7A normal pendulum swing changes to a circular motionif a polarioid filter is placed over one eye.
5.117Sunglasses and motion distortion
With a dark filter over one eye(say, half a pair of sunglasses),watch the swing of a simplependulum. Even though you knowthe pendulum's motion is in oneplane, the pendulum appears torevolve in an ellipse when the filteris in place (Figure 5.117). Tothe uninitiated, the surprising re-sult can be quite striking. . . andmysterious. The apparent three-dimensional motion can be en-hanced by hanging a string fromthe pendulum's pivot, for thenthe string acts as a reference ob-ject and the pendulum appearsto turn about it.
If you should drive while wearingonly half a pair of sunglasses, acar passing on your left will seem
to have a considerably differentspeed than one passing on yourright even if they actually have thesame speed. in neither case is theapparent speed the correct one.In addition, the apparent distancesof objects in the landscape will bewrong and even dependent onwhich side of the car the objectsare.
What causes the apparent threedimensional motion of the pendu-lum? What exactly does the filterhave to do with this motion andthe distortion of a car's speedand the distance of objects in thelandscape?
1212 through 1222; 1541through 1543.
5.1_1sTop patterns before TV screen
lf a flat top with a surface designis spun before a TV screen (witha stable picture and in an other-wise dark rcoml. Psychedelic pat-terns appaar on the top's surface.Undoubtedly the pattern stemsfrom the top's surface design,butwhy is the light of a TV needed?
170, p. as.
5.119A stargazer's eye jump
Why do you have a better chanceof seeing a dim star neighboringa bright star if you jump youreyes to one side of the stars?
332, Vol. 1, p. 35-3,‘ 412, p.439.
5.120Retinal blue arcs
Blue arcs of the retina areanother physiological problem cur-rently receiving attention. Purkinjefirst reported seeing them fromglowing tinder as he was kindlinga fire. For about 30 seconds hesaw two blue arcs extending fromthe tinder. You can see them your-self‘ under controlled circumstanc85
She comes in colors everywhere 143
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Figure 5.120Blue arc in your left eye'sfield of view. [After J. D.Moreland, Vision Research. 8.99 (l968).]
by using small holes punched intoa card that is then placed over alight. After sitting in the darkabout a minute (don't wait toolong), switch on the light. Depend-ing on the hole’s shape, variousshaped blue arcs (e.g., Figure5.120) can be seen for up to asecond.
What causes these arcs—scatteredlight inside the eye? Why, then,.are they always blue? Shouldn'tthey depend on the color of thescattered light? Perhaps they aredue to bioluminescence. Or may-be they could be due to a secon-dary electrical stimulation of nervefibers or neurons by other activenerve fibers. If the latter is true,the shape of the arcs as a functionof stimulus shape should tell ussomething about the retinaltopography. 1n any case, we stillhave to explain why the arcs areblue.
1224 through 1227.
‘One of Moreland‘s several papers (1224describes in further detail how to opti-mize the observation and how to de-monstrate it to a small audience.
l
5.121Phosphenes
Prisoners confined to dark cellssee brilliant light displays (the“prisoner's cinema") in theirperfect darkness. Truck drivers alsosee such displays after staring atsnow-covered roads for longperiods. In fact, whenever thereis a lack of extemal stimuli, thesedisplays-called “phosphenes"-
appear. They can be made at will,however, by simply pressing yourfingertips against closed eyelids,and some hallucinogenic drugsapparently give magnificentphosphene shows. They can alsobe produced by an electrical shockIn fact, it was high fashion in theeighteenth century to have aphosphene party (even BenjaminFranklin once took part) in which
visual latencylight intensity
5.122Streetlamp sequence
Sometime when you're driving atdusk, watch the streetlights tumon: they brighten in sequencedown the street. Does it reallytake electricity that much timeto travel from lamppost to lamp-
post? If there are intersectionswith several streetlamps, you'llfind those lamps turning onsooner than the lamps betweenintersections (Figure 5.122).This certainly can't be due toa lag of electricity. Why, then,are there time lags between thelamps?
1212 through 1222.
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Figure 5.1 22
I44 The flying circus of physics
a circle of people holding handswould be shocked by a high-volt-age electrostatic generator, phos-phenes being created each timethe circuit was completed orbroken.
In 1819 the Bohemianphysiologist JohannesPurkinje published themost detailed accountofphosphenes. Heapplied one electrodeto his forehead and theother to his mouth, andby rapidly making andbreaking the currentwith a string of metalbeads, he was able toinduce stabilized phos-phene images (1223). *Phosphene research is no longer
so academic, because recent workhas shown that those blind peoplewho experience phosphene dis-plays may someday be givenartificial vision by use of thosediplays. A miniature TV camera,placed inside an artificial eye,would send its electrical signalsto a small computer located insidea pair of eyeglasses. The computerwould in turn stimulate the brainby a network of electrodes thathad been placed adjacent anoccipital lobe. When the TVcamera detected an object in itsleft field of view, for example,the computer would stimulatethe electrode that would producea phosphene image in the leftportion of the person's field ofview. The person would thereforesee the external world.
Why are such visual displays
produced under electrical and pres-sure stimulations or when there isan absence of external stimuli?
1223; 1572; 1573.‘From "Phosphenes" by Gerald Oster.Published in Scientific American. Copy-right © 1970 by Scientific American,Inc. All rights reserved.
5.123Spots before your eyes
If you stare at a clear sky you willfind your entire field of viewcovered with moving specks. Thosespecks are always present, butusually you don't notice them.(Why is that?)
Although the jerking motion ap-pears to be random, if you feel yourpulse while watching the specks,you will find the motion correlatedwith your pulse and also see thatthe specks always follow certainroutes in your field of view. Whatare the specks, and what causes thejerking along those particularroutes?
1091, Vol. 1, PP. 222-223; 1168,‘1233. PP. 407-408.
5.124Purkinie's shadow figures
Close your eyes, place a hand overone, turn to face a bright light, andwave your other hand back andforth across your face so that theshadows of your fingers repeatedlycross over your closed, but ex-posed, eyelid. In the center of
your field of vision you'll see acheckerboard array of dark andbright squares, and down fromthe center there will be eitherhexagons or iust irregular figures.If you're using the sun as thelight source, you'll also see eight-pointed stars and various spirallines. What causes these severaldesigns?
1091, Vol. 2, pp. 256-257; 1234.
5.125Early moming shadows in youreyes
If you stare at a sunlit room im-mediately upon opening your eyesafter a night’s sleep, why will youbriefly see dark images in yourfield of view? If the images areshadows of objects in your eye,then why don’t you see theshadows all the time, and whydo they fade so quickly afterthis early moming glimpse?
1091, Vol. 1, pp. 212 ff," 1168.’1233, pp. 406'-407,‘ 1235.
color perception
5.126Purkinje color effect
In dim light a particular blue maybe brighter than a particular red,but in good illumination the rela-tive brightness may be reversed.Why should the relative brightnessof reds and blues depend on theillumination level?
332, V01. 1, p. 35-2.
She comes in colors everywhere 145
5.127Mach bands
How sharp is your shadowrs edge compncate the patterns’ of comm-,)_ they thought were X-ray diffraction pat.
when you stand in a strong light Figure 5.127 shows how the edge :°'"stLe5“um;'9 f'°m 'h:“‘:’ssa9_° °fs|),<_ _ , ays ro g common raction its.such as sunhght? If you |°°k care‘ pattem can be seen with 8 place They did find light and dark patterns onfully, you will see two shadows, the Of °8l'db08l'd held in from 0f 8 their films, and using those patterns theydarker one neatly inside the owe,-_ fluorescent lamp. Why are the calculated the wavelength. Unf0flu-The inside contour of the lighter bright and dark bonds and your "‘*‘°'Y- '=*-"" “'°"‘ '°"”'°° "‘*" "‘°*’ Pa‘
_ 9 terns you see in your own shadow andsfmdow has 8 dark ba_nd' the out. galfihtdow can they were not at all indicative of X-ray dif-side contour has a bright band. 9 P ° °E1'3P 9 - ,,a¢,,°,, (1 228,_There lS nothing llfllqllé 8b0lIi 954, pp_ 129_132. 1228
your body, because every shadow chapter 2. 1229 mmugh 1232has such edge patterns (though ‘I n early attempts to measure the X-raymore than one light source will wavelength, some physicists used what
\ //\\ //
Q --""""
Figure 5.127Mach bands can be seen in the card's shadow with this arrangement. If the lamp is one foot above a whilesheet ofpaper, then place the card one or two inches above the paper. Small horizontal motions of thecard may help you see the bands better. The graph shows the luminosity for various points on the paper.(Figures from Mach Bands: Quantitative Studies on Neural Networks in the Retina by Floyd Ratliff}published by Holden-Day, Inc.)
I46 The flying circus of physics
Land color effect
color perception
5.128Seeing the colors of your mind
lf an obiect looks blue, blue lightmust come from the obiect, right?In fact, each color you see corre-sponds to light with a certain fre-quency or a combination of severalfrequencies. This seems veryreasonable, but Edwin Land threwa wrench into the explanation witha few simple experiments that youcan do yourself.
What do you have after makingtwo black-and—white slides of acolored scene, using a red filterfor one slide and a green filterfor the other? Why, two black-and-white pictures of course.I-iow can you get anything elsewith black-and-white film?
But now, using two projectors,simultaneously project thoseslides onto a screen (Figure 5.128).Use a red filter with the slide made
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Figure 5.1 28Projection arrangement toshow Land color effect.
5%-
proiector light is sufficient forprojecting the "green" slide. What
each slide is only black and white,and the only colored light youuse is red, the superimposed pro-jection gives the full range of colorin the original scene.
filters used. All you need are twodifferent colors or even one colorand one white light. Both slidesneven be made in a single color
as long as the light frequency usedfor one slide is at least slightlydifferent from the light frequencyused for the other.
What usesthis recreation ofthe color of the original scene eventhough the color information isseemingly lost in the individualslides? Onca again, if an obiectlooks blue, must blue light neces-sarily be coming from that obiect?
1236' through 1239; 1566,‘ 1567.
with the red filter; the normal white
do you see on the screen? Although
There is nothing special about the
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533, pp. 104-105' 1091, Vol. 1,pp. 175-176.‘ 1516.
chromatic aberration
5.129Making colors with a finger
Watching with only one eye, movea finger across your view of a sun-lit window that is across the roomfrom you. When the finger firstbegins to block and distort theimage of the window, the side ofthe image nearest the finger turnsyellow-red (Figure 5.129). Asyour finger reaches the oppositeside of the image, that oppositeside turns blue. (You can see thesame thing using an incandescentbulb, but the blue is fainter.l Why
color perception
5.130Colors in a black and white disc
ls it possible to see colors in blackand white surfaces? Normally, itisn't, but try the following: con-struct a disc of alternating blackand white sectors, and then as thedisc is spun at low speed, concen-trate on it (but ignore the individ-ual sectors). After a few minutesyou'll find that the leading edgesof the white sectors will turn red,the trailing edges blue. (Differentshades will be seen for differentillumination levels.) At a fasterspeed the whole white sector willbe pink-red, and a green-bluewill cover part of the black section.With a still-faster speed, the colors
nnotbe distinguished but littlesparks of violet-pink and green-
She comes in colors everywhere 147
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Figure 5.1 30Disc that shows colors when spun.gray light seem to jump about.The disc in Figure 5.130 will giveall three effects simultaneously.Why do you see those colors?Why must you watch the disc forseveral minutes before the colorsappear?
332, Vol. 1, p. 36-1; 1091, Vol.2. PP. 255 ff,‘ 1231,’ 1240; 1241.
stroboscopei Iuorescence
5.132Floating TV pictures
While watching TV in an other-wise dark room, quickly run youreyes from about a foot to theleft of the screen to about a foot tothe right. You will see a bright,detailed, ghostlike image of the TVpicture floating in space to theright of the screen (Figure 5.132).You may even see three or four
Figure 5.132Ghost images of TV picture.
images, all right-tilted parallelo-grams. Why are these ghost imagesformed, and what's responsiblefor the tilt? Do you see the samesense of tilt if you move youreyes in the opposite direction? Arethere ghost images for a rapid ver-tical scan of your eyes?
1247.
phosphorescence
5.131Color effect from fluorescentlights
rotated faster (about 5 to 15 s),the color effects disappear. ButIf it is put under a fluorescent
you will see two concentric ringsthat are composed of altematingred, blue, and yellow bands. oucan also see colored fringes-yellowor orange, depending on the back-ground-if you watch a spinningcoin under a fluorescent lamp.Why does the fluorescent lightingcause these color effects? Can theybe photographed?
If the disc described above isVP
Y
1242 Uirough 1246.
hght, a new color effect vnll appear:
5.1333-D movies, cards, and posters
There are two methods of makingcommercial three-dimensionalmovies and comic books. Onemethod involves printing picturesin two colors, red and green, andthen using cheap glasses with redcellophane over one eye and greenover the other. The other methodemploys polarizers in the glassesand in front of the two projectioncameras, and the cameras projectsimultaneously onto the screen.I-low do these methods give astereoscopic illusion? As youprobably know, three-dimensionalmovies have not gained widespreadpopularity, which means that theremust be some drawbacks. Other
than the annoyance of wearing theglasses, what are the problems?
3-D baseball cards and postcards?Some bright red and blue posters,paperbacks, etc. give an impres-sion of depth if red letters areprinted on a blue background: theletters appear to be closer to theviewer than the background. Why?Do such depth illusions with dif-ferent colors depend on the illu-mination level? What other methodscan produce a stereoscopic illusion?
l-low is the 3-D effect gained in
533, pp. 105-106,‘ 1070, pp. 107-110,’ 10.92; 1213,‘ 1255 through1260; 15.91 duough 1607.
148 The flying circus of physics
5.134Enlarging the moon
Probably the most striking illusionin the natural landscape is theapparent enlargement of the moonwhen it is near the horizon (Figure5.134). Is this illusion broughtabout by atmospheric conditions,or is it a psychological effect? Canyou estimate the apparent enlarge-ment?
165.PP- 154-155533, PP. 62-63;954, pp. 155-166," 1248through 1253.
K1
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Nlilifiilififl.N$H'BOB&
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By permission of John Hart.Field Enterprises.
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Figure 5.135
5. 1 35Rays of Buddha
Not as frequently you will see
Moon-to-sun line
Sometime when you find a crescentmoon in the daytime sky, mentallydraw a line along its symmetryaxis (Figure 5.136). Does the linepoint to the sun? Shouldn’t it?
166; 1250 dirough 1254.Figure 5.136
crescent moon point to the sun?
She comes in colors everywhere 149
Occasionally you will see a sunset °'"°'9"19 7'0"‘ 1'18 50'1" Poll" I"in which brilliant rays of light the west. are-he wuss the entiregmgfgg from the gagging sun, fan. sky and converging to the antisolarning out across the western sky (Fig- 90"" In the 88$! But Wilt. Howum 5_135)_ This d|,p|ay is an,“ by could a cloud or mountain blockmountains or clouds blocking part part of the sunlight to give a fanof the sunlight. What color are display? After all, the sun is verythe rays? What color is the sky far away from us, and the sun sagainst which you see the rays? rays should all be parallel
rays of light converging to the pp :52 567 '65 p 185ff ,) aces oowu ?*____-, ___.» antisolar point in the east. Very pp 75-277 1513
rarely you may see those rays
165, pp. 149 rr; 954, pp. 151- I
Shouldn't the line through the _ 4_
5.137Bent search beams
When seen from the side, search-light beams appear to bend over.Does the beam really get scatteredor refracted downward by theatmosphere?
I65, pp. 149 ff} .954, pp. 151-166; 1250 dirough 1254.
5.138Rear lights and a red light
If, while driving at night, youshould be about a block behinda car approaching a red light, therear lights of that car may appearto stop somewhere beyond theintersection. When you reach thered light yourself, however, youfind the other car waiting as itshould be in front of the redlight. What causes this particularillusion?
1261.
light fluxperception
5.139Snowblindness
What causes snowblindness (white-out)? After long expostue to thewhite light ofsnow and ice fieldsyour eyes feel as though they werefull of sand. Intense pain may fol-low for days. Is snowblindnessmore likely to occur on a sunny
or a cloudy day? In his diary andstories of five years ofpolar ex-peditions, Vilhjalmur Stefanssonrecalls:
. . .it might be inferred thatsnowblindness is most likelyto occur on days of clearsky and bright sun. Thisis not the case. The daysmost dangerous are thosewhen the clouds are thickenough to hide the sunbut not heavy enough toproduce what we callheavily overcast or gloomyweather. . .everything lookslevel. . .You may collideagainst a snow-covered icecake as high as your waist-line and, far more easily,you may trip over snow-drifts a foot or so in height. . .(1113).*
In such conditions you can't evendistinguish the horizon. Whatrole do the clouds play inincreasing the probability ofsnowblindness?
1113, pp. 149, 1.99-202,‘ 1122;1262.
'Vilhjalmur Stefansson, The FriendlyArctic, copyright © 1921 by theMacmillan Company. Permissiongranted by Mclntosh and Otis, Inc.
5.140Resolution of earth objects byastronauts
What are the smallest objects or-biting astronauts can distinguishon the earth's surface? In particu-lar, can they see large cities in theday or night or other large objectssuch as the pyramids? The earlyMars fly-bys were disappointingto many people, especially non-scientists, because their picturesshowed no signs of intelligent life.What signs of intelligence could yousee on the earth if your photos hada resolution of, say, one kilometer,which is a typical value for weathersatellite photos? If that resolutionis not sufficient, how much is re-quired to see signs of life?
360, pp. 182- 184,- 1263dirough 1265- 14.98.
reflectionray opticsresolution
5.141A Christmas ball's reflection
A shiny Christmas tree ball can giveyou a picture of nearly the entireroom in its reflection. How will itreflect a point source of light in anotherwise dark room? Hold a ballabout 10 centimeters from one eyeand latch the reflection of thepoint source. (A pinhole punchedin foil that covers a lamp providesa good point source.) The reflectedimage is an extended line of light,
150 The flying circus of physics
not a point. But, immediately afterswitching on the room lights, theline of light quickly contracts toan undistorted image of the pointsource. First, why is there a distor-tion of the point image in the darkroom? Second, why does thedistortion depend on the illumina-tion of the room?
1266.
5.142Moire patterns
If two similar patterns withslightly different periodicitiesare superimposed, a larger pattern,called a Moiré pattern, appears.You can easily see this by foldingover a sheer curtain or by lookingthrough a comb held at arm'slength in front of a mirror. In thecomb example, the comb and itsimage merge to form a larger comb-tooth pattern. For a more quanti-tive observation, place one metalsheet covered with circular holesseveral inches behind another suchsheet to get a resultant circularMoire’ pattern when the screensare viewed together from a distance.How does the observed Moirepattern change with your distancefrom the screens? How does it varywith changes in the separation dis-tance of the screens? Which wayand how fast does the Moire patternmove as you walk parallel to thescreens? Finally, does the motionof the pattem depend on your dis-tance from the screens?
954, pp. 85-87,‘ 1267 dlrough1272.
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Bioelectricity 5,2 6.3 ‘(6.1 through 6.5) Frog legs Getting stuck to electric wireioule heatingfibrillationpower
6.1Electrocution
What exactly happens to youif you touch a live wire? Whatis it that can hurt or kill you?The voltage? The current?Both? Are you bumed? Isyour heart's rhythm disturbed?l-low does the danger depend onthe frequency of the current?In particular, why is Europe's50 cycles per second supposed-ly safer than America's 60cycles per second? Is directcurrent more dangerous thanalternating current, or does itjust depend on circumstances?
You may not be killed out-right, but if you continue tohold on to the electricalcomponent, you may eventual-ly die: the longer you wait,the lower your body's resis-tance becomes, and thus,you get closer to a lethaldose of current. Why doesyour body's resistance changewith time?
1273,‘ 1274.
Exceptionally good references: Singer(1349). Uman (786), Schonland (301),Malan (300). and Corliss (1611).
with the nature of nerves andmuscles, Galvani (1 780s) employed a deceptively simple arrangement. A frog leg was hungfrom a bronze support that was
In a classic experiment dealing
urebolted into an iron railing (Fig6.2). The hanging leg could alsotouch part of the railing, buteverytlme it did, it contractedand was thrown into spasms.When the spasms died out, theleg would droop and touch therailing, and the contraction andspasms would begin again. Whatcaused this reaction? Can youproduce some numbers to sup-port your answer?
1275
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Figure 6.2Frog leg sent into spasms when ittouches the iron railing.
If you should grab a “live” wirethat passes about 25 milliampsthrough your hand, you prob-ably won't be able to releasethe wire? Why not? [Do notgrab such a wire on purpose,for it may lead to your death(see Prob. 6.1)].
1273.
6C4
Electric eel
A healthy eel can produce some-thing like one amp at 600 volts.What could possibly be the sourceof such enormous power? Doesthe eel continuously discharge inthe sea water? Why doesn’t itshock itself?
The navigational ability ofaquatic animals has long been un-explained. Recent work, howevsuggests that some of the animals
created by ocean currents moving
the animals orient themselves.of all, can you show how the ec-
moving water? Next, can you ex-
detect such a small field‘!
1276 through 1282.
The electrician’: evil and the ring’: magic 153
l-low can an electric eel shock you?
er,
may be able to detect electric fields
through the earth's magnetic field.These fields would supposedly help
Firstel
tric fields would be produced by the
plain how an animal could possibly
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Figure 6.5“When I was a little girl wedidn't have microwave ovens,and sometimes it took a wholehour to prepare a meal. ”
electric Current
thermoluminescence
6.6Time to turn on light
When you tum on a light switch,how long does it take for the lightto come on? Must you wait forthe electrons in the wires to reachthe light bulb? Once the currentis flowing, how soon does the bulbbegin emitting visible light?
1312.
Electrostatics(6.7 through 6.l3l
absorption
electric fieldcharge separation
6.5Microwave cooking
An ordinary gas oven will cook aroast from the outside inward, buta microwave oven will cook the in-terior first. Hence, your micro-wave-cooked roast may be welldone inside and pink outside.Should you be caught in front of alarge, active radar dish or hold yourhand inside a microwave oven, youtoo may be well done inside andpink outside. Why do microwavescook this way? As a matter of fact,how do microwaves cook meat atall?
1492.
electric fielddischarge
6.7Shocking walk on rug
Being shocked after walking acrossa rug or sliding across a car seat isa common experience. Grantedthat you must be building upcharge somehow, can you explainmore about what’s happening?For instance, why must you walkacross the rug—why doesn't thecharge build up if you merelystand still? Why does the effectdepend on the season?
This electrifying experienceis normally part of a physics classat some point: glass rods arevigorously rubbed with cat's fur-or something like that. Why arethey rubbed? Will they chargeless rapidly if they are rubbed
less vigorously? Does frictionactually have anything to do withthe charging? And why does thepolarity of the rod depend onwhat's rubbed against it? Finally,why is the charge decreased ifthe rod is held in the smoke of amatch?
300, pp. 168-170; 537; 1288dtrough 1297.
6.8Kelvin water dropper
Another common physics demon-stration is the Kelvin water dropper(Figure 6.8). Briefly, water dripsthrough two tin cans, the cans beingwired together as shown. After ashort time, one connected pair ofcans becomes positive while theother pair becomes negative. Why?The apparatus is seemingly sym-metric. How, then, do the twopairs develop opposite charges?In particular, can you explain howthe charging first begins?
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Figure 6.8Kelvin water dropper.
154 The flying circus of physics
6.9Electrical field and water streams
Water streams, while initially welldefined, eventually break up intodrops. You can stop that breakupvery easily by holding a chargedobject near the stream. If the ob-ject is fairly strongly charged, thestream will also be attracted to it.Can you explain these results? Ofcourse, you really should first ex-plain why the water stream normal-ly breaks up.
322, pp. 86-87, 91-95; 1283through 1287.
6.10Snow charging wire fences
Electrical shocks are often as-sociated with blowing sand andsnow. For example, with snowblowing in the Colorado Rockyarea, “wire fences on the plainsnear the mountains frequentlyaccumulate charges strong enoughto knock over men or cattle, andsometimes spit sparks to nearbygrounded objects. Plains residentsoccasionally report sparks thatjump as much as a yard fromtheir fences" (354). (One jumpingan inch will knock you down andleave you sick for several hours.)Why does the blowing snow chargthe fences?
854, pp. 704-70% 1298Utrough 1301;1527.
6.1 1Scotch tape glow
If you unroll scotch tape in a darkroom, you’ll see a brief glow alongthe line where the tape is beingripped from the roll. What causesthe light emission? Does it haveany particular color? If so, whythat color?
1194, p. 252,‘ 1302.
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6.12Sifting sugar
One day as I was sifting confec-tioner's sugar for a cake frosting,a curious thing happened to thesugar. When I started, the sugarwould fall straight down, butgradually more and more of thesugar would be thrown to theside (Figure 6.12). Why was itdeflected?
6.13Gas truck chains
Why in the past were chains draggebeneath gasoline trucks? Shouldyou drag a chain from your car’?
d
6.14Charge in shower
When you take a shower, thesplashing water produces negativecharges in the room's air and elec-tric fields of up to 800 volts permeter. Similar negative fields arefound near natural waterfalls. Inaddition, when large crude-oil car-riers are cleaned with high-velocitywater jets, electric fields of up to300 kilovolts per meter can becreated. What is the cause of suchfields? In the case of the super-tankers that is not merely an aca-demic question, for there have beenseveral large explosions during thecleaning of those ships.
539; 129s; 1307 through 1:111.
6.15Happiness and negative charge
It is thought that if you enter anegatively charged atmosphere,such as the bathroom discussedabove, a feeling of well-being willcome over you. Being chargednegatively makes you happy;being charged positively makesyou ill at ease. So, perhaps yourfeeling good after a shower has asmuch to do with the negativecharge in the bathroom as withfeeling clean. Can you explainwhy negative and positive chargemight affect you this way?‘
1307,‘ 1408.
1303 through 1306-_ ‘Also see Prob. 3.18 on the Chinook.
The elect:-ician's evil and the ring's magic I55
6.16Fall through the floor
Why don't you fall through thefloor? Fundamentally, what sup-ports you?
6.17Sand castles and crumbs
If you want to make a sand castleat the beach, you use wet sand, notdry. Common table salt shows thesame tendency to be much morecohesive when wet. Other powderssuch as cocoa and chalk, however,are cohesive even when dry. Whatforces are responsible for thecohesiveness of a powder? Whydoes it matter whether a powdersuch as sand or salt is wet? Doyou think a line powder should bemore or less cohesive than a coarseone?
Crumb formation is essential formaintaining a fertile soil, yet ifthe soil is misused, a useless dustball may develop. What is respon-sible for crumb formation in soil?Why don't other things, such assand and face powder, formcrumbs?
1313, pp. 288-290; 1314; 1315.
6.18Food wrap
Some clear food wraps can betightly stretched over a containerand folded down the sides, andthey will retain the tension andcompletely secure the container.The food wraps "stick." l-low dothey do this?
Magnetism(6.19 through 6.24)
6.19Magnetic—field dollar bill
If you hang a dollar bill from oneend and bring a large magnet (witha nonuniform field) toward it, thebill will move toward one of thepole faces. Why?
1316.
6.20Bubbles moved by magnetic field
A large magnet placed near acarpenter's bubble level will forcethe bubble to move. How doesthe magnetic field do that? Doesthe bubble move toward or awayfrom the magnet?
1316.
induction
6.21Electromagnetic levitation
You can levitate a metal ring on acoil through which a steady AC cur-rant passes (Figure 6.21), but if thecurrent is quickly turned on, thering will jump into the air verydramatilly. Why is there a dif-ference in behavior in these two
ses?What supports the ringagainst gravitation when it is beinglevitated, and what determinesthe height at which it floats?l-low stable is the levitation (does
the ring sit against the pole and ata tilt)? In predicting the behaviorof various rings, your intuitionmay fail. So, for fun, first try toguess what will happen in thefollowing circumstances and thenectually see what does happen.Will a thin ring float at the sameheight as a thicker ring if thedensity and diameter are the same?Whet happens should both ringshe on the coil when the currentis slowly increased? Finally, whathappens if one of the rings iswider than the other?
1817 through 1321.
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induction
6.22‘lirming in the shade of a magneticfield
Can partially shading a magneticfield from a copper disc cause thedisc to rotate? Over one of thepoles on an altemating magnet,place a copper disc that is free torotate (Figure 6.22). The disc isrepelled but shows no desire torotate. But now insert anothercopper sheet between the disc
156 The flying circus of physics
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and the magnet, partially shadingthe disc from the magnetic field.Immediately the disc begins toturn. Can you explain why?
1321, pp. 82 ff.induction
6.23Car speedometer
Will a horseshoe magnet attractaluminum? No, normally it won't.(Why not?) There is a special ar-rangement, however, in which amagnet will move aluminum.Suspend a horseshoe magnet on astring above an aluminum disc
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(Figure 6.23). Somehow suspendthe disc so that it's free to rotateabout its center. If the magnet isset spinning, the disc will spin also.Will the disc turn in the same senseas the magnet? Why is aluminumonly affected in this case?
This is basically how your car'sspeedometer works, except thatin your car the rotating magnetis inside an aluminum can to whicha pointer is attached and the canis restrained by a spring.
155, p. 344; 592, p. 87.Magnet
Ball
Return Hramp _
wgi 1°"hrFigure 6. 24Ball undergoes perpetual motion.
6.24Perpetual magnetic motion
Of the many fascinating perpetualmachines proposed throughhistory,* that of the Bishop ofChester (1670s) is one of thesimplest (Figure 6.24). The mag-net that was fixed on the columnwas to draw the iron ball up theramp until the ball readied thehole in the ramp. The ball wouldthen fall and be returned to theramp's base, and the procedurewould begin again. Very straight-forward, right? Shouldn’t itwork?1325.
‘See Refs. 1322 through 1324.
Radio andionospherephysics(6.25 through 6.31)
ionospheric physics
plasma frequency
electromagnetic waves
6.25Radio, TV reception range
There are several things about radiothat have always puzzled me. Forexample, why can AM stations bereceived at night over a much largerrange than during the day? Some-times you can pick up a stationhalfway across the United Stateson a cheap transistor radio. (Oneconsequence of this is that the FCCrequires most AM stations to cuttheir power or even to leave the airat dusk.) When Marconi transmittedthe first wireless signals across theAtlantic, many people were amazed.Why didn’t those signals go directlyinto space instead of following thecurving surface of the earth as theydid?
FM and TV stations, however,hardly even get their receptionareas out of the city. Occasionally,such as during a meteor shower,these signals do travel surprisingdistances; at other times, such asduring major solar flares, theyare tremendously reduced, world-wide communication being almostdestroyed. First, why is there sucha difference between the ranges ofTV and FM on one hand and AMon the other? Next, why are there
The elects-ician's evil and the ring‘s magic 157
occasionally such dramatic changesin the transmission ranges of TVand FM?
170, pp. 138-139; 215, pp. 43 ff;1326,’ 1327.
l’8SOf'l8I‘lO8
6.26Crystal radio
The crystal radio of my boyhoodwas very simple, being only anantenna wire, a capacitor, a longwire coil, earphones, and finally,a crystal (Figure 6.26). Do youunderstand how it worked? Forexample, why did moving thecontact on the wire coil changestations? Why was the crystalnecessary?
Every now and than there arestories about people who can hear
Antenna
W "\-**’°°°°
Capacitor Q
? Crystal
Ground
,f\\,_\g\\O3
.______________,Figure 6.26Crystal radio.
lol radio stations on their teethfillings, on their bedsprings, etc.Could there be any truth to thesestories? If so, then what is it inthese strange radio sets that istaking the place of the crystal inthe crystal set?
158, pp. 577-578,‘ 211, pp. 417-4181. P.
5.27Airplane interference with TV
How does a nearby airplane inter-fere with your TV picture?
6.28AM car antenna
Why are AM radio antennas mount-ed outside a car and usually ver-tically? l-low much does it matterif they are mounted in the wind-shield glass?
6.29Multiple stations on radio
Normally I hear one local stationfor a given setting on my car radio.Yet when I drive near a radio sta-tion's antenna, I can sometimes hearthat station plus another for onesetting. Why? Sometimes I caneven get one station at many settingof my radio diaL Again, why?
charged particles in magnetic fieldatomic and molecular excitation
6.30Auroral displays
"After darkness has fallen,a faint are of light maysooner or later be seen lowon the north horizon, orcentered somewhat tothe east of north. Gradual-ly it rises in the sky, andgrows in brightness. Asit mounts in the sky, itsends, on the horizon,advance to the east andwest. Its light is a trans-parent white when faint,and commonly paleyellow-green when bright-rather like the tendercolor of a young plantthat germinates in thedark. The breadth ofthe arc is perhaps thricethat of a rainbow. Thelower edge is generallymore definite than theupper. The motion up-ward toward the zenithmay be so slow that thescene is one of repose.As the arc rises, anothermay appear beyond it,and follow its rise. Attimes four, five, or evenmore arcs may thusappear. They rise together,and some of them maycross the zenith and passonwards into the southernhalf of the sky.
158 The flying circus of physics
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“This may be all thatappears on some nights.But on others the auroraenters after a while on anew and distinctly dif-ferent phase, much moreactive and varied. Thetransition from the quietto the active phase maybe speedy, even sudden.The band becomes thinner,rays appear in it, it beginsto fold and also to becomecorrugated in finer pleats.It becomes a rayed band ofirregular changing form,like a great curtain of drap-ery in the sky. Its colormay remain yellow-green,but often a purplish-redborder appears along thelower edge, perhaps inter-mittently. Vivid green orviolet or blue colors some-times appear. At timesthe rays seem to be dart-ing down, like spears shotfrom above. Sometimes
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may look up into a greatauroral fold nearly over-head, when the rays inits different parts willseem to converge, form-ing what is called acorona or crown. Oftensuch a corona rapidly
fluctuates in form, andits rays may flash andflare on all sides, orroll around the center.
"At the end of an out-standing display the auroramay assume fantastic forms,no longer in connectedcurtains and bands. Theremay be a widespread col-lection of small curtains,stretching over a largepart of the sky, whichbrighten and fade, or, asit is said, pulsate. Finally,the sky may be coveredby soft billowy clouds,not unlike a mackerelsky with rather large"scales"; but these"scales" and patchesappear and disappear,with periods of notmany seconds. At lastthe sky becomes altogetherclear, with no more aurora.But later the whole se-quence may begin anew,and continue till dawnpales the soft aurorallight (1328)."Explaining the aurora in detail is
still a matter of current research,but can you explain in general whythe aurora is formed and why someof these colors and wavelike struc-tures appear? Why are auroraldisplays so much more frequent athigh latitudes? Why are there moredisplays over northern Canada thanfor example, over Siberia at thesame (geographical) latitude?
219, pp. 242-246‘; 1328,‘ 1329.
The electriciarfs evil and the ring's magic l59
refractiondispersion
6.31Whistlers
In World War I the Germans eaves-dropped on Allied field telephonemessages by detecting the smallleakage from the telephone wiresinto the ground. The initial pickupwas by two metallic probes driveninto the ground a couple hundredyards apart and at some distancefrom the telephone wires. Once thesignals were fed into a high-gainamplifier, they became audible tothe German intelligence personnel.But during such monitorings, theGermans also heard mysterious,relatively strong whistlings whosepitch would steadily fall. Thesesounds have since been associatedwith ionospheric phenomena ap-propriately called "whistlers" andother sounds such as clicks, tweeks,chinks, and a whistling of rapidlyrising pitch called the “dawnchorus" have been detected. Canyou explain the sources of thesesounds?
219, pp. 302-304; 1330; 1331.
Atmosphericdischarge(6.32 through 6.49)dischargeelectric fieldelectric potential
5.32Lightning*
Lightning is so familiar that itsbeauty runs the risk of beingoverlooked. So, before we get intosome of the strange or paradoxicalfeatures of lightning, let's ask sosimple questions about its com-mon properties. In a lightning dis-charge there are at least two strokes:usually there is first a "leader,"then a “retum." Which do youand why don't you see both?1'Why do you even see one- whatproduces the visible light?
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Does the visible stroke go up ordown? Why is It so crooked?How much current is involned ' aflash? How bright is a flash? Ap-proximately how wide is the light-ning channelyou see? One hundredmeters? One meter? Several milli-meters? How long does the flashlast? Several seconds? Severalmilliseconds? A mia-osecond or so?
220; 299, PP- 110-123,‘ 300,‘301; 332, Vol. II, Chapter 9;1332; 1333,‘ 1550,‘ 1590,
‘Suggestions for photographing light-ning flashes are given by Orville (1334).The first lightning photograph ever takenis reproduced in Jennings (1335).
T lf you are driving through rain atnight, a multiple-flash stroke can giveseveral stroboscopic images of yourmoving windshield wiper (1336).
6.33Earth's field
big question, however, is whythe e is lightning at all? What isresponsible for the electric fieldthat is between the earth's surfaceand the clouds? Outdoors there isa 200-volt difference between the
eights of you nose and feet. Whyren't you shocked by that voltagefference (Figure 6.33)? Canotors be driven by this electric
field? In some cases, yes.
299. pp. 97- 109,‘ 300. PP. 105-106; 332, Vol. ll, Chapter 9;1296; 1337 through 1339; 1548;1549; 1568.
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160 The flying circus of physics
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6.34Lightning forms
The cloud-to-ground lightningstroke is not the only type oflightning. The cloud-to-airstroke, for example, termin-ates in midair (Figure 6.34al.If the cloud is too distant to beseen, you may suddenly be awedby such a "bolt from the blue."Under some circumstances you
Figure 6. 34bRibbon lightning.
will see several parallel strokesthat give the impression of aribbon hanging from the clouds(Figure 6.3411) The most excitingstroke, however, is probably“bead lightning" (Figure 6.340),which appears to be a series ofbrilliant beads tied to a crookedstring. In these several examples
Figure 6.34cBead lightning.
what causes the strokes or thespecial appearance of the strokes?In the cloud-to-air case, wheredoes the current of the dischargego?
299, pp. 128- 129; 300, p. 5,‘301, p. 45; 1340,‘ 1341; 1611,Section GL,' 1623.
6.35Ball lightning
One of the most controversial sub-jects in physics is whether or notball lightning exists. This argumentpersists in spite of the enormousnumber of sightings and manypublished accounts. Perhaps asmuch as 5 percent of the world'spopulation have seen it (1350,1351), yet many will arguevigorously that it is an illusion, suchas an afterimage resulting fromhaving seen a bright flash of light.
The luminous, silent balls of light
reportedly float through the airor slowly dance about for severalseconds. They can sometimes passthrough window glass without atrace of damage; at other times,the glass is shattered. They areseen in all manner of structures(even in metal airplanes) as well asoutdoors. Though they are usuallysilent, their demise is accompaniedwith a pop. Finally, they are dead-ly. G. W. Richmann was apparentlya victim while trying to repeat theresults of Franklin's kite experi-ment. A pale blue fireball aboutthe size of a fist left the lightningrod in his lab, floated quietly to
Richmann's face, and exploded.With a red spot on his forehead andtwo holes in one of his shoes,Richmann was left dead on thefloor.
In reviewing the many explana-tions of ball lightning, can youidentify those with any real pos-sibility of being correct? Can youalso devise other explanations orargue that ball lightning can onlybe an illusion?299; pp. 130-133; 1349mrough 1370; 1611, SectionGL8.
The elect:-ician's evil and the s'lng's magic 161
Figure 6.36
6.36H-bomb lightning
Lightning flashes were also photo-graphed surrounding anothercatastrophic event, the fireballof the 10~megaton thermonucleardevice triggered in 1952 at Eniwe-tok Atoll. The strokes propagatedupward from the surface of thesea, and the branching was alsoupward (Figure 6.36). As the fire-ball expanded and reached the
were previously visible (the visibleflashes had disappeared by then),
points where the lightning channels
the tortuous channels were againvisible against the backdrop ofthe fireball. The charge produc-tion for the lightning must havebeen set up very rapidly, butprecisely what caused it is stillnot well known. Can you suggestpossible explanations? Can youalso explain why the channelsbecame visible again against thefireball background?
1347,‘ 1348.
6.37Volcanic lightning
When the volcano that formed thenew islet, Surtsey, rose furiouslyfrom the Icelandic sea in 1963,brilliant lightning displays dancedin the volcano’s dark clouds. Whatprovided the tremendous chargingfor the lightning‘? One possiblemechansim was sea water strikingthe molten lava. How would thatproduce the charge?
1342 drrough 1346'.
6.38Earthquake lightning
Should an earthquake producelightning discharges? The Japanesehave learned that lightning dis-charges in a clear sky are signs ofimpending earthquakes. Indeed,earthquakes there and in other areasare sometimes associated with bothnormal lightning and ball lightning.Why should there be any connectionbetween the two phenomena?
1371,’ 1372.
6.39Franklin’s kite
Benjamin Franklin’s kite experi-ment was probably first introducedto you somewhere in elementaryschool, but do you understand allthe little points about what Franklindid, and why he was not killed?The following is Franklin’s letterto a friend describing the experi-ment:
To the top of the uprightstick of the [kite’s] crossis to be fixed a very sharppointed wire, rising a footor more above the wood.To the end of the twine,next the hand, is to betied a silk ribbon, andwhere the silk and twinejoin, a key may be fastened. This kite is to beraised when a thundergust appears to becoming on, and the personwho holds the string muststand within a door orwindow or under somecover, so that the silkribbon may not be wet;and care must be takenthat the twine does nottouch the frame of thedoor or window. As soonas any of the thunderclouds come over thekite, the pointed wirewill draw the electricfire from them, and thekite, with all the twine,will be electrified, a|1dthe loose filaments ofthe twine will stand out
162 The flying circus of physics
every way, and be at-tracted by an approach-ing finger. And whenthe rain has wet the kiteand twine, so that it canconduct the electric firefreely. you will find itstream out plentifullyfrom the key on the ap-proach of your knuckle.At the key the phial* mayhe charged, and from elec-tric fire thus obtained,spirits may be kindled, andall the other electric experi-ments be performed, whichare usually done by the helpof the rubbed globe or tube,and thereby the samenessof the electric matter withthat of lightning completelydemonstrated.Why did he put a pointed wire on
the kite’s top? Why the silk ribbonbetween the key and his hand?Why the key? Why was the twineattracted to his finger, and whydid loose filaments stand out?What caused the light emission hesaw when his knuckle was broughtclose to the key? Why wasn'tFranklin killed? If a lightningstroke had hit the kite or string,would he have survived? In EuropeG. W. Richmann was killed in tryingto repeat the Franklin experiments'l'so don't you try it, even withFranklin's precautions
299, pp. 37-44; 301, Chapter 2,‘1373,‘ I374.
‘An early form of capacitor.
'See Prob. 6.35.
6.40Lightning rod
My grandmother's lightning rodhas a sharp point, stands severalfeet taller than the house, and isburied several feet into the ground.Why are those features desirable?What is the rod really supposed toaccomplish? There has been con-siderable debate over this questionever since Benjamin Franklin'sinvention of the lightning rod.Some claim that the rod helps dis-charge a cloud as it passes over-head, thereby avoiding the cata-strophic breakdown of lightning.Others claim that the rod merelyprovides a safe route to groundfor any flash near the rod.
There have also been many mis-conceptions and controversiesabout the performance and in-stallation of lightning rods. For awhile after their first introduction,strong arguments were made for atop with a round metal knob oreven a glass knob. Convincingarguments were also made that thelower part should be attached tothe top soil only, for an explosioncould occur if the flash were car-ried deep into moist ground. Re-cently a company was fitting itsrods with a radioactive source attop. That source was to aid inionizing the air, thereby furtherseducing the flash to strike therod rather than the protectedbuilding. Would a radioactivesource really be of any aid?
299, pp. 188 ff; 300, Chapter 15;301, Chapters 2, 6; 1296; 1373through 1381.
6.41Lightning and trees
There's an old wives tale aboutlightning seeking out oak trees. Infact, a strikingly high proportion oftrees shattered by lightning are oaks.it is hard to believe, however, thatlightning knows the difference be-tween an oak and any other typeof tree. Why then is there suchpreferential shattering? How ex-actly does the lightning stroke makea tree explode, anyway? Of course,a strike does not always result in anexplosion. For example, Orville(1389, 1390) has published a re-markable photograph of a directhit sustained by a European ashtree. Upon close examination thefollowing day, the tree bore no in-dication of its experience.
How does lightning start forestfires? Why aren't fires started in alllightning strikes in wooded areas?
299, pp. 177- 187; 300, p. 151;301, p. 60; 1382 through 1390.
6.42Lightning strikes to aircraft
Lightning strikes to aircraft arefrequent, but it is very rare thatthere is any damage other thanperhaps several tiny holes in thefuselage. Cars, buses, and othersuch vehicles also enjoy immunityfrom damage. Soon after lift-offApollo 12 was struck twice by
The electriciaifs evil and the r'ir|g's magic 163
lightning with no apparent ill ef-fects to the spacecraft or its crew.In each of these cases why is thereno damage to the vehicle or injuryto the occupants? Indeed, theoccupants may never even beaware of the strike.*
299, pp. 232-235, 249 ff; 300,pp. 151- 152; 301, PP- 51-54;1296; 1379; 1391, p. 22; 1392mrough 1397.
a |g ning stri e by noticing a suddenincrease in St. Elmo's lire (see Prob.
objects. The luminous streamers maybe ‘I0 or 15 feet long and hall a footwide (301).
6.43Rain gush after lightning
Perhaps you have noticed suddengushes of rain or hail momentsafter lightning strokes in thunder-storms. Is there any connectionbetween the gush and the stroke orthe thunder? Or is this just a coin-cidence?
164. PP- 358-359; 300, pp. 165-166; 301, p. 152; 1398 through1490; 1619.
6.44Clothes thrown off
If you're struck by lightning, youmay very well have your clothingand shoes thrown off. What causesthat?
301, p. 131.
'Anhalert airplfine passenger may foresee possible elevation, but is there anyI‘ t ‘
6.45Ground fields in lightning hit
If you are caught in a thunder-storm you should not stand undera tree, and you should keep yourhead lower than your surroundings.Why is the tree dangerous? Aslong as you stand away from thetrunk, aren't you safe enough?
Should you ever lie down? Thatwould give your head the minimum
or hurt by lightning. Not only dothey commonly stay outdoors andoften seek shelter under trees, butthe separation of their hind legsfrom their front legs increases thedanger (Figure 6.45). They arethus similar to a man lying down.Again, why is this dangerous?
299, p. 223," 301, pp. 61-64;additional danger encountered in £350’ P’ 279'. 1391' pp‘ 282'
6.47) on the wing tips and other pointed lying down? Cows are often killed 83.
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164 The flying circus of physics
6.46St. Elmo's fire
St. Elmo's fire is a fairly con-tinuous luminous discharge seenfrom such things as masts ofships, wing tips of airplanes, andeven bushes. There is a cracklingnoise associated with the blue,green, or violet color of the light.Can you explain, first of all,what causes this light, and second,why those particular colors?
A favorite stunt of mountainguides, when the air isthroughly charged, is to imi-tate Thor by waving an ice-axe over their heads. Themetal parts of the ice-axedraw down an impressivedisplay of electrical poly-technics. A geological ham-mer will sometimes spit longhot sparks in one position,but if the head is turnedat right angles to the formerposition, the sparkingstops. . . They usually de-tect charged air by raisinga finger above their heads.When the air is heavilycharged, sparks will sizzlefrom the fingertip, makinga noise like frying bacon (354).
Another example, somewhat dif-ferent in appearance, is the electricsparks, several meters long, whichmay spring up from the tops ofsand dunes during thunderstorms.In this case, the blowing sand mustcontibute to the sparking, but how?
165, p. 233,‘ 301, PP. 47-50.‘354, p. 744; 961; 1402, p. 219;1403.
6.47Living through lightning
There are many cases of peopleliving through direct and indirectlightning hits. There are evencases where the lightning hasstopped a person's breathing forperhaps 20 minutes, yet the per-son has fully recovered with noapparent brain damage due toelectrical shock or oxygen starva-tion. lt has been suggested (1401)that such a shock momentarilychanges the brain's crucial needfor oxygen. In any case, shouldn'tthe victim be severely burned andhis heartbeat halted? How muchenergy (or power) is deposited insuch a victim?
299, pp. 226-2.20; .201, p. 1.21,-14a 1.
6.48Andes glow
Single flashes of light and con-tinuous glows can be seen over thepeaks of certain mountain ranges.They have been described as “notonly clothing the peaks, butproducing great beams, which canbe seen miles out to sea" (1404).Generally these mysterious lightsare called Andes glow, thoughthis doesn't mean they are re-stricted to the Andes. Whatcauses this glow? St. Elmo's firefrom many points on a peak?St. Elmo's fire is usually only afew centimeters long, so howcould it be seen miles away?
165, p. 233; 1404 mrough 1406.
6.49Electrical pinwheel
A demonstration sometimes seenin physics classes involves a pin-wheel that is made to rotate by ahigh DC voltage (Figure 6.49).Why this happens was a point ofcontroversy over the last two cen-turies, but recently the device hasbeen somewhat neglected. Doesthe pinwheel turn because ofsomething that it throws off orpulls on or for some other reason?Will it work in a vacuum or in adust-free environment? Why doesthe color of the discharge dependon the polarity of the pinwheel?Why do the tips need to be sharp?Finally, can you calculate howfast the pinwheel will turn undergiven conditions?*
155, pp. 434-435' 1407.‘Also see Prob. 6.33.
,"' ' Sharp point/1 ‘,\ /
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Figure 6.49Rota ling pinwheel driven byelectrical discharge.
The alectrldarfs evil and the ring's magic 165
power more efficiently, some
6_50 ly. More threatening, however, is sound of the electrical dis-Powebline blues that numerous people have received charge. Said C. B. Ruggles,
shocks when touching metallic ob- whose farm is split by theIn order to transmit electrical jects in the vicinity of the extra-
high-voltage lines.electrical companies have erected In a “cent survey’ 18 familiesuextra_high_v°ltagen (-765,000 living near Ohio.Power Co.’svolt) transmission lines. Such “"9 repmted bemg shockedlines may he beneficial on the bl’ t°"°hi“g farm m°°hme'y'whole, but they have worried those wire femes °r eve“ damppeople living near the lines. Dis cl°th°5““°5- Tw° w°m°“turbingly, the lines often glow an ¢°mP|ai"°d °f 5h°¢k5 Tewlvederie blue and can cause disconnected While °" the t°i|°t~ otherfluorescent tubes to light mysterious- ¢°mP|fli"t5 W9" bad TV 1'9‘
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line: “You’d swear wewere living near a waterfall”(1558).
l-low would a powerline such asthis cause objects in its vicinity togive shocks? I have heard thatsome people run electrical motorsby connecting them to antennassurreptitiously buried near thepower lines. Is it possible to getpower this way?
1558.
166 The flying circus of physics
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7.1UFO propulsion
When "your gravity failsand negativity don't pullyou through."-- -Bob Dylan, “Just LikeTom Thumb's Blues"*In light of physical laws, let's
reconsider the possibility that theUFOs sighted during the last fewdecades are intelligently controlledcraft. Consider the method ofpropulsion, for instance. No localdestruction has ever been noted atthe site of a landing or lift-off.For objects as large as spaceships, is this possible with any kindof chemical or nuclear power? l-lowmuch energy would be involvedwith those sources? Could thevehicle somehow use the earth'selectric or magnetic field? if so,how much acceleration would bepossible, and would there be analtitude limitation?
One of the most popular pro-pulsion mechanisms in science fic-tion has been gravitational shield-ing. l-l. G. Wells used it long agoto get men to the moon. Supposea craft could suddenly shield it-self from the earth's gravitationalfield. Would it lift off? If it did,how fast would it move? In par-ticular, would it move at anywherenear the fast speeds reported forUFOs?
1409.
'© ‘I965 M, Witmark 8: Sons, Allrights-reserved. Used by permissionof WARNER BROS. MUSIC.
7.2Violating the virgin sky
Cyrano de Bergerac uses the mostincredible physics ever recordedto keep the villainous de Guichefrom Floxanne's house while she isbeing married. Dropping from abranch into de Guiche‘s path,Cyrano swears he has iust fallenfrom the moon.
CYFIANO: From the moon,the moon! I fell out of themoon!
DE GUICHE: The fellowis mad-
CYRANO (Rapidly):You wish to know bywhat mysteriousmeansl reached the moon?
I myselfDiscovered not onescheme merely, but six-Six ways to violate thevirgin skyl
(De Guiche has succeededin passing him, and moves
toward the door of Rox-anne’s house. Cyranofollows, ready to useviolence if necessary.)DE GUICHE (Looksaround.): Six?CYFIANO (With increasingvolubilitylz
As for instance—Havingstripped myselfBare as a wax ndle,adorn my formWith Crystal vials filledwith morning dew,And so be drawn aloft,as the sun risesDrinking the mist of dawn!
DE GUICHE (Takes a steptoward Cyrano.):
Yes—that makes one.CYFIANO (Draws back tolead him away from thedoor; speaks faster andfaster.l:
Or, sealing up the airin a cedar chest,Flarefy it by meansof mirrors, placedIn an icosadedron.
DE GUICHE (Takes anotherstep.l: Two.
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168 The flying circus of physics
CYFIANO (Still retreating):Again,l might construct arocket, in the formOf a huge locust, drivenby impulsesOf villainous saltpetrefrom the rear,Upward, by leaps andbounds.
DE GUICHE (Interested inspite of himself, and count-ing on his fingers.):
Three.CYRANO (Same business):
Or again,Smoke having a naturaltendencv to rise,Blow in a globe enoughto raise me.
DE GUICHE (Same busi-ness, more and more as-tonished.): Four!CYFIANO: Or since Diana,
as old fables tell,Draws forth to fill hercrescent horn, the mar-rowOf bulls and goats—toanoint myself there-with.
DE GUICHE (Hypnotized):Five!-
CYRANO (Has by this timeled him all the way acrossthe street, close to abench):
Finally—seated on aniron plate,To hurl a magnet inthe air—the ironFollows-l catch themagnet—throw again-And so proceed in-definitely.
DE GUICHE: Sixl—All excellent,—andwhich did you adopt?
CY RANO (Coolly): Whynone of them. . .A seventh.
The oceanl. . .What hour its risingtide seeks the fullmoon,I laid me on the strand,fresh from the spray,My head fronting themoonbeams, since thehairRetains moisture—andso l slowly roseAs upon angel's wings,effortlessly, Upward.’
‘From Cyrano de Bergerac by EdmondRostand, translated by Brian Hooker,published by Holt, Flinehart and Winston,Inc.
cosmology
7.3Olbers' paradox
Some have argued that theuniverse is infinitely large andcontains an infinite number ofstars. Olbers' paradox is that"if the universe is infinite inextent and contains an infinitenumber of stars evenly distributed,the sky should be blazing all overin brilliant light" (1414). Ofcourse, the intensity of the lightfrom distant stars will be less thanfrom nearby stars. But if the starsare evenly distributed, then theirnumber increases with distancefrom the earth iust enough to
Figure 7.3“I'm not sure, but it looks likeinfinity.” (Phi Delta Kappan.)
balance the decrease in light in-tensity from each star. Hence, thetotal light coming from any givendistance should be the same asfrom any other distance. With aninfinite number of stars, the night-time sky should be bright andevenly lit. Why, instead, is thenighttime sky relatively dark?
1410 through 1416; 1587.
atmospheric physicsgravity waves
7.4Noctilucent clouds
Shortly after a summer sunsetin the high latitudes, ghostly,silvery-blue clouds may appearagainst the dark sky. They arecalled noctilucent clouds (lu-
The walrus has his last say and leaves us assorted goodies 169
minous night clouds), and theirorigin is still highly controver-sial. They may be associatedwith extraterrestrial dust enteringthe atmosphere, but this has notyet been proved. Why are theyvisible only after sunset? Slnoethey are seen when the sky isdark, about how high are they?Why are they usually seen onlyin the high latitudes and only inthe summer’? Why do they oftenappear in a wavy pattern, asthough the clouds were the surfaceof a sea?
3&, pp. 150-151; 954, pp.284-287; 1417 through 1423.
7.5Water Witching
Some people claim they can locateunderground water by walking overthe area with a forked stick, rod,or something similar (Figure 7.5a).When directly over water the in-strument reportedly dips to indicatethe (unseen) water (Figure 7.5b).
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Figure 7. 5aA water witch's forked stick.
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This procedure—called dowsing,water Witching, or divining—is con-troversial: theme are many successstories on the one hand but a com-plete absence of explanation inphysical terms on the other. Whatcould possibly be the force thatinfluences either the instrumentitself or the person holding it? Isthere some clue, perhaps even asubconscious one, that tips oft‘the water witch to the presence ofwater?
1520 through 1523.
shock wavesenergy transfer
7.6Snow waves
A footstep in a field of snow mayset off a snowquake that propagateaway from the site and causes alowering of the snow level and aswishing sound. If the disturbanceencounters a barren area, it will bereflected back through its origin,and the swishing of the second pas-sage can be heard. What causesthese snowquakes to propagate,and what determines their speed?Why does their passage lower thesnow level and cause a swishingsound? Finally, why will a barrenarea reflect them?
1426; 1427,’ 1455.
7C7
Fixed-point theorem
If you stir a cup of coffee and thenlet it come to rest, at least onepoint on the coffee’s surface willbe back in its original place. (Thestirring must be smooth, with nosplashing.) lf you were to rip outthis page, crumple it, wad it, andthen lay the wadded hall back inthe book, at least one point onthe page will be directly over itsoriginal position. Why is thisguaranteed in these two casesevery time?
1428 through 1430.
170 The flying circus of physics
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Should we won"y about a geophysical weapons gap?7.8
The great leap downward
The Republic of China commandsan awesome new weapon—a geo-physical weapon. It has been sug-gested that should all of its 750million people leap simultaneouslyfrom 6 1/2-foot-high platforms,they would set up shock waves inthe earth. By jumping again eachtime the shock waves pass throughChina, the Chinese could build thewaves up to the point that theycould destroy parts of the United
States, especially California, whichis already endangered by earth-quakes.
What path would such a shockwave take through the earth? Howfrequently should the Chinese jumpto amplify the wave, and how muchenergy is added to it by each jump?ls there any way another country'spopulation could defend itselfagainst this geophysical weapon,
-"""' "1" '-_'-'_r."r'-.-r-.-'.'. yj-j-'f .-,1 I."-'_.=_='.,-1.-.1 -'::_.: ;. . . .; - r . .| , _. . ,ft :=;<:»;=:=»€- "I; - .1, U , r I , = ,., I1;,-,1 _r ...;:_:,5;'; -"-.-,;:*-:;: "-151; r'_.-';.’I'.',-:-.=-.._r ' I 1='-;:-:-=,=-:'-:-; 1'1:-3:1‘. .="-f-.'I_'»';I=- "'=.=.=I»."»;'5 II:1-.-1r.I. ‘ _.-_;.;'_;_[§;'. fig; ‘ ’!_.;=rj:i_'. |lf}'}',-§:=_-;= _r.{i_!,;g,j_-;ji.f.., ‘ f_-_'.__¢_-,-.;i_J_:j;3-_--:.;i§.|i__.;¢_;,-,-.-_-,-.;._i 5.-.-_.I H /-" J54:-.'==>_'i I_r_;!=r',_I;r, ffei-1._!,':.;--ii. Jig‘-;;':;¢-,'; 16* |’ ,I I 5 by I. , Hr; -’ -' 2 -. - _<_..-sI.== '.1.--4.-Ia-..--'-I:-I,I I, , I 1
. r J H * ii I 5 K‘.
..[:Ili.;.
J |
r
r 1,;-.-.,
»
.7 -i»:-I. .~ 1.:-~.1 "<I- -3-’ - A‘.-;'_~.~.‘ 5;-r :;-- '.~. .~ --
for example, by some appropriatetype of retaliatory jumping (Fig-ure 7.8)? Does it matter howthe Chinese jump? For example,one writer has argued it is essentialthe Chinese jump with stiff knees,for bent-knee jumping would im-part far less energy to the ground.ls that true?
1424,’ 1425.
7.9Beating and heating egg whites
Why does beating egg whiteschange them from a fluid to athick foam? For instance, inmaking meringues the egg whitesare beaten until they peak, (whenthe beater is lifted out, the sub-stance is stiff enough that it is
left in a peak). What does thebeating do to the egg white tocause it to stiffen? Similarly, whatis physically responsible fortransfomiing the egg white—initial-ly a colorless, transparent fluid—in toa white solid when, for example, youfry an egg?
316, pp. 123-126, 87-90; 1431.
Scotch tape rheology
SUGSSGS
7.10Pulling off Scotch tape
Scotch tape cannot really get intothe surface irregularities of what-ever it is being applied to, yet itholds well when you try to peel itoff. The adhesion is partly due to
The walrus has his last sap and leaves us assorted goodies I 71
4 dk
as_|_'_<,c'=,<~.'.r£|I\1|:i”-.\r,_,i'.((,-ii"'r,-.---\\-.,I| ‘... -.i-_,q._|-- .;‘ii/"iii?/iI‘*-iIi.'“|.|""‘.’l '.I. I"i')'i'*=- in-F as -..-...-ri"i Ii‘.
I -‘.1__"<=--r-”»‘.=.E’;.@¥*.":i .'-” - ==. '-'--‘"9’ "'**-1' ‘-3s it »*§*-‘.-f-i- .- .-sh.|l';':l5':)\-,~i:’.ii:i,'\'-',';'='§%Zi{iI"3'3)i ‘iii. ‘gr .~. iI.=|)'_lj i‘ ’-.
In” '-' ',.. 1\_; f<5,|(,-_-
-I' --is%iIiie-=;-:-:sisai‘-'is-.I- -- '-*l-‘-rI*ii'.i "i>l)'-.i-is’:-fr lzriiiiiii
-.iIiiii‘=g|'-'-*r.=.=.<i'»"-'-'-:-i-.--."-'-:-:-2-:;.. ll‘-'I:', __ "’ K)i‘§)__)_i,'
% ii"?-Qfii‘ %&
Figure 7. JOCompression point in tape beingpulled upward.a line of compression that runsahead of the line of separation asyou peel the tape (Figure 7.10).The line of compression an beseen if you stick two tape stripstogether and slowly separate them.What causes the compression?
950; 1432.shear
SU'B§
7.11Footprints in the sand
l-lave you ever strolled along thebeach as the water was receding?As you step onto the firm sand,the sand around your foot im-mediately dries out and turns white.The popular explanation for thewhitening is thatthe water issqueezed out of the sa" ..| by yourweight. That, however, is not thecase, because sand does not behaveat all like a sponge. So, what doescause the whitening? Does it lastas long as you stand there?
.924, p. 373,‘ 937; 938,‘ 1313,pp. 288-294,‘ 1433, pp. 624-625.‘ 1434; 1435
Si78$ cosmic rayssolar flaresparticle reactions7.12
Balloon filled with water and sand
Partially fill a rubber balloon wisand and water so there ismore than enough water t_o coverthe sand but not enough to fill the
, 9
s-
th
entire balloon. Then tie up the topand try squeezing the balloonPretty easy at first, isn't it? As ycontinue to compress the balloohowever, you ll suddenly find apoint where the balloon just refusesto bulge even though you squeezefor all you're worth. What causesthis sudden and determined resitance to further squeezing?
924, p. 373,‘ 938,‘ 1313, pp.288-294; 1433, pp. 624-626;1434; 1435
OllI1
7.13Buying a sack of com
In the days when shucked comwas sold by volume rather than byweigh t, vendors would make thecom assume as much volume aspossible. Hence, a bag of corn,while appearing full, may havehad less corn in it than anotherbag of the same size sold by amore-honest merchant. Facedwith this problem, should thebuyer have tried to press a bag soas to make the com denser? Does
uss
the com's volume decrease if yopress on the bag? Actually, preing is exactly the wrong thing todo. Why?
938,‘ 1433, pp. 624-626; 1434;1435
7.14Radiation levels in an airplane
Do solar flares and galactic radia-tion present a real danger to peoplein high-altitude jets? When an air-plane takes off and begins its as-cent, why does the net radiationlevel it experiences decrease forthe first 1500 feet and then beginto increase with altitude? If thereare significant variations in theextraterrestrial radiation, whatcause those variations?
1296, PP. 392-393; 1436; 1437.
ionization and excitationCerenkov radiation
7.15Flashes seen by astronauts
Astronauts on the lunar missionssaw white, starlike flashes whenthey were in space. The flashesoccurred about once or twice aminute and were seen with eyesboth open and closed. Apparentlycosmic rays caused the flashes buthow? Why did the astronauts seepoint flashes (sometimes withfuzzy tails) rather than a glow overthe whole field of vision? Can apassenger in a high altitude jet seethe flashes? (Figure 7.15.)
1438 through 1451.
172 The flying circus of physics
%
( Ail,ouat,ow,oooa,BE&5... }
X §4-
N\AN,TNO$E cosmic asARE 1<It.i.Ims ME
T11is
Figure 7.15(By permission of John Harl.Field Enterprises. )
X ray, UV and (Fl
interaction with matter
7.16X rays in the art museum
Ultraviolet light, infrared light, andX rays are often used to findpaintings over which second
oilpaint-
ings have been made. A painter's
be traced, and lost paintingsfound. The technique has al
modifications to a picture can thus
smay beo been
used to expose forgeries. For ex-ample, the famous art forgervan Meegeren would paint histion over an old but worthlesing so that the old canvas wo
Hans
uld
imita-s paint-
lend authenticity to the counter-feit. X-ray analysis revealed vanMeegeren as a fraud.
lf ultraviolet and infrared lightand X-rays will interact with thebottom painting, surely theymust also interact with the topone. How, then, are the twopaintings distinguished?
110, pp. 190- 193; 1452 through1454.
7.17Nuclear-blast fireball
What exactly causes the fireball,that brilliant ball of light, in anuclear blast? That is, whatproduces the light? How long doesthe fireball last, and what causes itsdecay? Finally, why is it initiallyred or reddish-brown and laterwhite?
219, pp. 306-309,‘ 371, pp. 20 ff;1459.
7.18Defensive shields in Dune
ln Dune (1460), a classic sciencefiction novel by Frank Herbert,people wear personal shields thatset up some type of "force field"that will only pass slowly movingobjects l-lence, the shield wouldprotect you from bullets and knifeattacks but still allow you fresh airto breathe. ls such a protectiveshield physically possible?
Explaining materialscience to mygrandmother(7. )9 through 7.24)
7.19Friction
Can you explain friction to mygrandmother? I don't mean withany really sophisticated ideas,with some simple model. Is itcaused by surface irregularities
Othat jam and mesh together?it due to electrostatic forces?molecular forces bring aboutlocal adhesion? Or does the ha
but
risDo
rdersurface penetrate the softer one,causing them to stick? This sub-ject is so old, so commonplace,so thoroughly investigated thatsurely there is a simple explana
3; 1462 through 1465.
7.20The flowing roof
and
tion.
The National Cathedral in Washing-ton, D.C., was built to imitate thecathedrals of medieval England.The roof was made of lead becauseEngland, with her abundance of
cathedrals Unfortunately, whenlead, had put lead roofs on her
the roof oh the National Cathedralwas only a few years old, it wasdiscovered that "the beautiful,delicately colored, lead roof waslipping inexorably downward,sliding past the nails and battens"
f(1461) Apparently this was dto two factors: the latitude o
S
U6
The walrus has his last say and leaves us assorted goodies 173
Washington and the high purityof modern lead. How do thesefactors explain the slipping of thelead?
1461.
7.21Cracks
Diamond cutting is the art offracturing a crystal in precisely theright way. Sculpture also requiresgood control over fracturing. Ifyou have ever cut glass tubing,you have probably used the trickof first putting a small scratch onone side and then snapping thetube. This procedure avoids ajagged edge.
What determines where a crackwill go? Why does one start andpropagate at all? I can fracturea piece of glass with a stress that ismuch less than that needed tobreak the atomic bonding, butthe bonding is neverthelessbroken. l-low is the atom-atomripping accomplished with suchrelatively small applied forces?
1466 through 1474.
7.22Chrome corrosion
Your car's chrome finish may cor-rode with time, although recentlythat problem has become muchless likely. Corrosion would setin at the defects in the outerlayer of chromium (Figure 7.22),so in the past car engineers didtheir best to make a continuous,thick chromium layer to reduce
=HE:=5$3‘¢{52§'ii'1§§lJilgirF5ilfilmiififiI;E‘";'~".>'='-iii.!Ir.i§§§-i§fi§i§?l!ia§;~;;':g2r;!.r£:apie,;;,la»,.35;;5rig,.35»;-5;:,canwhee;:5;r:2‘I§-.-.'.'r:a<,=:;.=,=,=,=;;=.;i=2;5-2:2;;.l=.=:=!=;arlr-?,g:zl'>,;5=,' Chromium
"Figure 7.22Chrome corrosion develops atthe defects in the chromium.the possibility of such defects.However, blemishes were stillbound to occur through normalcar usage. Then it was noticedthat corrosion became muchless likely if the chrome finishwere full of many small defects.So now small defects are put inon purpose. Why does a defectin the chromium layer lead tocorrosion, and why do moredefects lead to less corrosion?
7475.
7.23Polishing
Laborious polishing, say of silverutensils, is the curse of many aperson. What does the rubbingdo? Does it cause fine scaleabrasion of the surface, meltthe surface, or smear the hillsinto the valleys on the surface?Actually, “the nature of the polish-ing process has been an unsettledquestion ever since Isaac Newtonattempted to explain the physicsof the process three centuriesago" ( 1477),’ although recentwork has shed more light on it.What is meant by a “smoothsurface"? Smooth comparedto what? What happens to the
surface, on the molecular level,if the polishing is either abra-sion, melting, or smearing?
1476; 1477.‘From "Polishing," by E. Rabinowicz.Copyright © 1968 by ScientificAmerican, Inc. All rights reserved.
7.24Sticky fingers
l-low do adhesives stick? 'I'hat'sa simple question to ask but a verydifficult one to answer. You maybe tempted to dismiss it by mum-bling something about intennolec-ular forces, but don't, for thereare inherent difficulties in such aquick answer.
For example, what holds my cof-fee cup together? Intermolecularforces? Suppose I crack it in twoand then carefully piece it backtogether. I'll do such a good jobthat the crack will hardly bevisible. Will the two pieces staytogether? Aren't the intermolec-ular forces involved the same?
Glue, paste, or some otheradhesive would help here, butexactly how? Does the adhesivehave to be sticky? Does it haveto be fluid? Why will someadhesives work in this case where-as others will not? Are theresome materials that cannot bemade to adhere with any ad-hesive?
There are cases in which onereally should worry about twomaterials spontaneously adheringwithout an adhesive. In the earlydays of manned space explorationthere was a real concern that anastronaut's metal-soled boots
I74 The flying circus of physics
would spontaneously stick to themetal space capsule. What prompt-ed the concern? We should bethankful such ready adhesionisn't common, for otherwisethe world would have long agoground itself down into a stickymess.
.950; 1432; 1478 through 1480.
The walrus has his last say and leaves us assorted goodies 175
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212 Flying circus of physics
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Index
Absorption, acoustical, 1.15 Athletics. 88¢? 590115radiation, 3.38, 3.71, 3.75, P11011110 b01T1b$. 3-24. 3-27. 3-97.
3.76, 3.79-3.84, 3.91, 3.93, 6.36, 7.173,95, 6,5 Atmospheric physics, 1.28, 1.29
Acoglaratiqn, 2,21 1.35, 1.36, 1.38, 1.73-1.76,Acoustics, 1,26, 1,27 3.63, 3.97, 4.66, 4.73, 4.65,Adhesion, 7.24 5.7-5.9, 5.13, 5.16, 5.16,Adiabatlc process, 3.16, 3.18— 5.50, 5.58-5.65, 5.99.
3.23, 3.32, 3.46, 3.47, 4.76 5.100. 5.102, 6.106, 6.25.Airfoil, 2.55, 4.31, 4.94 6-30-6-34Airplane, 1.24, 1.73, 3.1, 4.31, Aurora. 1-75. 6-30
4.32, 4.37, 4.94, 6.27, 6.42, Avalanche. 1-6. 3-477.14
Air tube, 4.2 Ball lightning, 5.107,~6.35Altitude, 2.6, 3.1, 3.2, 7.14 Balloon. 3-5. 7-12Aluminum foil, 3.71 Banl°. 1-6Andes glow, 6.48 Barometer, 3.3pg-,9|g oi coma.-,1, 3,102 Baseball, 2.2, 2.4, 2.9, 2.12,Angular momentum, 2.40, 2.41, 2-13. 2-66. 4-39. 4-40
2.44-2.49, 2.51. 2.56, 2.56, Bathroom physics, 1.46, 1.46.2,59_2_73_ 4,54, 4,57 1.51, 2.39, 3.52, 3.78, 4.67,
Antenna, 6.26 4.73, 4.107, 4.123, 5.3,Anticorona, 5.79 6-14Anflf|'g919' B31|"l1Ub, 3.78, 4.67, 4.73, 5.3,
Antinode, 1.2, 1.44 6-14Antiroll tank, 2.60 Bars. 1-66. 2.4. 2-13. 2-66Aquaplaning, 4.44, 4.120 Bav of Fundv. 4-57Arghgry, 2,67 BB8C|"lb6||, 4.20
Archimedes's death ray, 3.76 Beach p1'lY$11->6. 1-5. 1-37. 1-42.Archimedes's principle, 4.7, 4.9, 1-49. 4-2. 4-14. 4-43. 4-47-
4,11 4.50, 4.60, 5.19, 5.20Afcs, 5,43, 5,120 Bead lightning, 6.34Art forgeries, 7.16 3BBf'$ 13W. 2-53Artillery, 1.29, 1.65, 1.69, 1.76, B885. 5-55
2.52 Beetle, 2.15, 4.45
Bell, 2.63Belt of Venus, 5.62Bernoulli effect. 1.54, 3.34,
4.19-4.41, 4.44Bicycle, 2.26, 2.29, 2.31, 3.16,
5.27Big Bertha, 2.52Billiards, 2.27Binaural hearing, 1.70, 1.72Bioelectricity, 6.2Birds, 1.37, 4.77, 4.97, 4.98,
5.9Bishop's ring, 5.82Blackbody radiation, 3.73,5.106Blacklight, 5.113Bleaching, 5.103Blood pressure, 4.3Blow-holes, 3.8Blue arcs, retinal, 5.120Blue moon, 5.84Blue Ridge Mountains, 5.86Blue sky, 5.59, 5.61Boat, 3.77, 4.7, 4.33, 4.44,4.46,
4.91Boiling water, 1.12, 3.61, 3.62Bolt from the blue, 6.34Book, 2.33, 2.50Boomerang, 2.55Bores, 4.56Bottles, 1.48, 1.57, 2.44Bowing, 1.7, 1.10Boyle's law, 3.6Brakes, 2.19Brewster's angle, 5.19Bride 1.34 2.57 4.B4
219
Brocken bow, 5.79Brontides, 1.36Brownian motion, 1.67Bubbles, 3.44, 3.108, 3.109,
4.81, 6.20nucleation, 1.13, 1.46, 1.48,
3.33vibration, 1.12, 1.13
Buckling, 3.106Bullet, 2.49Buoyancy, 3.15, 3.23-3.25,
3.28, 3.29, 3.32. 3.34-3.373.109, 4.6, 4.7, 4.9-4.12,4.14, 4.16-4.18, 4.70
Butterfly, 5.94
Cake, 3.2Camera, 5.24Candle, 3.1 10Capillarity, 3.38, 3.100-3.107,
3.110Capillary waves, 4.45Carburetor, 3.53Cars, 1.1, 1.65, 2.3, 2.5, 2.19-
2.21. 2.23, 2.24, 2.26, 2.36-2.38, 2.41, 2.42, 3.20, 3.53,4.30, 4.79, 4.90, 4.120, 5.48.5.53, 5.85, 5.138, 6.13, 6.42
Cats, 2.45, 5.30Caves, 3.8
Cavitation, 1.46, 1.48, 4.105Cellophane, 5.52Celts, 2.72Center of mass motion, 2.7, 2.8,
2.14Cerenkov radiation, 7.15Chair, 2.14Chalk, 1.1Champagne, 3.6, 3.19Cheerios, 3.100Cheerleading horn, 1.63Chimney, 2.51, 3.34Chinook, 3.18Chlandi fiures 1.7
220 Index
Chocolate syrup, 4.125Christmas ball, 5.141Christmas tree lights, 5.63Cigarette, 3.36, 5.89Click beetle, 2.15Clothes, 1.16, 3.79, 5.22, 6.44Cloud maps, 5.72Clouds, 3.23-3.29, 3.32, 4.100
5.70, 5.71, 5.73, 7.4Coffee, 1.22, 3.91, 4.70, 4.101Coherent light, 5.115Coin, 4.78, 5.4Coke, 1.13, 3.19Collisions, 2.10-2.13, 2.16Color, 3.92, 5.126, 5.128-
5.131Combination tones, 1.64Combustion, 3.11 1, 3.112Condensation, 3.17, 3.22-
3.24, 3.26-3.32, 4.101Conduction, acoustical, 1.20,
1.71, 1.72thermal, 3.42, 3.45, 3.48,
3.49,.3.59, 3.69, 3.78,3.80, 3.81, 3.84, 3.91,3.93, 3.96, 3.112
Confessional acoustics, 1.27Contrail, 3.32Convection, 3.44, 3.56, 3.59,
3.66, 3.70, 3.79, 3.84-3.89, 3.93, 3.96, 4.71.4.98, 4.101
Convertible, 3.20Cooking, 1.12, 2.17, 3.2, 3.55.
3.56, 3.59, 3.65, 3.71, 3.75,3.80, 6.5, 7.9
Cooling rate, 3.40, 3.52Com, 7.13Corona, 5.80, 5.81, 5.83Corrosion, 7.22Corrugated pipe, 1.54Corrugated road, 2.59Cosmic rays, 7.14Cosmology, 7.3Crc 3.113 3 - 2
Crapper, 4.107Creep, 4.119Cross section, 2.1Crown flash, 5.47Crumbs, 6.17Crustacean, 5.111Crystals, 3.98, 5.93Crystal radio, 6.26Cultivation, 3.101Current, electric, 5.121, 6.1,
6.32Current, ocean, 4.61, 4.62, 6.4Cusps, 4.60Cyrano do Bergerac, 7.2
Dam, 2.40, 4.1Davy mine lamp, 3.112Death, 2.5, 3.7, 4.14, 6.1. 6.47Death Valley, 3.21Decompression, 3.9Desert, 4.102Dew, 5.26, 5.41Dewbow, 5.41Diabolo, 2.70Dichroic crystal, 5.56Die swell, 4.127Differential, 2.41Diffraction, acoustical, 1.37,
1.40, 1.42, 1.43optical, 5.95-5.98, 5.105
Diffusion, 3.92, 4.16, 4.131Dike, 4.1Dilatancy, 4.127Discharge, 5.86, 6.32-6.49Dispersion, optical, 5.13, 5.16,
5.32-5.34, 5.58-5.63,5.79, 5.84-5.93. 5.129
radio, 6.31Distrail, 3.32Diving, 3.7, 3.9Divining, 7.5Doppler effect, 1.65, 1.66Drafting, 4.79Dragster, 1.1, 2.21, 4.90Dro,3.65 3.109 4.108 4.113
4.121, 5.28, 5.32-5.41Drowning victim, 4.14Drum vibration, 1.3Dry dock, 4.9Dune, 7.18Dunking bird, 3.64Dust, 3.11 1Dust devil, 4.71
Earthquake, 1.45, 6.38, 7.8Eat, physics you can, 1.2, 1.18,
1.19, 1.22, 1.56, 1.57, 3.2,3.6, 3.19, 3.50, 3.54-3.57,3.91, 3.100, 4.70, 4.110,4.113, 4.119, 4.122, 4.124-4.126. 5.54, 5.88, 5.108,6.12, 7.9
Echo, 1.30-1.32, 1.34Eclipse, 5.25, 5.99Edge oscillation, 4.89Edge wave, 4.47Eel, 6.4Egg, 2.71, 4.23, 4.124, 7.9Ekman spiral, 4.61Elastic fluid, 4.122, 4.123, 4.129Electric eel, 6.4Electric field, 5.47, 6.4, 6.9, 6.14,
6.15, 6.32-6.34, 6.36-6.40,6.43, 6.45, 6.50
Electrocution, 6.1, 6.3, 6.47Electrostatics, 6.7-6.18Entropy, 3.116Eskimo roll, 2.35Explosions, 1.29, 3.111, 3.112Eye floaters, 5.96
Falkland Islands, 2.52Fata Morgana, 5.8Feedback, acoustical, 1.41, 1.56Fences, 4.92, 6.10Fibrillation, 6.1Fiddlestick, 2.34Film creep, 4.119Films, 4.109-4.112, 4.114.
4.115, 4.119, 5.91, 5.92
Fire, 3.35, 4.72 Greenhouse, 3.83Fireflies, 5.110 Gulf Stream, 4.62Fireplace, 3.34 Gyroscopic motion, 2.69-2.73Fire-walking, 3.69Fish, 4.12, 4.82, 4.111, 5.1, 5.5 Haidinger's brush, 5.57Fixed-point theorem, 7.7 Halo, 5.43, 5.46Flachenblitz, 5.47 Hammers, 2.11Flags, 4.29 Harp, 1.8Floaters in eye, 5.96 Haze, 5.78, 5.86Flux, 2.1, 3.81 Heat island, 3.93Fluorescence, 5.113, 5.114, 5.131 pipe, 3.59, 3.64Flying, 4.31, 4.32, 4.35, 4.77, stroke, 3.90
4.97, 4.98 Heiligenschein, 5.26FM radio, 6.25 Helium, 1.21Focusing, acoustical, 1.27 Honey, 4.125Fog, 3.19, 3.30, 5.85 Homs, 1.60, 1.63Fogbows, 5.44 Hourglass, 2.16, 4.6Foghorn, 1.42 Hula-Hoop, 2.30Fork, 5.95 Humidity, 3.3, 3.90Freezing, 3.11, 3.39, 3.40, 3.42, Humming, 5.116
3.44-3.51 Hydraulic jump, 4.58Friction, 2.19-2.22, 2.79, 4.54. Hydroplaning, 4.44, 4.120
4.76. 4.106. 7.19and sound, 1.1, 1.2 Ice, 1.19, 2.25, 2.37, 3.38, 3.43
Frisbee, 4.34 3.46, 3.50, 3.54, 3.104, 5.42Frost flowers, 5.51Fundy, Bay of, 4.57
Galvani, 6.2Gegenschein, 5.76Gelatin, 4.124, 4.126Geysers, 3.66Ghosting, 5.6Ghost mirage, 5.14Ghost wakes, 4.75Glare, 5.49Glasses, 5.49, 5.112, 5.117Glory, 5.79Glue, 7.24Goggles, 5.1, 5.65Golf, 2.6, 4.36, 4.96Gramophone, 1.60, 1.64Gravitation, 2.74-2.79, 7.1Gravity waves, 4.15, 7.4Green flash, 5.16
5.43, 5.45Ice blink, 5.72lcehouse, 3.58Ice skating, 2.54Impedance matching, acoustical,
1.60. 1.62Incandescent bulb, 3.72, 6.6Incense swinging, 2.58Indians, 1.20Indudtion, magnetic, 6.21-6.23Infrared, 7.16lnfrasound, 1.45Insects, 2.15, 3.88, 4.28Interference, acoustical, 1.24-
1.26optical, 5.34, 5.52, 5.59, 5.74
5.79. 5.91-5.101. 5.115water waves, 4.41, 4.42, 4.44-
4.47, 4.59Invisible man, 5.2
Index 221
ionosphere. 6.30,
Joule heating, 6.1Judo, 2.48Jumping, 2.8Jumping beans, 2.7
Karate, 2.10Kayaking, 2.35Kelvin-Helmholtz instability, 4.85Kelvin water dropper, 6.8Ketchup, 4.126Kinetic gas theory, 3.94Kitchen physics, 1.2, 1.12, 1.18,
1.19, 1.46, 1.56, 1.57, 2.17,3.2, 3.10, 3.19, 3.50, 3.55-3.57, 3.59, 3.62, 3.63, 3.65,3.71, 3.75, 3.80, 3.91, 3.100,4.13, 4.17, 4.19, 4.23, 4.24,4.58, 4.59, 4.119, 4.121,4.122,4.124—4.126, 5.4, 5.54, 5.95,5.108, 6.12. 7.9
Kites, 4.99, 6.39Knuckles, 1.17Kundt tube, 1.47
Lake, 4.102, 4.109, 5.67, 5.101Land color effect, 5.128Lapse rate, 3.37Laser, 5.17, 5.104, 5.115Lasso, 2.32Latency, visual, 5.117, 5.122Latent heat, 3.22, 3.40, 3.43, 3.52,
3.54-3.62, 3.64, 3.68, 3.93Lead, 3.69, 7.20Leaves, 4.102, 5.25, 5.28Levitation, 4.21, 4.22, 5.104, 6.21,
7.1, 7.2Lightning, 1.38, 5.47, 6.32-6.48
bugs, 5.110rod, 6.40
Liquid crystal, 5.93Liquid rope coil, 4.125Looming, 5.7Lowitz arc, 5.46
222lndex
Mach band, 5.127Magnetism, 6.19-6.24Mamma, 3.29Maps, 2.78, 5.72Margarine, 4.126Masonry wall, 3.107Mayonnaise, 4.126Meandering, 4.64Mesh, 4.87, 5.105Microwave, 6.5Mie scattering, 5.78-5.90Milk, 4.70, 4.110, 4.113, 5.88Mine lamp, 3.112Mirage, 5.7-5.11, 5.14Mirror, 5.12, 5.15, 5.74Mock sun, 5.42Moire patterns, 5.142Moment of inertia, 2.33, 2.37-
2.39, 2.42, 2.74Moon, 2.74, 2.76, 2.77, 4.52-
4.54, 5.13, 5.18, 5.37, 5.69,5.84, 5.134, 5.136, 7.2
Mountains, 2.78, 3.22, 3.60, 5.7Mother-of-pearl clouds, 5.73Mud, 3.113, 5.87Mushroom, 3.24Music, 1.3, 1.4, 1.8, 1.10, 1.23,
1.26, 1.51,1.52,1.54Mustard, 4.126
Nappe oscillation, 4.89Nerves, 6.2Noctilucent clouds, 7.4Noise, 1.68Non-Newtonian fluids, 4.122-
4.131North Sea, 4.1Nuclear bomb, 3.24, 3.27, 3.97,
6.36, 7.17
Ocean physics, 3.9, 4.9, 4.10,4.12, 4.16, 4.41-4.43, 4.46-4.54, 4.61, 4.62, 4.112, 5.195.21, 5.67
Oil, 4.78, 4.101, 4.1_08, 4.125, 5.91
Olber’s paradox, 7.3Optical activity, 5.54Orbits, 2.75. 2.76, 2.79Orchard, 3.95Osmotic pressure, 3.103-3.107Oven, 3.56Oxbow lake, 4.64
Paint, 4.126Panama Canal, 4.4, 4.5Parachute, 4.90Parhella, 5.42Pendulum motion, 2.44, 2.56,
2.58, 2.61-2.64, 4.90Pepper, 4.1 17Percolator, 3.67Perpetual motion, 6.24Phosphenes, 5.121Phosphorescence, 5.131Photochemistry, 5.1 10-5.1 12Pie pan, 3.75Pillars, 5.39, 5.45Pinhole optics, 5.23-5.25Ping-pong ball, 2.18Pipes, 1.44, 1.46, 1.54, 3.11, 3.70Plastic wrap, 5.52, 6.18Plumes, 3.37Poisson spot, 5.98Polarization, 5.19, 5.36, 5.48-5.57Pole vaulting, 2.8Polishing, 7.23Pond, 3.44Pool shots, 2.27Porpoise, 4.51Pouring. 1.48, 4.118Power, 1.62, 2.15Power lines, 6.50Prairie dog, 4.27Precession, 2.26, 2.69Pressure, barometric, 4.13
gas bubbles, 4.105hydrostatic, 4.12, 4.13, 4.130negative, 3.103phase change, 3.48-3.49
Pressure cooker, 2.17
Projectile motion, 2.2, 2.49, 2.52 Rope tricks, 2.32Protein structure, 7.9 Rotating frame, forces in, 2.52-Pump, 3.16 2.54, 4.61, 4.65-4.67Purkinje, 5.122, 5.124, 5.126 Rubber band, 1.11, 3.13Purple light, 5.58, 5.60 Rubdown, 3.52
Quicksand, 4.130 Sailing, 4.33Saint Elmo's fire, 6.46
Race cars, 1.1, 1.65, 2.42, 4.30, Salt ring, 3.634.79, 4.90 Salt water, 4.4, 4.5, 4.16-4.18
Radiation, 7.14, 7.15 Sand castles, 6.17Radiation force, 5.104 dunes, 1.6, 4.102, 4.106Radiator, 3.68, 3.70 footprints, 7.11Radio, 1.64, 6.25, 6.26, 6.28,6.29 ripples, 4.104Rain, 2.1, 5.31, 6.43 vibrations, 1.5, 1.6, 1.7Rainbow, 5.32-5.41, 5.44 Santa Ana, 3.18Ranque-Hilsch vortex tube, 4.76 Sap, 3.103Rayleigh iet, 4.113 Satellites, 2.75Rayleigh scattering, 1.30, 5.58,5.59 Schooling, 4.82Rayleigh-Taylor instability, 4.15, Scotch tape, 6.11, 7.10
4.18 Screen, 5.105Rayleigh waves, 1.31, 1.34, 7.8 Scuba diving, 3.7Rays of Buddha, 5.135 Sea gulls, 1.37Records, 1.4 Searchlights, 5.75, 5.137Reflection, acoustical, 1.27, 1.30, Seashells, 1.49
1.31, 1.74 Seasons, 3.81optical, 5.2, 5.6, 5.12, 5.15, 5.17, Secondary flow, 4.63, 4.64
5.19-5.22, 5.26, 5.27, 5.30 Seiches, 4.555.32, 5.42, 5.47, 5.91, 5.141 Shadow, 1.76, 5.23, 5.25, 5.87,
Refraction, acoustical, 1.28, 1.29, 5.124, 5.125, 5.1271.33. 1.35, 1.38, 1.39, 1.73 Shadow bands, 5.99, 5.100
optical, 5.1, 5.3-5.11, 5.13, Shampoo, 4.1235.16-5.18, 5.32, 5.42, 5.46, Shark, 4.515.51, 5.91, 5.92, 5.99, 5.100, Shaving cream, 4.1265.102, 5.104 Shearing, 1.5, 1.6, 4.126, 7.11
water waves, 4.48 Ship, 2.60, 4.9, 4.37, 4.46Refrigerator, 3.74 Shock waves, 1.73, 1.74, 1.76,Resonance, acoustical, 1.1. 1.2, 4.56, 4.58
1.44-1.59 Shower, 1.51oscillations, 2.56-2.68 Shrimp, 3.89water waves, 4.55, 4.57 Signal-to-noise ratio, 1.68
Rice Krispies, 1.18 Silent zones, 1.29Rivers, 2.53, 4.64 Silicone putty, 4.127, 4.128Rockets, 1.69 Singing, 1.51, 1.52Rocks, 2.40, 3.105, 4.7 Sink physics, 1.46, 1.48, 3.10,Rope coil, liquid, 4.125 4.13, 4.17, 4.19, 4.23-4.25,
4.47, 4.58, 4.59, 4.67, 4.87,5.3
Siphon, 4.105, 4.107, 4.129Skating, 3.46Skid, 2.37Skiing, 2.46, 2.59, 3.45, 4.95,5.65Skipping rock, 2.40Sky brightness, 5.64, 5.66
color, 5.58-5.62, 5.68polarization, 5.50, 5.55-5.57
Smoke, 3.35-3.37, 4.103, 5.89,5.90
Snow, 1.14, 1.15, 3.45, 3.48-3.50, 3.96, 3.99, 4.92, 4.93,6.10
avalanche, 3.47blindness, 5.139wave, 7.6
Soap, 4.117, 5.91, 5.113Soaring, 4.98Solar flares, 7.14Sol-gel change, 4.126Sonar, 1.39, 1.66Sonic booms, 1.73, 1.74Soup, 4.122Space. 3.82, 3.84Speakers, 1.60, 1.62, 1.64Speckle pattern, 5.115Speed of sound, 1.21-1.23, 1.28,
1.29, 1.35Speedometer, 6.23Spillway, 4.89Splashing, 1.13, 4.88, 4.113, 6.14Spoon, 4.24Sports, 2.2, 2.4, 2.6, 2.8-2.10.
2.12, 2.13, 2.27, 2.46, 2.48,2.66, 2.67, 3.45, 3.46, 4.33,4.36, 4.39, 4.40, 4.50, 4.88,4.95, 4.96
Spray gun, 4.25St. Elmo's fire, 6.46Stacks, 1.37Stars, 5.66, 5.97, 5.102, 5.106.
5.119. 7.3Steam devil, 4.73Stewardess, 3.1
Index 223
Stones, 2.40, 2.72, 3.105, 3.115Streetlights, 5.63, 5.122Stress, 1.14, 4.124, 5.93, 7.11-7.1String telephone, 1.9
vibrations, 1.8-1.11Stroboscope, 5.116, 5.118, 5.131Sublective tones, 1.64Submarine, 1.39, 3.7, 4.10Sugar, 4.78, 5.108, 6.12Sunbum, 5.109Sun dog, 5.42Sunglasses, 5.49, 5.112, 5.117Sun pillar, 5.45Sunsets,5.16, 5.58, 5.60-5.62, 5.100Suntan, 5.109Superball, 2.18, 2.28Supercooling, 3.39Supernumerary, 5.34Surface tension, 3.5, 3.102, 3.108,
3.109. 4.13, 4.101, 4.114-4.117, 4.119—4.121
Surface wave, 1.31, 1.34, 7.8Surfing, 4.49-4.51Syrup, 4.125, 5.54Swimming, 4.88, 5.1, 5.92Swinging, 2.56, 2.53
Tacoma Narrows Bridge, 4.84Tailgating, 4.79Taylor's ink walls, 4.66Tea leaves, 4.63Teapot, 1.56Television, 5.116, 5.118, 5.132,
6.25, 6.27Temperature of space, 3.82, 3.84Thermal expansion, 3.110-3.115Thermometer, 3.12Thixotropic fluids, 4.126Three-dimensional perception,
5.133Thunder, 1.38, 1.74Thunderstorm, 3.41, 3.86Tides, 4.52-4.57Tight-rope walking, 2.43
_ 12 2 =3.49 4.120
224 Index
Toilet paper, 2.39 Watches, 2. , .11Toilets, 4.107 Water bug, 4.45Tomato soup, 4.122 bell, 4.114Tops, 2.69, 2.73, 5.118 Waterfall, 2.65Tomado, 1.33, 1.45, 4.68, 4.69, Water glass, 4.13, 4.15
5.107 hose, 4.8Torque, 2.23, 2.24, 2.31, 2.35, pipes, 1.46, 3.11
2.39-2.41, 2.44-2.46, 2.4e- sheet, 4.1152.51, 2.56, 2.58, 2.74 spout, 4.68
Toys, 1.9, 1.54, 1.58, 1.61, 2.7, stream, 4.19, 4.22, 4.24, 4.114-2.18, 2.27, 2.28, 2.30, 2.34, 4.116, 6.92.47, 2.68-2.70, 2.72, 2.73, witching, 7.53-34. 3-77. 4-21. 4.34, 4.49, Waveguides, acoustical, 1.254.99, 4.127, 4.128. 5.118 Wave speed, 4.43, 4.56
Tfflifli. 2-25. 2.59, 4.26 Waves, water, 4.41-4.60, 4.115Triangle, luminous, 5.21 Weight, 2.16Triboelectricity, 6.7, 6.10, 6.12 Weissenburg effect, 4.124Triboluminescence, 5.108 wells, 3,4Tllflflfil. 3-5 Wetting, 3.100, 3.102T1.ll’bl.l|9l'109, 1.33, 4.85-4.33, Whip crack, 1,77
5.99. 5-102 Whirligig beetle, 4.45Whiskey, 4.119Whispering, 1.43, 1.50
gallery, 1.31Whistlers, 1.25Whistling, 1.56-1.59, 1.61
wires, 1.55Wien's law, 3.97Wind, 1.35, 1.53, 1.55, 3.18, 3.86,
4.33, 4.38, 4.83-4.85Windchill factor, 3.52Window, 5.6Windshield, 4.28, 5.53, 5.77Wine glass, 1.2Wings, 4.30. 4.31. 4.35, 4.37, 4.94
4.97Wire mesh, 4.87, 5.142Work, 2.21
UFO's, 7.1Ultrasound, 1.66Ultraviolet light, 5.103, 7.16Unicycle, 2.61U-tube, 3.15
V-2 rockets, 1.69Vee formation, 4.77Ventilator, 4.27Venus, Belt of, 5.62Vibration and sound, 1.1-1.11Vikings, 5.56Violin. 1.10Viscosity, 4.124-4.126, 4.130Vision, 5.115-5.141Visual latency, 5.117, 5.122Volcano, 5.82, 6.37Vortices, 1.47, 1.57, 1.61, 4.67- x'TflV$. 5-127. 7-15
4.85 4.90 4.92 4.94 4 98' ‘ ' ' ' ’ Yoyo, 2.474'm0' 4‘1o2-4'1o4 Yubana, 3.61
Wakes, 4.44-4.46, 4.75, 4.77- Zenith blue, 5.61432 Zodial light, 5.76
Sltort Answers
There are several very realdangers in writing answers. evenshort ones. to The Flying CircusFirst or all, my references and myphysics may be wrong. Thisdanger may especially be true withthose questions dealing with topicsstill under research. such as balllightning, whose nature issometimes tackled in every otherissue ol some of the |ournals. All Ican say about my answers here isthat they are the best I can do tl"l avery small amount oi space andwith the currently availableliterature. Please remember tl1atthese short answers are but the tipof the iceberg. there is muchphysics below each. And youshould not take them as the lastword; instead. you should takethem as starting points and thenupdate them as new papers andarticies appear
The second danger in writinganswers is more senous andmakes me hesitate in even trying.You may llip to the answer sectionol this book so quickly that youmiss the excitement of thequestion Unless you savor thequestions. even to the point olsome frustration, you will miss thepoint of this book. The potential torlearning how to examine the worldll'l which you live lies much more inthe first part ol this book than in thesecond. So. please spend as muchtime as you can worrying over yourown answers before you turn tothis section or search the library lorrelerences.
1.1 The squeal heard in theseseveral situations results Irom"stick and slip ' For example. the
. - — 1 "r _ m
incorrectly held chalk first sticks onthe chalkboard, but when the writerbends the chalk sufficiently, itsuddenly slips and then vibrates.periodically striking the chalkboardand producing the squeal we hear.As the vibrations decrease. thefriction between the chalk and theboard increases until the chalksticks once again1.2 The finger excites thelongitudinal oscillations. that is. thevibrations along the perimeter olthe rim. The nm also oscillatestransversely, that is. perpendicularto the rim. This second type ofoscillation causes the lluid motionsince it is a motion into and out ofthe liquid. The antinodes of thetransverse oscillations and henceoi the lluid motion are 45" from theantinodes ol the longitudinaloscillations. Since the lingersposition must be a place ofmaximum longitudinal motion andthus a longitudinal antinode. thelluid motion must have an antinode-15° behind the linger.
1.3 Imagine that one membraneis oscillating and the other is notThe moving membrane begins toexcite the other by pushing on theair between them. As the secondmembrane begins to oscillate.however, the air thereafter hindersthe oscillations ol the lirslmembrane. eventually stopping itBy the time the air has maximizedthe oscillations ol the secondmembrane and stopped the first,the situation is reversed. and theair then transfers tho oscillationback to the first membrane.
1.4 To press the bass into therecords at the same intensity tevetas the higher lrequenc es wouldrequire an oscillation ol the needlethat would carry it into the adjacent
groove.1.5 and 1.6 In both ol thesecases the sound apparently resultsIrom the oscillation of the sandwhen pans cl it are forced to moveunder a sheanng stress. In thefootstep the sand beneath the footis forced downward; in the sanddune a small avalanche causessome sand to slide over anotherpart. Although the noise productionis not understood, it is apparentlyconfined to sand heving mostlysphencal grains of unilorm size1.7 The drawing ol the bowstnngon the edge of the plate sets theplate into vibrations. The pattem olthe vibration, that is. where thereare the maximum and minimumamplitudes. depends on the shapeof the plate and where it is forcedto have no vibrations because it isheld in place. During the bowing.the sand, initially in the areas ofmaximum vibration [calledantinodes). is thrown to the areasol no vibration (called nodes},eventually collecting in order toindicate the vibrational patternThe line dust would do the sameexcept that it is carried by the aiicurrents set iri motion by thevibration. Since these currentsblow across the plate from thenodes to the antinodes and thanupward, the dust is carried to theantinodes and deposited.1.8 More ol the higher lrequenq;harmonics are excited when thebanio is plucked with the tingernailor with a sharp pick than when thestring is pulled with a finger. Thesehigher lrequencies give a twangyquality to the banio's music1.9 The voice vibrates the can.which then excites waves on thestnng. These waves excite thesecond can in a reverse way to be
Rnluilrl 225
heard- The can does not respondto the lower frequencies in yourtalk, and thus those frequencieswill be missing at the other end.making your words thin.1.10 The bow alternately sticks
l to the strings and then slips.1 leaving the stnngs oscillating
dunng the intermediate time ofsliding.1 .11 The frequ ency of a vibratingstring depends on the string'sdensity, length. and tension. If astring is tightened. the first tworemain constant. and theincreased tension raises thefrequency of vibration. If a rubberband is stretched. however. allthree of the quantities change sothat the frequency is essentiallyunchanged.1.12 The first sound comes whenthe bottom of the pan is heated andsmall bubbles form. each with aclick and collectively with a hiss.With further heating. the bubblesdetach from the bottom. rise intothe cooler water. and thencollapse. creating a louder noise.This noise continues until the wateris sufficiently hot for the bubbles toreach the surface to break. Thenthe water is in lull boil, and thenoise of the bubbles react-ing thesurface is a softer. splashingsound1.13 Part of the sound ol thebrook is due to the bubbles formedin the running water The creationol abubble has little sound, but thevolume oscillations and thecollapse of a bubble produce muchmore sound1.14 ll the ground is very cold[-10 F or lower]. the ice beneathyour feet cannot melt due to yourweight and will snap instead. (Also
566 FC 3.46-3.49‘ I
1.15 The small spaces in thesnow's surface absorb the soundjust as acoustic tile does in mostmodem offices. As the snowbecomes more packed, this soundabsorption is reduced.1.16 Any periodic motion canproduce sound waves. Theperiodic |erk|ng as the individualthreads snap when you rip clothwill set up sound waves for you tohear the ripping1.17 The popping is due to thebursting of tiny gas bubbles in thefluid lubricating the linger |ointswhen the fingers are pulled and thefluid pressure is thereby reducedSeveral minutes are neededbefore the gas is reabsorbed andready for an encore.
1.18 The sound is caused by therelease of air from the cerealgrains as those grains becomesoggy in the milk and eventuallyburst
1.19 The cracking I5 due to thethermal stresses in the ice as theice warms The frying ' sound.however. is due to the bursting oltiny air bubbles trapped in the iceas the surface reaches thosebubbles. ice free ol such bubbleswill melt with only the cracking1.20 The tact that the speed ofsound is greater in ground than inair is not important since horsestravel much slower than soundThe main advantage in listening tothe ground is that there are lessobiects in the sound's path toscatter and attenuate the sound.1.21 The resonant frequencies of"ll - .- .- . .-.rI" ..
your mouth [as any otherresonating volume of gas) dependdirectly on the speed of sound inthe gas in it. The speed of sound isgreater tn helium than in air. andtherefore your voice will have ahigher pitch.1.22 Air trapped on the powder isreleased as the powder dissolves.Since the speed ol sound is lowerin air than in water. the speed olsound in the air-water mixture islower than in pure water. Duringthat period while the air escapesthe container. the resonantfrequencies of the water whichdepend directly on the speed ofsound. will also be lower. Hence.you hear a lower tone until the airescapes1.23 Because resonantfrequencies in a wind instrumentdepend directly on the speed olsound. those frequencies increaseas the player warms the instrumentwith his or tier breath and therebyincreases the speed of sound in it.Warming of the stnng instrumentsby lriction will expand the string.thus decreasing the tension on thestrings. which decreases theresonant frequencies ol the stnngvibrations.1.24 Within a couple ol metersfrom the ground, the sound directlyfrom the airplane can interfere withthe sound reflected from theground to enhance certainfrequencies. The height at whichconstnictive interference can occur[where one sound wave willreinforce another] depends on thewavelength of the sound. thenearer the ground. the shorter thewavelength will be for constructiveinterference. So. near the groundyou will hear more of the shortwavelengths, and thus high
226 Flying cltcul nl pltyllcl with II'II\IiI'l'II
lrequencies. As you raise your earmore, longer wavelengths and thuslower lrequencies will be heard.1.25 The sound that is reinlorcedin its travel through the culvertmust rellect Irom the walls at acertain angle, which depends onthe wavelength of the sound. Thelonger wavelengths that arereinlorced and eventually heardmust retlect at a greater angle thanthe shorter wavelengths andtherefore travel less along theculvert's length between eachreflection and take longer to reachthe end A listener at the end willthus first hear the shorterwavelengths (higher lrequencies}and then progressively longerwavelengths (lower frequencies].1.26 To have a distinct echo. theretlected sound must come nocloser than 50 msec to the directsound. Eliminating reflections fromthe walls will drastically reduce theacoustic nchness of the room. Thewalls are designed to dittuse thesound throughout the room. Someof tho scatterers on the wallsshould be small to scatter the shortwavelengths [high lrequencies]whereas other leatures should belarger to scatter the longerwavelengths {lower 'lt'Eqt..lEl'lClB5].The scattering should be dilluseenough to eliminate dead spots oldestructive ll’llBI'lBl'EtI'tCB in theroom.1.27 Sound rays emitted fromone focus tn an elliptical room willcross at the other locus. thusmaking a conversation at the lirstlocus audible at the second.1.26 Sound travels faster inwarmer air than cooler ll the airtemperature decreases upward.the top portion of an initially
honzontally traveling sound wavewill propagate slower than thelower part, and the wave path willbend upward. with such a normaltemperature distribution. the soundwill not be able to travel very taralong the ground before thisrefraction has bent it away from theground. On a cold day the airtemperature may increase upward.especially |ust over a body olwater, thus retracting the sounddownward instead of upward.Hence the sound will be kept nearthe ground longer.1.29 The speed of sound tn airincreases as the air temperatureincreases. Thtis, as a sound wavereaches the increasingly warmerair in the stratosphere. the higherportion oi the wave will travel tasterthan the lower portion, causing thewave path to bend over andeventually turn downward. Soundwill be hoard where it reaches theground. In the meantime, somedirect sound from the source willtravel horizontally until it tsscattered or absorbed by‘ theobjects on the ground. Betweenthe outer region ol this hottzontalpropagation and the region wheresound ts returned from thestratosphere, there ts a region tnwhich sound Irom the source is notheard. It the sound returned Iromthe stratosphere is reflected by theground sufficiently well that it canreturn to the stratosphere, it can bebent over and returned to theground once again to give yetanother region ol sound. the outerwhite area tI'l Figure 1.29.1.30 The scattering ol sound byobjects small with respect to thewavelength of the sound willdepend inversely on the lounnpower of the wavelength. The
shorter wavelengths {higherfrequencies] will therefore bescattered more than the longerwavelengths {tower frequencies].An echo ol a yell will thus be higherpitched because the higherlrequencies are more stronglyreturned.1.31 In continuously reflectingfrom the walls of the dome, thesound waves are reinforced in anarrow belt around the perimeter olthe wall. lf the listener standsinside this belt, he or she can hearthe whisper. Further from the wall,however, the reinlorcementdecreases and the whisperbecomes inaudible A whisperworks better because it has moreof the high frequenq; sounds thandoes normal talking. and theaudible belt is wider with higherfrequencies.1.32 Suppose you are lacing apicket lence. The sound rellectedfrom a particular picket on your telt.say, will retum to you slightlysooner than the sound reflectedIrom the next picket more to yourleft, because that next picket I5 alittle further away from you. Thesound returned lirst comes fromthe nearer pickets. and thenprogressively later sound returnsIrom progressively more distantpickets, producing a musical toneto the echo. The frequency of thetone is the inverse of the timeinterval between rellections fromad|acent pickets.1.33 Sound from outside thetunnel may not be able to reach theinside, because it is retracted sostrongly by the high velocity windsaround the tunnel. The interior ofthe funnel may also appear to besilent, because hearing is difltcutt itone is suddenly thrust into a low
Anlwlrl 221
pressure region. (Heanng isdillicult in flying until the ears havea chance to adjust to the pressurechanges in ascending anddescending.)1.34 There is no one answer tothis question since, depending onthe bndge. either eflect maydominate or both may be equallypresent.1.35 Sound goes further alongthe ground downwind not becausethere is less attenuation. butbecause the sound waves arerefracted downward in thatdirection, whereas they arerefracted upward in the upwinddirection. Because of the obstacleson the ground. the wind velocitynormally increases with height. Aninitially horizontally traveling wavemoving downwind will have itsupper portion moving at a greaterspeed than its tower portion.causing the wave to retractdownward. By similar reasoning. asound wave traveling upwind willbe refracted upward1.36 Brontides are most likelythe anomotor, sound propagationof FC 1 29. with the unseen anddistant sources being anythingfrom BJlp|O5tOI1S to thunder.1.37 Sound waves are dillracledby the aperture between the stacksand thus sent into the area behindthe stacks. The angular width olthe ditlraction pattem (the angleover which the sound will bespread by the aperture) is greaterfor longer wavelengths. Thus, it thebirds had a lower frequencysqueal. the sound would spreadmore.1.38 For reasons similar to thosein FC 1 2B and t 29, the soundwaves trom a lightning stroke will
be retracted upward by the wamierair near the ground. Beyond arange ol about l5 miles, the soundis refracted so much that it istraveling upward and then, ofcourse, cannot be heard by aground observer.1.39 This problem involves asimilar retraction ol sound wavesby a change in temperature withheight Normally the watertemperature decreases downwardwith depth- Hence. a sound waveissued horizontally will be bentover and sent downward becauseits upper portion, being in warmerwater. will travel taster than itslower portion, being in coolerwater. The retraction 0| the soundmay be so severe that all thesound is bent downward and awayfrom the submarine.1.40 Sound is diflracted by theaperture |ust as in FC 1.37.Although the door may be almostclosed, the sound coming throughthe remaining opening spreadsthrough the room.1.41 Sound Irom the guitarplayers speaker would be pickedup by his or her guitar, reamplilied,and then emitted by the speaker ashort time later. The frequency ofthe ringing is the inverse ol thetime needed to emit a sound oncethe guitar pickup is activated1.42 The angular width ol thedillraction pattern (i.e , the angleover which the sound is spreadwhen it propagates through theopening) is greater the narrowerthe opening is. Hence, thenarrower width provides morespread and should be onentedhonzonlally as shown in the liguie1.43 Barring reflection ot thesound from nearby obiects, you
hear your lnend when your friend isturned away because the sounddilfracts around his or her headThe angular width cl the diffractionpattern is larger tor longerwavelengths [smelterlrequencies)- Since whispering iscomposed largely of highlrequencies, it is heard poorly frombehind because the whispering isdiffracted less.1.44 The eltective length of atube is increased by about onethird of the tube's diameter loreach open end. This lengtheningwill increase the wavelengths olthe tube s harmonics [thusdecreasing the resonantlrequencies) and can be noticeablein wider tubes1.45 The low trequency soundcan oscillate your chest. torexample. because the variations inair pressure are sulliciently slowthat your chest can tollow them.Internal hemorrhage can resultfrom organs being lorced to rubegainst each other during theiroscillations. Lower intensity levelsmay |ust cause dizziness andnausea. Common car sicknessmay partially result from theinfrasound produced by the car.1.46 With increased flow ratesthrough the restricted portions ofthe pipes, turbulence can oco..ir,leading to cavitation (formation olbubbles}. Oscillations ol the airbubbles can be amplitied by thepipe and the walls, ceilings. andlloors to which the pipes areconnected.1 .47 The vibrations cl the rodcreate a standing sound wave inthe tube Powder at the antinodesol air motion in the tube isgradually shaken toward the nodes
Z28 Flying drcul 0| phyllcl with lnlwzrl
where it collects in the larger pilesshown in the figure If the air llow issulliciently rapid, vortices arecreated The smaller ripples of dustare formed where two adjacentvortices rise oi descend together.1.43 From the noise of thepouring water, those frequenciesthat will resonantly excite the aircolumn In the bottle will be pickedout. enhanced. and heard. Olthese the loudest frequency will bethe lowest one, but the value olthat frequency depends on thevolume ol the air column. Thegreater the volume, the lower thofrequency. Tlius, as water ispoured Irom the bottle. theresonant frequency that is hearddecreases.1.49 Noises from theenvironment, including the slightwhispers of a breeze passing theshell. will excite the shells airvolume at its resonant frequencies.The coming and going of theseresonant lrequencies gives thelistener the illusion ol hearing theocean waves come and go1.50 The length and tension ofthe vocal cords determines thepitch ol the voice. As the airpressure in the trachea increases.the cords are suddenly lorcedapart and then returned to theirnormal position. Continuedoscillations of the cords producethe air presstire variations thatexcite the resonant harmonics olthe mouth and nasal cavities.Usually a man's voice has towerpitch than a woman is because aman usually has thicker and longervocal cords which will vibrate atlower lrequencies. A boy's voice' breaks ' during the rapid growth olthe larynx, and the vocal cordschange lrom being shon and thin
to those of a man. Duringwhispering the vocal cords areremoved lrom the larynx by relaxingthem. The frequency ol the soundwill then depend on the osultationscreated by other obstacles in the airstream and on the resonantlrequencies of the mouth and nesalcavities.1.51 Were you to sing in a largeopen area, you would hear yourvoice only as it is being produced.In the shower stall each sound willrellect many times lrom the closewalls, prolonging the sensationwhen it IS heard, and thus addingbrilliance (continuation ol the highfrequency sounds) and fullness[continuation ot the low frequencysounds) to your singing1.52 A glass will oscillate atcertain resonant lrequenciesShould a singer sing tor severalseconds at one ol theselrequencies, the oscillations of theglass can build up to the levelwhere the glass cracks.1.53 The wind can howl bywhistling through wires and baretree limbs (FC 1.55] or by creatingedge tones (FC 1.56) on rootcorners or other sharp obstacles.1.54 Air flows trom the held endto the circling end, because therapid motion of the circting endreduces the air pressure there,whereas the air pressure at theheld end is atmospheric pressure.As the air ttows through the tubeand over the corrugations. it beginsto oscillate. The frequency of theseoscillations is determined by thespacing of the corrugations and thellow speed ol the air. From thesmall range of oscillationsproduced with a given twirlingspeed, the tube picks out its own
resonant lrequenqr to enhance,and that is the tone you hear lrornthe tube. A faster twirling speedmoves the range ol air oscillationsinto higher frequ encies. and ahigher frequency harmonic of thetube is then exicted and heard1.55 As the wind passes a wireor bare tree limb, the air canbecome unstable and shedvortices Irom the obstacle On atelephone wire. for example.vortices will be released alternatelyon the lop and bottom of the wireThese vortices create the pressurevariations that eventually reach ourears to be hoard. ll the wind isstrong enough. the pressurevariations on the two sides ol thewire can cause the wire to vibrate.but that vibration is not necessaryto the production 0| the sound.Because the pressure variationsare due to the vortices producedon the two sides, the wire is forcedto vibrate perpendicular to the airflow.1.56 In the edge-tone setup.vortices are shed from the edgewhen the air stream stnkes it. Thereaction lorce of the edge thencreates the sound we hear. Someof the sound returns to the sourceof the air stream. causing instabilityin the stream. which creates morevortices downstream. When thevortices reach the edge. moresound is produced, and the wholeprocedure is repeated. tn thehole-tone production, the soundthat is returned to the source ol theair stream changes the speed ofthe air stream and causes volteiirings to form [such as in cigarsmoke nngs]. When these ringsstrike the hole, more sound isproduced arid. again. theprocedure is repeated
7 The common tea kettle whistles J
Aneurc-re 229
ff
by hote-tone production. The capon the kettle has two small holesspaced with a small cavity. Whenair from inside the kettle passesthrough the first hole. that hole actsas the air stream source for thesecond hole. At first the air streamis too slow for the necessaryinstability of the air at the secondhole to cause sound. As the waterapproaches boiling, however. theair moves faster so that thevortices at the second hole arestrong enough for the sound to beheard1 .57 A coke bottle. a flute. and arecorder are different whistles thanthe ones in FC 1 56 because of theaddition of a resonant cavityadiacent to the edge or hole wherethe instability is produced. Fromthe range of frequencies in thesound made at the edge or hole.the cavity selects its resonantfrequency to enhance. and that isthe frequency heard.1.58 The air stream blown intothe police whistle creates an edgetone from which the adiacent cavityselects its resonant frequency. Theball inside the cavity periodicetlyblocks the air holes and causes thewhistling to warble.1.59 Normal whistling throughyour lips appears to be a hole tonefFC 1 B8] with an adjacentresonating cavity (the mouth], butthe details of the air flow do notseem to be worked out.1.60 The horn and the aircontained in it provided resistanceagainst which the disphragm couldwork and which would transformhigh velocity motion over a smallarea to low velocity motion over alarger area. Along narrow tubewould store the energy in standing
waves and select only its resonantfrequencies. A diaphragm openedto the room without a horn wouldbe able to move so freely thatrelatively hltle of its oscillationenergy would be transferred to airmotion.1.61 The sound is apparentlydue to pressure variations in theunstable vortices emerging fromthe central stem1.62 There are two main reasonsfor the difference in size. A largepaper cone cannot respond quicklyto a high frequency sound.breaking up into assorted wavesover its surface instead Thus, asmaller cone is used for the higherfrequency range. Second. thespeaker should spread its soundover a wide angle to fill the room.The angle ol the diffraction patternwill depend on the relative size ofthe wavelength and the speakercone. Short wavelengths [highfrequencies] on a large cone willhave a small diffraction pattem andthus will be beamed into the room.Therefore. the short wavelengthsmust come from a small speaker tobe spread well into the room.1.63 Normally the sound directlyfrom the mouth dittracts to spreadnearly uniformly in all directions Acheerleading horn with a largefront end will have considerablyless diffraction because the openend is larger than the wavelengthsin the cheerleader s yell Thus, thesound in the direction of the homwill be louder than if no horn isused.1.64 The bass notes will beproduced in the ear even if noneare issued from the speaker. tf twodifferent frecpencies are incidenton the ear, its nonlinear response
produces vibrations havingfrequencies equal to the sum ordifference of the incidentfrequencies, or the sum ordifference of some integral multipleof those frequencies. The mostprominent of these extra notes isthe difference frequ enqr. whichgives the listener a bess note1.65 The frequency heard by alistener depends on the relativespeeds ol the listener and thesource. Such a shill in the detectedfrequenqr from the frequencyissued according to the source iscalled the Doppler shift As a racecar approaches a stationarylistener. the car s whine is Dopplershifted up in frequency; as the carrecedes. its whine is Dopplershifted down lt'1 frequency1.68 Exactly how a bat extractsinformation from its signal iscurrent research and not wellunderstood. Some bats emit ashort constant frequency (CF)signal whose retum indicates thetarget's presence and whosereturn frequency can indicate thetarget's speed [see the Dopplershift in FC 1.65). Other bats emit afrequenqi modulated (FM) signal.The frequency response of thetarget is analyzed to indicate thetarget's shape, size, surfacetexture, and range. Because theFM stgnal is swept over a range offrequencies. the bat cannotanalyze it for a Doppler shift for thetarget speed- Thus, some batsemit a combinatlon FM-CF signalto obtain all the possibleinformation about the target1.67 The fluctuations are notquite loud enough (i e.. theprassure changes on the ear drumnot quite large enough} to beheard. Even if the Brownian motion
230 Flying cIrI:i.i|i 0| physics wtlh answers
were more intense. it probably stiltwould not be heard because thebrain will ignore any continuous.constant noise signal.
1.68 Suppose you are talking tosomeone in a social room. Youhear that person's voice bothdirectly and in a diffuse way after ithas reflected from the room. Ifthere are other such conversationsoccurring in the room, there is ageneral diffuse level of talk withwhich your acquaintance mustcompete. The power of that diffusebackground depends on thevolume of the room, the acousticabsorption of the walls and theother ob|ects in the room, somecharaoienstic mean free path ofsound between the walls. and thenumber of other conversations. Ata critical number of conversations,the diffuse background begins todrown the direct level of tallr fromyour friend. Any additional numberof conversations means your lnendwill raise his or her voice. but all theother people will do the same andthe party will become hopeless1.69 Because the rocketsexceeded tho speed of sound. thesound from their explosions couldreach a listener before the soundof the flight through the air.1.70 Such a live conversation ina noisy party provided at least oneadditional piece of information thatthe tape does not: directionality.You can distinguish a particularconversation from a very noisybackground it you can distinguishthe direction of the conversationthrough your normal binauralhearing.1.71 Much of the sound you hearwhen you talk. especially the lowfrequency components, comes
through bone conduction Othershear you without those lowfrequency tones that. to you, addfullness to your voice Listening toa tape of yourself on a good qualitytape player reproduces whatothers normally hear ot yourspeech1.72. You can determine thedirection of a sound source bythree means: comparison of theintensity. phase. or amval time ofthe signals at your two earsIntensity differences are uselulonly with short wavelength soundbecause long wavelengths diffractaround the head to give aboutequal intensities at the ears.However, the long wavelengthsounds will have different phasesat the ears, the phase dilferencedepending on how much fromstraight forward the sound sourceis angled. At intermediatewavelengths. corresponding toabout 4000 Hz, neither techniqueworks very well, and determinationof the source direction is moredifficult.
1.73 tf an airplane exceeds thespeed of sound at the height atwhich it is tlying, the air itcompresses will form a shockwave. Behind the airplane is acone whose outer boundary is theshock wave. As the cone sweepsthe ground, an observerexperiences first a pressure riseand decline and then another riseuntil normal pressure is resumed.The second shock wave is madeby the plane's tail- Sometimes thetwo increases in pressure areindistinguishable. other times theywill come as two distinct booms. Ashock wave may never reach theground if it is sufficiently refractedby the warmer air it encounters
dunng its descent. [For similar ‘refractions of sound waves byvariation in the air temperature,see FC 1.28 and 1-29.)1.74 Current research is beingdone on thunder production andcharacteristics. The tremendousheating of the discharge column inthe lightning stroke rapidlyexpands the air, creating acylindrical shock wave that is thebasic noise source for the thunder.Near the stroke, one maydistinguish a hissing, probably dueto corona discharge (FC 6.46), anda click, probably somehow due toan upward moving discharge in thestroke {FC 6.32). Continuation ofthe thunder [rolls and rumbles) ,may result from echoes of theinitial sound from the environment.1.75 The attenuation of sound bythe atmosphere [due to viscosityand thermal conduction) is toosevere for a sound made at aheight of 80 km or more to reachthe ground. If the sound is due tothe collision of ice crystals in one’sbreath, the temperature should beat least as low as —40"C.1.76 Shock waves from theartillery cause the visible bandsbecause the refraction of the air isaltered on their passage orbecause there is momentarily \increased condensation in a cloudor fog bank through which thewaves pass [similar to FC 3.2?t.1.77 The whip crack may be due \to the slap of the tip against itself orfrom the shock wave as the lipexceeds the speed of sound.2.1 To simplify the problem, letus assume you are wearing arainhat and need not worry aboutthe rain on your head. If the rain is ltoward your front or directly
Rncnierl 23 l
overhead. then you should run asfast as possible to shelter. It,however. the rain is on your back.then you should run with a speedequal to the honzontal velocity otthe rain. that is. along with the rain.2.2 Experience surely helpsgreatly in the outtie|der's ability toextrapolate a traiectory. Thereference suggests that theelevation angle may also be ofhelp. By running to keep the rate ofincrease in the hall's elevationangle constant. the player willamve at the proper place at theproper time. The player may havethis procedure so ingrained in hisor her playing that he or she maynot even be aware of the change inthe elevation angle.2.3 Upon approaching anintersection whose ttght has iustturned yellow. you can stop at amaximum negative acceleration.race through at some maximumpositive acceleration. or maintainyour same speed. For example. letus consider the totloviiingparameters. your car is moving at20 mph (30 ttlst when the light iturns yellow. the intersection is 30ft wide. the duration of the yellowlight is 2 s. and the maximumacceleration is either I 10mi's? [torincreasing your speed} or -10 Ills?(for stopping]. Assuming idealconditions (e.g.. that your engineinstantly responds to a push on theacceleration pedal) we cancalculate the distances to theintersection needed tor your threeDp|lDn5. tn order to race throughsuccessfully. you would have to becloser than 50 tt when the yellowappears. To stop successfully. youhave to be further away than 45 It.Between 45 It and 50 ft, you haveeither option.
2.4 Since the ball is over theplate tor only about 0.01 s. thetiming should be to about :0.0l s.The error along the vertical mustbe less than 1 mm. "The 1962world championship was finallydetermined by an otherwiseperfect swing of a bat which cameto the collision t mm too high toeffect the transler of title 14).2.5 It the wall is such that youcannot |ust drive around it. andassuming ideal conditions ofbrakes, road conditions. and so on.and ignoring any considerations ofhow people in the car might gelhurt tor impacts on certain sides ofthe car. then calculations indicatethat you should steer directly forthe wall and attempt to stop asquickly as possible. Twice as muchtorce would be needed to tum thecar in a circttar arc in attempting toavoid the wall as would be neededto stop the car in a straight stop.2.6 tn driving, the greatest speedwill be given to the clubhead for thegreatest torque you apply to theclub. For a given torque, however.the clubhead speed will depend onhow the torque is applied.According to one study {51, themore one hinders the uncocking ofthe wrists. by using a negativetorque on the wnsts dunng part ofthe swing. the greater will be theclubhead speed. The propernegative torque and this hindrancemay be pan of the timing" soughtby golters.2.7 The beans contain a smallworm that |umps upward2.8 A pole valuter must maximizethe kinetic energy in order tomaximize the height to which he orshe travels. but a high |umperoblalns most of the height from the
last spring rather than from thekinetic energy in the approach. Abroad |umper may bicycle his or herlegs to correct an initial forward tili2.9 Ruth could have hit homeruns oft stationary balls. So. unlesshe was fooled by the ball andswung too soon. a stow bell merelyadded to the chances of a homen.in2.10 The tollow-through will docomparatively little damege since itis pnmarily pushing on theopponent The karate strike isfocused a couple of centimetersinto the opponent's body. so thatinitial contact is made when thestnking hand is at its maximumspeed and thus so that the impactforce is maximum.2.11 It the point is to deform thestnrck object. such as in torgng.then an inelastic collision isdesired. A greater traction ol thehammers energy will be lost tl"teach collision the tighter thehammer s mass. S0. in forging youshould use a light hammer. tn piledriving you want to transfer kineticenergy to the pile and avoid anyloss of energy to deformation. So.use a heavy hammer there.2.12 The softer the ball. thelonger it will be in contsct with thebat. and the more work the battercan do on the belt during thecontact Thus. folow-throughshould definitely be used on asoftball.2.13 The optimum bat size wouldbe one that requlres the leastenergy from the batter to give aparticular speed to the ball.However. batters typically chooseheavier bats tor home runs ortighter bats for more ease in
232 Flylng clrcus ol physics with II‘lIIiIiFII'I
wielding the bat. giving littlethought as to the energy impartedto the ball, With several simplifyingassumptions, one source (4) findsthat the optimum bat mass is about3.4 times the mass of the ball.More exact calculations wouldraise this result but not to the ratioof 7 common ll'l baseball or 5common in softball.2.14 The tncllonal force from thefloor is the external force2.15 When the beetle is on itsback, e peg prevents the rumpmuscle from swinging the front halfof the body upward to initiatejumping Tension is slowly built upin the muscle until the peg finallyslips, and then the rapid rotation ofthe front half of the body hurls thebeetle upward. Before the beetlecan lump again, the tension willhave to be rebuilt2.16 Dunng the falling of thesand. each hourglass weighs thesame in spite of the fact that someof the sand is in the air. Theadditional force on one side is dueto the impact force of the send.‘What will the balance say when thesand first begins to fall or |ust afterthe last of the sand has hit?2 17 Each hole has a differentcross-sectional area. The sameqilindefs weight spread overdifferent areas will maintaindifferent pressures. For example,the largest area hole has the leastweightper unit area, thus requiringthe least pressure to raise itTherefore, it will regulate thelowest pressure in the pan.
2.18 The large ball collides withthe small belt after reboundingfrom the floor transferring itsmomentum and kinetic energy tothe small ball The small ball ls
then able to reach a greater heightthan from which it started. Themaximum gain in velocity for thesmall ball from the collision is threetimes what it has upon reachingthe floor Thus, the maximumheight to which it can return ls ninetimes the height from which it wasdropped The closer the smallbatl's mass is to the larger ball'smass, the less this return heightwill be.2.19 The coefficient of slidingfriction is less than the coefficientof static friction. Thus. there isg reater friction to stop the car if thetires tum smoothly on the roadrather than slide over the road. Ondry. smooth asphalt the frictioncoefficients for rolling may be asmuch as .8 whereas for sliding .6or less ll sliding begins. theasphalt and tire melt and the carthen slums along on a thin layer ofliquid. All other things being equal.the sliding would require about20% more distance than the rollingstop. Thus. you will have thoquickest stop if you apply thebrakes rust slightly less than whatwill lock them.2.20 The tnctional torce on thetires does not depend on thesurface area in contact with thepavement. and so a wide slick ls aseffective as a narrow one. if thetires are spun over the surface asrs done In drag racing, then thewide tire has an advantage in that ithas a wider surface to heat and isless likely to melt. (Melting greatlyreduces the coefficrent of friction.See FC 2.19.)2.21 The first part of the run islimited by the traction with thepavement Greater tractionreduces tho time spent in this panbut will not affect the final speed
more than a few percent. That finel ispeed will be determined by thepower limitation of the dragster inthe second pan of the nin \2.22 The finger that is firstmoved slides beneath the stici-iwith a kinetic coefficient of friction.The stick does not slide over theother finger because the staticcoefficient of friction there is larger.The magnitude of friction on eitherfinger depends not only on thefriction coefficient, but also on theweight of the stick on the finger. Asthe moving finger is brought towardthe center, more and more of thestick's weight is on that finger.Eventually the friction on the fingeris greater than on the other finger yin spite of the difference in friction 1coefficients Then the first fingerstops and the other finger begins toslide. Such an exchange of motioncan occur several times beforeboth fingers are at the center.2.23 Sudden braking in a turnthrows the car forward, decreasingthe weight on the rear wheels,which than are more likely to slideoutward. Conversely. eccele ratingrocks the car backward to increasethe rear wheel traction.
2.24 The initial speed must be *stow or the maximum static frictionwith the road will be exceeded and ;the tires will slip. Hence. a small ‘amount of torque is first needed-What gear is best dapends on thedriver's abitity and the smoothnessof the clutch. tf the driver alwaysspins the wheels in first. the torquecan be cut in half by going tosecond gear.2 25 If left untied. throw e shoe orsome other article opposite thedirection you want to go. If the iceis ideally frrclionless. then the total
Hniliiien 235
linear momentum of the systemmust remain zero and you willtherelore slide oll.2.26 The angular momentum ofthe motorcycle wheels issigniticant and much larger thanthat ol the bicycle wheels. To turnthe motorcycle you teen it. Thetorque of the tront wheel's weight.calculated with respect to the pointot contact with the road, causesthe wheel to precess. therebyturning the motorcycle. (Similarprecession is common In tops. SeeFC 2.69) A bicycle cannot dependon precession because the angularmomenta ot its wheels are muchless. To turn a biqicle you have tolean it and also turn thehandlebars. If you want to turn left.tor example, do you tirst turn thehanclebars to the left or right?2.27 The kinetic energy of thecenter ot mass ot the cue ball [thetranslational kinetic energy) istranferred. but the cue ball retainsits rotational kinetic energy.Therefore. the cue ball continuesto rotate just after the collision butslips and does not move across thetable. Eventually the rotation slowsbecause of the tnction from thetable and the ball begins to roll. It itwas onglnally struck high. it willthen tollow the ball with which ithad collided.
2.28 Consider a 5LpEl"C|&|l thrownat an angle to the floor with somespin. In addition to the spin. thecenter of the ball has a velocitycomponent downward and oneparallel to the tloor. Collision withthe tloor merely reverses thevertical component so that isupward afterward. The spin andthe velocity corrponent parallel tothe floor change in a morecomplicated way- Consider the
or
point ot the ball making contactwith the floor. The sum of its ;velocity around the bat|'s centerplus the center's velocitycomponent parallel to the tloorgives the total velocity ol thisparticular point parallel to the tloor.The collision reverses that totalparallel component of the point. aswell as changes both the spin andthe center's parallel componentThe recoil direction of the ball canthen be found by determining thenew tull velocity vector of thecenter. For example, suppose aball is thrown to the floor at 45° andwith no spin. Alter the collision itwill move at 23.2“ with respect tothe perpendicular to the floor andwith a spin in which the trontrotates downward. Multiplecollisions with appropriate initialspins account for the several tricksshown in the figures.2.29 and 2.31 A stable bicycle isone whose lorkpoint (the point ofintersection of a progection alongthe front steering axis and ahorizontal line through the wheelcenter} talls as the wheel tums intoa lean when the bike is tilted. Ofthe three other designs drawn inFigure 2 29b, the third is unstablewhile the second is too stable,being too unresponsive to theridei’s changes ol direction.Gyroscopic etlects have little to dowith riding stability, although if thebike ls pushed olt nderless, thenthe gyrosoopic eflect from thewheels will help stabilize the bikefor a while.2.30 The oscillatory motion ot thepoint ot contact between theHula-Hoop and the person keepsthe hoop moving. That point ofContact leads the hoop in the triparound the person. The initial ho
speed should be greater than theeventual driving speed.2.31 See 2 29.2.32 The lorces in a spinninglasso have apparently not beenanalyzed, and you might try toinvestigate them eithertheoretically or experimentally. Theshort length of rope from the handto the circular section both lifts anddrags the circular section around ina rotational motion. Once a fastrotation is created, there is somegyroscopic stability due to theangular momentum.2.33 The rotation about the axesof maximum and minimummoments of inertia are stableagainst small deviations. Flotationabout the axis ot the intermediatemoment ol inertia is not, and anysmall perlurtziation sends the bookwobbling.2.34 Friction from the stickprevents the ring from just falling.Pan of the stabilization ol thespinning rings comes from theperpendicular torce from the stickas the ring spins around the stick.The spinning rate increases as thering falls because some of thepotential energy is converted intorotational kinetic energy. Sincenothing has been written on thistoy, why don't you try someexperiments or develop somemodels to predict the increase lI'lrotational speed’?2.35 Wl'ien inverted in water, thekayaker extends the paddle andpushes toward the bottom toprovide a torque that rotateshimselt or herself and the kayaktoward the surface. To maintainsufticient angular speed to righthimselt or hersell. the kayaker will
up attempt to keep his or her body as
234 Flying circus of physics with answers
close to the axis ot rotation aspossible so as to reduce themoment ot inertia around therotational axis.2.35 The car can probablyproduce a certain maximumangular acceleration of the wheel.The larger the tire's diameter, thegreater the distance covered ineach revolution of the wheel, andthus the greater the linearacceleration of the car. If the car ispower limited. then adding greaterdiameter tires will decrease theangular acceleration. and the cerwill have the same linearacceleration.2.37 The best proceduredepends on several factors: thespeed of the spinning as comparedto the linear speed of the car’scenter of mass, which wheels havetraction. and whether or notstopping the spinning ts more orless important than stopping thelinear motion. For example,consider that your car has its rearspinning to your nght, that yourspeed down the road is negligible.and that your tront wheels still havetraction. To stop the spinning. youshould turn your front wheels intothe spin [i.e., to the nght} andmodestly accelerate the car. Thetorque from the tires about thecenter ct mass ct the car willdecrease the angular momentumof the spinning. As the spinningdecreases. esse the tront wheelsback to the left so that you areoriented properly on the road onceegain.2.38 A tire statically balancedwith a single weight will not bedynamically balanced whenspinning. On the other hand. thetire can be dynamically balancedand thus have no wobble. but if
only a single weight is used. thetire will stilt sutfer vibrations. Theusual tire balancing is acompromise between the twotypes of balancing. lf two weightsare used. both types of balancingcan be obtained. .
2.39 The torque you apply bypulling on a sheet of paper mustovercome the torque due to thefriction between the dispenser andthe cardboard tube of the toiletpaper roll. It the required force onthe sheet is too much. then you willtear the paper each time youattempt to rotate the roll. The fatter =the roll, the smaller the torce youwill need for a given torque but thegreater the torque from the tnctionbecause ol the increased mass.The critical radius tor mostdispensers is about 2 cm.2.40 A stone that skips on sandusually has its trailing edge stnkefirst, causing a torque thatproduces both the short hop and arotstron to bring the leading edgedown for contact After the trontend stokes, the stone takes a longjump. The short hops appear to bemissing from the skipping overwater. Again the trailing edge hitsfirst. but now the stone planesalong the water. tilting back as acrest develops in front of it. andthen finally lakes along rump. Youmight try high-speed photographyto analyze the forces and torquesmore carefully.2,41 An inside wheel is not rigidly iconnected to an outside wheelInstead, there is a differentialbetween them that, with a set oftour bevel gears, allows theoutside wheel to tum faster thanthe inside wheel.2.42 A canter-mounted engine
will have less moment of inertiaabout the car's center and willtherefore require less torque toturn.2.43 For a thin rope or wire. thewalker must constantly oscillateleft and right. first falling one way.then moving the support pointbeneath the center ol mass.overshooting. falling the other way.then moving the support point thatway. and so on. Using a polemakes the balancing easier. Byshitting the pole left or right, thewalker can position the center olmass ol himself or hersell and thepole over the wire With the centerof mass over the support point, thewalker is balanced.2.44 The ball will orbit around thebottle but will not hit it unless theball is swung directly at the bottle.There is no torque on the ballperpendicular to the plane ot itsorbit, and therefore the angularmomentum vector perpendicular tothe plane must remain constant.With the bottle beneath the string‘spoint of attachment. thisconsenration of momentum meansthat the ball must orbit around thebottle except tor the direct collisionswing. You can hit the bottle in asneaky way, however. Twist thestring before you release the ballso that the ball spins while in flightand encounters a force such as theone used in throwing a curve (seeFC 4.39].2.45 The net angular momentumof the cat is constant throughoutthe tree fall because there are noextemal torq.ies on it. Byextending or retracting its legs. thecat can make the front half of itsbody have a different moment ofinertia about its body axis than therear hall‘. For example. it it extends
Answers 235
tr.
its tront legs end retracts its hindlegs and then rotates the rear hall,the tront hall will rotate in theopposite direction but not as tar.So there is a net rotation in thedirection that the rear hell rotated.The cat then extends the rear legsand retracts its tront legs andrepeats the process to gain alUl"ll'lElt' net rotation in thatdirectionBy then the net rotation is sullicientthat the cat can grab at the tloorand linalty right itselt completely.2.46 The Austrian tum involvesrotations similar to those the catuses in righting itself. It there is nonet torque on the sliter. thenrotation in one sense by the upperhalt ol the body must beaccompanied by a rotation in theopposite sense by the lower halt inorder to conserve angularmomentum. Turning can also becaused by shitting one‘s weightforward or backward. Consider thelirst tor skiing diagonally across aatope. With the center oi massioiward. the triction on the rear otthe ski will have larger lever armsIrom the center ot mass ascompared to the tnction on thetront oi the ski. Thus. lhare is a nettorque on the st-ii that will rotate theski and the skier.2.47 when the yoyo spins at theend oi tha stnng. the kinetic trlclionbetween the string and the bottomol the yoyo in contact with thestring is not very large. Suddenlymoving the stnng upwardincreases the contact toroebetween the yoyo and the stnng,with a sudden increase in thelnction that may stop the sliding.The static inction is more than thekinetic lriotion and thus. instead olthe sliding then resuming. the yoyowraps itsell up the stnng.
2.48 I have seen no studies onthe physics ol judo. and you mightexperiment with this question andwith other aspects ot the sport. Theslapping will tncresse the contactarea ot the body with the tloor atthe moment oi impact, therebydecreesing the impact torce perunit area. a decrease that isespecially desirable on the ribcage. The slap may also rotate thetrunk ot the body away trom theimpact and lurther protect it2.49 The spinning bullet will actas a gyroscope and attempt tomaintain its spin orientationthroughout the ltight. Thereloredunng most oi the parabolic path,the wind blows not along thebutters body axis but at an angle tothat axis. The resulting torquecauses a [JIBC1 --won ol the spin inthe same way a lop ts mede toprec-. .s. With the bullet slightlyl’JfDEliI_1ildB to the tell or right. it isdeflected trom it" intended path
2.50 The --.tcx will not tall it thetoltowing rule is met the center otmass ot all the books above anypail ct. .tr book mi =t lie on avertical axis that cuts through thatpanicular book This must be truetor each book in the stectr Youmight try dElBrt'l"lll'tlI'l] eithertheoretically or experimentaly themaximum shiit poszible tor a givennumber ol ldEI-'i -l r. »-is. Or. viceversa. how many identical |D0Ol\aare needed tor a given one .i- :iFor an overhahq ot t br-"tr length,you need at Ie .5! 5 |Jl~ .8: For 3book lengths you need 2.17 books.and tor to book lengths you need1 5 >4 1D“ bOi_.~-5.
2.51 The top part ot the chimneywould have less angularacceleration than the bottom partwere it not tor the rigid coupling in
the chimney. Consequently.stress develops along thechimney's length during the tall.The maximum stress during theiirst part ol the tall is approximatelyhallway along the length. and it isthere that the break will most likelyoccur. Should the break occurdunng the last part or the tall. it willbe approximately a third ot the wayup and due to shearing2.52 Protectites are deitecteci bythe Coriolis torce Irom what shouldbe a straight sighting- That torce isa ticlitious one an observer on therotating earth wtll invoke to explainthe path oi a projectile as the earthand the observer turn underneaththe pro|ectile Gunners will sightthalr guns to teke this apparentdeltection into account. but theeident ol the correction will dependon the latitude and will be in theoppc -- to senses in the twol'|9mlSjJhBl'"'= The Bntish gunsights were ~=-t tor Britain'snorthem latitude, not tor a southern50’2.53 The C ' nolis torce [FC 2 52}also causes a small dettection ot aiiver. to the right in the northemhBtT‘il‘4)l'IEt|'8 and to the leit in thesouthern hemisphere Thisdettection supposedly ll'lCt4" - - esthe erosion on those particularsides2.54 The torce that ll"lC1 i--ii -is thespin is the Coriolis torce [F0 2.52).2.55 The right-handed ‘boomerang is thrown in a vertical lplane so that it spins about ahorizontal axis. Since it is anair-loll. there is a sideways "lilt' on ;it. the tilt being larger on the tophall than on the bottom halt.because the top hell is turning inthe -ame direction that the
236 Flying drcttl of phgislco wllh lnlnrlrl
boomerang is traveling. whereasthe bottom half is turning in theopposite direction Therefore,there is a torque attempting to tiltthe boomerang, but instead oitilting. the boomerang veers to theleft and remains vertical. Sufficientveenng causes the boomerang toturn full circle in its flight2.56 You can pump the swing byraising your center of mass (e.g.,raising your legs] each time you gothrough the lowest point of theswing Your work will add energy tothe swing and thereby increase theamplitude. Starting the swing fromrest is harder to explain. By leaningbackward and momentarily falling,you gain kinetic energy and giveangular momentum to the swing,you and the swing acting as adouble pendutiim Upon reachingarm's length, you stop your fall,and swing with the swing as asingle compound pendulum untilyou have the opportunity to fallbackwards again.2.57 People fear that the penodicpounding of the bridge mightmatch a re -i 1 iant frequency oiu:.itI‘.l||3l|Oi'l of the bridge. Althougheach pounding oi the feet wouldadd only a little energy to theoscillation, if there is resonancebetween the pounding and theoscillation. the energy will bestored and built up, perhapsleading to such an extremeO5Ci||3|.lC!l"I amplitude that thebridge collapses. {Also see FC4.84)2 58 The incense swing ispumped as is explained tn theanswer to FC 2 562.59 imagine an initial singlebump in the road that sets the trontend of passing care oscillating.
When tha front end descendsduring the oscillation, it may forcethe tires to dig in lust then. ti manycars do this at approximately thesame place. a new bump willdevelop.2.60 The ship s roiling is 90“ outof phase with the ocean wavesstriking the ship. The water tank soscillatioi r are at the sameresonant frequency as the ship butwill lag the ship's rolling by another90° (Why?) The tank s oscillationsare therefore a net 180" out ofphase with the extemal waves andwill oppose the rolling oi the ship-2.6! The pendulum will nottopple if the vertical accelerationdue to the oscillation is greaterthan the acceleration of gravity. Ifthere is no fnctlon in the pendulumsystem. the pendulum will thenoscillate to and fro es tong as theend is stilt forced to oscillatevertically. If there Is significantfnction, tlten the pendulum willassume a statii: 'iary verticalposition2.62 ‘i uu hiavcr T0 CTIDOSE "13mass 5' . and the length such thatthe frequency of the strictly spnngoscillation matches the frequencyof the strictly pendulum oscillation.Then, ii the system is started inone of the types of oscillations. thetwisting oi the spring will feedenergy into the other type ofoscillation until there is a completetransfer of energy The transfer willthen reverse to feed energy theother way2.63 A double compoundpendulum, lf'l which both pendulaare hinged together. and whereone has a smaller mass and lengththan the other, will swtng together.if this is a bell and its clapper, then
the belt will never hng. Onesolution, and the one apparentlyused at Cologne Cathedral, is togreatly lengthen the clapper.2.64 The oscillations of thebalance wheel are near theresonant frequency oi the swingingof the pocket watch. It the watchcase oscillates with a frequencysomewhat greater than thebalance wheel, then the case andbalance wheel swing in oppositephese. and the watch gains time.The opposite result occurs tor awatch case having a lowerfrequency.2.65 The dominant frequencymay result from an acousticstanding wave set up in the fallingwater column, much as a standingwave can be produced in a tubewith one open end and one closedend. The factor oi one tourthresults from the speed of sound inwater being one fourth that in air.2.66 Vibrational standing wavesare produced on the bat when theball stnkes the places of antinodes.This result is undesirable becausethe vibration 'stings" the batter,wastes energy that could havebeen given to the ball. and maybreak the bat2.57 When the arrow is released,it receives a lateral impulse fromthe string and the bow‘s stock. Theresulting vibrations cause thearrow to snake around the bow'sstock without touching it, but sincethere is no interference fromrubbing with the stock, theoscillations are around thedirection oi flight, and the arrowflies true to the aim.2 B6 The horizontal and verticalvibrations of the notched stick arenot the same in frequency or
Hnlwazl 237
.5 iamplitude because ot theditterence in shape vertically andhonzonlally and because ol thepressure Irom a linger or thumb-The resulting vibrational motion oithe stick. and thus oi the pin, iselliptical. Depending on the lingerpressure and on which side thestick is nibbed, the ellipticaloscillations will be either clockwiseor counterclockwise. and theretoreso will the pin oscillations. Thefriction between the pin and thepropeller sets the propeller into acorresponding motion.2.69 I have no general rules torthe behavior ol tops, althoughsome ol the equations ol motionare worked out in the advancedmechanics books. Anasymmetncal top will certainly notbe stable and its behavior will beerratic. A top will precess (Le-. itsspin axis will rotate around thevertical) because ot the torque on itdue to its weight Superimposed onthe precession is a wobbling callednutation ll the asymmetnc top hasits spin axis initially vertical, it willremain there as long as itsspinning speed is above a certainvalue. Once lriotion decreases thespinning speed below that criticalvalue, the top will begin to wobble.2.70 The spinning diabolo is inessence a top or gyroscope. Toorient it properly. you must pull onthe cord in the correct directions.For example, it it is spinningcounterclockwise with its axisoutward Irom your body and thenits tar end dips. which way shouldyou pull on the cord? You shouldslightly loosen and lower thetett-hand cord while pulling theright-hand cord upward and towardyou. In this way the torque fromyour pulling will change the angular
momentum cl the diabolo to makeit horizontal again.2.71 The raw egg is not stablebecause it is asymmetric. and ittherelore cannot rise like the tippytops in FC 2 '23. ll the shell isbiielly touched during rotation. thelluid inside the raw egg will still berotating and will restart the rotationoi the shell when you remove yourlinger2.72 The bottom surlace ol thestones is not exactly ellipsoidal.being somewhat slanted towardone side. When the stone isdisplaced from its equilibriumposition by a tap on one end, theperpendicular toroe Irom the tableprovides a torque that causes thecell to rotate. A certain cell willrotate in a certain directiondepending on which way its bottomsurlace is slanted
2.73 It the top is spun on a roughsurlace. the lriclion on the point incontact produces a torque thatprocesses the top to an inversion.2.74 The mass distribution ol themoon is not spherically symmetric.The earth's gravitational lieldtherefore produi::es a torque on themoon that causes synchronousrotation oi the rnoon about its axis.With such a lorced synchronousrotation, the moon will alwayspresent us with the same lace2.75 An orbit must be around thecenter ot the earth, because thegravitational torce on the satellite isdirected to that point There is noway to put a satellite at theMoscow latitude so that it remainsat that latitude because the centeroi its orbit would then not be at thecenter oi the earth.2.76 Less energy ls required with
the tigure B path- To reach themoon, the ship must at least reachthe line beyond which the moon sgravitational attraction dominatesthe earth's. To reach that line withthe least energy, the ship shouldstay as close as possible to the linethrough the centers oi the earthand moon.2.7? The moon does pnmantyorbit the sun, iust as the earthdoes. the pull from the earthcausing a perturbation on thatorbit.2.78 A plumb line can bedeviated Irom the vertical byperhaps several tens oi arcseconds due to adiacentmountains and also due toadjacent absences oi mass suchas with a lake.2.79 The atmospheric trictionreduces the total energy ol thesatellite. but only halt ol thedecrease in potential energy goesinto heating. The other halt istransformed to kinetic energy. and.as a result, the satellite has agreater speed in spite ol the airdrag. The orbit axis is reduced, olcourse, so this procedurecontinues only until the satelliteeventually burns up.3.1 Assuming the air is trappedlt‘l the bra, the volume ol the air willdepend inversely on the pressurein the plane, which would be lessthan that at ground level andtherelore would result in a largerbra. Had the cabin been suddenlyopened to the atmosphere, thequick reduction in cabin pressureprobably would have exploded thebra.3.2 For the same oventemperature more water willevaporate from the cake at the
233 Flylng clrcus of physics wlllt answers
higher altitude than the lowerbecause of the reduced barometricpressure at the higher altitude.Thus. you will need more water inthe recipe. Also because of thereduced barometric pressure thegas inside the cake [consider anangel tood cake) will cause thecake lo nse more. perhapsincreasing the volume beyond thestrength of the cell walls endcausing the cake to tall. To avoidlosing the cake in this way. lesssugar can be added to decreasethe production of the internal gasHowever. rather than decrease thesugar and therefore the sweetnessof the cake. recipes increase theflour to obtain the same results. Anangel food cake will not brown aswell at high at titudes for the sameoven temperature because of thelower boiling temperature ol water(FC 3.62}. To obtain the samebrowning, high altitude recipesincrease the oven temperature.None of these tactors shouldreduce the tendemess of a cakeMore flour will increase tensilestrength and thus the toughness,but the greater expansion and thelower internal temperature (whichwill retard the coagulation cl theproteinl will decrease the tensilestrength about as much-3.3 The cottage does notmeasure the barometric pressurebut is sensitive to gradual changesin the humidity that mayaccompany pressure changes.The movement of the figures iscaused by a twisted piece of catgurwhose length changes with thehumidity.3.4 Although the general waterlevel in a well is governed by thelol rainfall or snowmelt. changesin the barometnc pressure can
vary the water level by severalinches. When the barometricpressure drops during a storm. thewell level will nse. The resultingincreased water tlow through theground may pick up enoughsediment to make the water unlit todrink.
3.5 The smaller balloon has asmaller radius of curvature andtherefore the elastic forces tangentto the surlace on any small surfacearea have agreaternet componenttoward the center of the balloonthan on the larger balloon. With agreater inward torce, there will be agrester iniemal pressure. Hence.the smaller balloon has greaterinternal pressure. This result alsoexplains why a balloon is initiallymore dillicult to blow up butbecomes easier as the balloonexpands: the components of theelastic forces toward the centerbecome progressively less.3.6 with the greater atmosphericpressure at the bottom ol thetunnel. much oi tha carbon dioxideremained in solution_ When thedignitaries returned to the surface,the gas then came out ol solution.They had to return underground toreduce the release of the gas to atolerable rate. thus indrcatirig towhat depths drinking can dnve aperson3.7 ll you do not release aircontinuously during the ascent.you will very likely mpture yourlungs because ot the volumeexpansion oi the air in the lungs asthe external pressure on themdecreases. An ascent Irom a more15 ft after inhaling air from en airtank can be latat.
The partial pressure lrom theCO; in the lungs does not increaselinearly with time as you ascend
because you are continuouslyexhaling pan ot it. The depth ofmaximum partial pressure of theCO2 has been determined from thefollowing: from the maximum depth(where alr was inhaled Irom a tankor submarine), expressed in feet.subtract 33 It and then divide theresult by 2.3.8 The air currents are pnmaritydue to chenges in the barometricpressure. ll the cave has morethan one entrance, air maycirculate between the twoentrances because of thetemperature difference betweenthe cave's interior and the outside.3.9 The tissues of the body will inot saturate or desaturate at the isame rate. Consider, for example,a dive with an essentiallyinstantaneous descent, followedby a 3U—t1'l1t'l stay at bottom andthen a programmed ascent. Thosetissues that absorbed the nitrogen qquickly will desaturate quickly esthe diver begins the ascent. Thosetissues that absorbed slowly willnot initially have as much pressuredifference between the absorbednitrogen ln the tissues and thenitrogen in the blood and willtherelore desaturate much slower.Hence, the initial stages of theascent are quick to desaturate thelast tissues. and the tinal stagesmust be slow to desaturate theslow tissues.3.10 As the hot water hests thetaucet valve, the valve's metalexpands and shuts oll the waterflow.3.11 Ice will tirst lorm on theinside wall of the pipe andgradually grow radially until there isa solid plug blocking the pipe- Untilthat situation is reached, the
flnlwerl 239
hexpansion ol the treezing watermerely pushes water beck into thewater main. But once the plug is Inplace. turther expansion ot thetreezing water between the plugand the valve will signiticantlyincrease the water pressure unlessthe valve is open. It the valve isctosad, the pipe will eventuallyburst at its weakest point. Hotwater pipes will be more likely toburst because the initially highertemperatures decrease the abilityoi the lreezing nuclei to initiate thefreezing, thus lowenng the freezingtemperature. The water in the hotwater pipe then supercools, that is,cools below 0°C, unttl treezing issuddenly and very quickly initiated-The resulting repid expansion otthe ice plug traps more waterbetween itself and the (closed)valve. making bursting more likely.3.12 The constriction issutticiently narrow tor the mercuryto pess it only under pressure.either trom thermal expansion ortrom the "centnlugal ' torce when itis swung in an arc. When cooling,the mercury thread breaks at theconstnction because theintermolecular ioroes in themercury are not strong enough topull the upper column oi mercuryback through the constnction. Ityou stick the thermometer into hotwater, the glass surrounding thebulb ol mercury will expand betorethe mercury itselt.3.13 The rubber molecules arestretched chains that, whenagitated by thermal motion whenthe rubber is heated, will pull moreon their ends and therebydecrease the length ol the rubberWhen you stretch the rubber andthose molecular chains, you doworl-t. part ot which goes into heat.
It the rubber is then allowed tocontract, part oi the wort-i done bythe elastic torce decreases theinternal energy oi the rubber andthus its temperature3.14 A watch would run atdilterent rates when at ditterenttemperatures were the balancewheel not properly compensatedtor a temperature change.Suppose the watch is warmed. Themetallic wheel would then expand.have a greater moment oi inertiaabout the center, and theretoreoscillate less quickly and slow thewatch. However. the expansion iscompensated such that theoscillation is kept approximatelyconsterit. The rim oi the wheel is intwo or three pieces, each havingone tree end and one end mountedto a spoke oi the wheel. The rim’pieces are bimetallic It thetemperature increases. the treeend oi each rim piece curls inwardbecause its metal strips haveditterent thermal expansions. thestrip on the outside expandingmore and thus bending the rimpiece inward. This bending inwardoffsets the expansion ot thespokes Although the wheelchanges shape because oi theheating, its moment oi inertia isabout the same and so are itsoscillations.3.15 Under ideal conditions theU tube is initially in equilibnum. Itthere is a disturbance Irom theoutside, the equilibrium will bebroken, and the oscillations willbegin. Suppose the disturbancedisplaces a small amount ot waterIrom the Iett to the right Thelett-hend vertical section then hasmore cold water than thenglit-hand vertical section and thedenser cold water on the lett will
push into the lighter warm water onthe right. Eventually the ditterencein water levels on the two sides wiltbalance out |hl5 drlterence inbuoyancy due to the temperatures,and the ttow will stop. The heatingand cooling on the tube then bringsthe water back to the originaltemperature equtlibnum, thebuoyancy force is theretorereduced, and water tlows Irom rightto lett because oi the ditierence inwater heights. This procedurecontinues periodically. Byexperimenting you coulddetermine how the oscillationdepends on the size oi the U tube.You will also notice that thereservoir must be larger than somecritical value or the argumentabove will not be valid.3.16 when you pump andcompress the gas. thecompression is essentiallyadiabatic (no heat transler with theoutside) and the internal energy oithe air increases, thus increasingits temperature. The hot air heatsthe valve. The station scompressed alr was hot when tirstcompressed but since then hascooled to room temperature andwill not heat the valve.3.17 The prevailing winds in theUnited States are Irom the westAs the moist winds Irom the Paciticare torced upward by mountains(tor example the FlockyMountains], the air adiabaticallycools because oi the reducedatmosphenc pressure and cannotretain as much moisture. Thewestern sides oi the mountainstheretore receive the releasedmoisture. The eastern sides willreceive comparatively much less.3.18 As the winds descend Iromthe mountains and into the greater
210 FI|,iI.ng ctrcun of physics wlllt Iinlltrerl
atmospheric pressure. the movingair is ediabatically compressed andthus healed (FC 3.15). ll thedescent is rapid, little oi this heatwill be exchanged with the local air,and theretore the wind will bewarmer than the local air. The w'indwill be relatively dry because cl theanswer in FC 3.17. How dry, warmwinds aliecl humans is notunderstood, but the positive andnegative ions in such winds maybe the source oi the irrationalbehavior (FC 6.14).3.19 The pressunzed gas in thebottle rapidly and adiabalicallyexpands when the bottle isopened, doing work in expandingagainst the atmospheric pressure(FC 3.16). The energy Ior that workcomes trom the internal energy clthe gas, thereby reducing itstemperature and causing some ctthe water vapor in it to condenseout as a log.3.20 The reterence suggests thatthe air current over the top cl thecar reduces the air pressu re in thepessenger area, implying that theair there had expanded endtheretore cooled slightly- Thisellecl would be similar to thecooling ct the air in the repidlyllowing air stream above anairplane wing, an ellect sometimesmade apparent by the log termedabove the wing.3.21 The winds lrom the Pacitichave dumped their moisture on thewest side ol the Flcckies lyingbetween the Pacitic and DeathValley tsee FC 3-17) and areadiebalically hested as theydescend the eastern slopes {seeFC 3.18). The hot, dry windentering the valley reduces it lo adesert. The lack ol shade and thegreater relleclion Irom sand than
would be obtained Irom avegetation-covered terrain alsoincreases the air temperature |ustabove the ground.3.22 The air ascending amountain expands and theretorecools as it moves into lessatmospheric pressure.3.23 Flising columns cl warm.moist air cool as they expand intheir ascent to lower atmosphericpressures. The lower temperatureeventually condenses out some olthe water to lorm the clouds andalso to warm the rising airsomewhat by the released latentheat in the condensation. Theclouds. theretore, are not heldtogether at all, but are constantlybeing termed. Sit sometime andwatch them lorm, change, anddecay.3.24 The atomic lirebal veryrapidly heats the air. which thenquickly rises. pulling ground-levelair, dirt, debns, and water moistureup in its tall to lorm the stem cl themushroom. As the hot air rises andcools by expansion, it eventuallyreaches the temperature ct thelocal air and thereslter spreadshonzonlally to lorm the top cl themushroom.3.25 The cause oi the notes inthe clouds is not well understood.One ol several explanations is thata natural or artiticiai accumulationcl treezing nuclei in an altocumuluslayer quickly brings about freezing.The resulting thin cirrus lilamentsiurther act as nucleation agents.spreading laterally to widen thehole, while ice crystals tall Irom thecentral cinus and thus removewater Irom that area.3.26 The air torced upward overa mountain expands and cools and
then condenses out some ol itswater moisture. It the condensationoccurs |ust at the mountain lop. alenticular cloud W1|| result. ll thewind is strong, the condensationwill occur on the leeward side olthe mountain in the turbulent wake.in both cases, the clouds mayappear to be permanent but are, intact, constantly being created anddestroyed.
The air torced over the mountainmay oscillate on the leeward sidelo produce clouds on each upturnin the oscillation. These lee waveshave a wavelength dependent onthe wind speed and also on thechange in air density with height. Itthere is little change in air densitywith |‘lB|g|'1t, the atmosphere isrelatively stable, and the lee waveoscillations will be slow, giving longwavelengths and thus largedistances between the clouds.Large changes in air density willcause more rapid oscillations olthe moving air, resulting in shortwavelengths and thus shortdistances between the clouds. Thetaster the wind speed, the greaterthe distance will be between eachuptum of the lee waves; theretore,a stronger wind will spread theclouds.3.2? The repid heating cl the airby the blast generates e shockwave, with high pressurepreceding tow pressure. During thelow pressure the air expands andcools, and some oi its water vaporcondenses. Alter passage ol theshock wave. the air pressureretums to normal, and the clouddisappears. Thus, the cloud isrelatively narrow and expandsradially Irom the blast area.3.28 Much 0| the visible lightincident on the clouds lrom the sun
flnluierl III I.
passes through the clouds and isabsorbed by the earth. As theground warms, its thermalemission (long wavelength light}increases. Wlien the cloudsabsorb this radiation. thetemperatue dillerence between thebase and top oi the cloudsbecomes sufticient to causeturbulence, which then destroysthe clouds.3.29 The mamma are lormedwhen a dense cloud layer overlaysand then descends into a dry layeras a downward moi-ing iiiermal3.30 Fogs are classilied intoseveral types according to howthey are lormed. Radiation logresults when the moist air cools byradiating its heat into space andcondensing out its excess watervapor as the humidity increases.Advection tog lorms when warm.moist air tlows over a cold groundor body cl water. The humiditydoes not have to reach 100% tor alog to lorm because in the modernatmosphere there are manycondensation nuclei that will attractthe water and initiaia the log athumidities as lew as 60%. Nesr theocean. these nuclei may be saltparticles. Near cities they are morelikely to be the particulate matterreleased by industrialsmokestaclts. The open-coalbuming oi London supplied a greatmany condensation nuclei. Oncethe burning diminished. thecondensation and the resulting togbecame less likely. Sometimes athermal inversion [layer oi warm airoverlaying a layer ol cooler air} willtrap industrial pollutants near theground. During such an inversionin December 1952 in London. thepollution tumed the log that waspresent black and within a lew
days reduced visibility to |ust a lewinches Approximately 4000people died from this smog.3.31 When your warm breathstrikes the cold glass, it cannothold as much water vapor anddroplets lorm. These drops willinitiate on condensetion nucleieither on the glass or in theadiacent air. A tresh hot piece oitoast will ‘exhale ‘onto a cool platell"l the same manner3.32 A vonex is shed by eachwing so that there is downllcw inthe center behind the luselage andupllow on the outside behind thewings on each side. Condensationmay come directly lrom the watervapor in the engine exhausts orfrom the cooling ol the air duringthe vortex motion. Since mostplanes have two prorrinent wingsthere will initially be two trails. Thedownllcw in the center betweenthe two vortex centers decreasesin momentum as it travelsdownward because ot thebuoyancy torce on it upward- Toreduce its momentum, this airdecreases in volume, which pullsthe two vortices closer togethereventually making the two trailsindistinguishable. The speed ol thedescending air increases in spite olthe decrease in overall downwardmomentum. Tlis downwardincrease in speed will magnityirregularities in the trails: the partsct the trails descending first willdescend even more quicklybecause ot the increase in speed,making those parts appear to haveburst downward. Soon mixingwithin the vortices reaches thecores, and the descent stops. Thenan underview ol the trails mayshow burst popcorn areasconnected by loops where two
trails are still distinguishable.3.33 The salt apparently acts asnuclei tor the bubble lormation.3.34 The air hested by the lire islighter than the cooler air in theroom and will be pushed into thechimney by the cooler air. Oncethe circulation is initiated. it willcontinue even it the chimney is notexactly over the lire. The taller thechimney is, the beher the dralt intothe chimney will be, because ataller chimney will hold more warm,light air. Consider a parcel oi air atthe entrance lo the chimney, justover the lire. It is being pushed rnlothe entrance by the cooler roomair, but it is also being pusheddownward by the alr above it. ll theair above it is warm, however, thatdownward push will be much lessthan the upward push. The moreoverhead hot air there is. that is.the higher the chimney is. theeasier it will be tor the room air topush each percei ol hot air into thechimney. Some chimneys will puttit the dreit is low and ii cool outsideair periodically pours into thechimney top.3.35 The hot smoke and gasesare more likely to nse in the coolerevening than during the warmerday.3.36 Initially the hot gases havea laminar llow because theirascent is relatively slow. Dunng theascent, however, the net upwardtorce on them [resttting Irom thebuoyancy on the hot gases in thecooler surrounding air) acceleratesthem sulliciently that the llowbegins lo break up into eddies.Typically the acceleration requiresabout 2 cm to obtain the necessaryspead tor turbulence3.37 The general characteristics
212 Flying ch-cue of physics uillIt
of a stack piume depend largely onthe change In atmospherictemperature with height near thelevel of the chimney emission. Ifthe temperature increases quicklywith height la situation that iscalled an inversion}, the hot gasesemitted by the chimney will not beable to rise and thus will streamhorizontally in the wind as shown inthe first of Figure 3.37a. ll thetemperature decreases from theground to the chimney height andthen increases for greater heights.the gases will not be abie to risebut can mix downward as in thesecond figure. If the temperaturedecresses moderately with heightfrom the ground up, the plume willbe like the thlrd figure. If there is avery marked decrease intemperature with height. the plumewill attempt to nse but can also bebrought back to the ground in aloop by thermal eddies.
A plume can be split into twopans if the breeze is light enoughnot to distort the vortex pair that iscreated as the hot gases leave thechimney top- The gas flow in thecenter of the chimney exit isstrongly upward, but the gas on theoutside of an emerging puff isdownward. In a light breeze, thispattern splits down the middle toform the two piumes as shown inFigure 3.3?b.3.38 Ice crystals will growpreferentially in one plane, calledthe basal piane. and grow muchslowar along an axis, called the ce.xis, perpendicular to that plane.The actual orientations ol the icecrystals in the tce over a lake willvary from place to place and willresult in ditlererit melting rates overthe lake. An area with mostlyhonzontal c axes will melt such thatthe vertical lce crystals become
isolated and look like candles|utting upward. Lake water seepsupward between these candles bycapillary action to give that area adark appearance Areas withvertical c axes will have largerhorizontal crystals that meltinternally to form a honeycomb ofhollow tubes- These areas will bebnghter. The darker areas absorbmore sunlight than the brighterareas. heat faster, and thereforewill be weaker and moredangerous than the brighlar areas.3.39 The melting point of water is0“C, but the freezing point will likelybe lower, depending on the purityof the water. Very pure water canbe supercooled [i.e., cooled belowthe melting point without freezing)to about —40“C. Impurities witinitiate freezing at highertemperatures (but not higher thanthe melting point). the exact valuedepending on the type andconcentration of the impurity. Asthe water is cooled, randomfluctuations in the free energy ofthe system (due to its microscopicthermal motion) produce small toeislands. If the water is still relativelyfar from the‘ lreazing temperature. 'these islands quickly disappear. At"freezing temperature." the islandsgrow to a certain critical radiusbeyond which they can continuegrowing because the continuedfreezing will lower the free energy ofthe whole system. This criticalgrowth will occur at 40'C for purewater but at a higher (subzero)temperature for impure water.because the impurities reduce thenecessary critical radius of the iceislands.3.40 The critical feature is theincreased evaporation from theinitially warmer water. If equal
masses of warmer and coolerwater are set outside In freezingweather and in open-toppedcontainers, the evaporation Iromthe warmer water will reduce themass remaining lt't that container.With less mass to cool, the water inthat container can overtake thecooling of the initially cooler waterand reach the freezing pointsooner. The actual cooling rate candepend somewhat on thecomposition of the containers, thecirculation above the containersand the circulation tn the water.Although Bacon commented onthe effect and although the result iswell known in Canada, people inwarmer countries find itmysterious. The physics |ournalsrediscovered it recently only after ahigh school student in Tanzaniaconvinced his skeptical teacher ofthe result3.41 Thunderstorms oocur mostfrequently in the midafternoon toearly evening and overlandmasses. A graph of the worldwidethunderstorm activity will bedominated by the thunderstormsover Africa and Europe. makingthe maximum activity atapproximately 7i=.ivi. London time.A graph of the earth's electric field{see FC 6.33) will have the sameshape, with the maximum at aboutthe same time, because thethunderstorm activity rechargesthe esrth, bringing negative chargeto the ground and positive chargeto the upper atmosphere bylightning and point discharges (seeFC 6.32 and 6.46).3.42 The moisture on your sklncan freeze to bond your skin to themetallic ob|ect. The freezing ismore likely on metal than wood,say. because the thermal
Answers 243
conductivity of melel is high, andyour finger tip will be rapidly
‘ cooled. (See FC 3.78.}3.43 Normally the water drainsfrom ice as soon as some of itmelts. With the wet paper aroundthe ice, the external heat will haveto be conducted through the waterlayer. thereby slowing the supply ofheat to the ice.3.44 Water has the greatestdensity when it is about 4°C. Thus,when water bagins to freeze on apond, the lighter ice floats. thewater iust above freezing nses.and the watar slightly warmer (near4°C} sinks. The surface willtherefore be colder and will freezefirst. The surface will also ooolfaster. because it radiates its heatinto the atmosphere and becausethe alr circulation over the surtaoaremoves heat. The ground at thebottom of the pond is warmer andwill supply heat to the bottomwater. The bubbles of relativelywarm air will supply heat toprevent. delay, or decrease thefreezing.3.45 It the srow is near themelting point. fnction from the skisinitially melts a thin layer oi snowon which they can glide Thecontinuous shearing of the waterlayer by the moving skis providesthe continuous heat needed tomaintain a water layer. The type ofmalarial used in the skis, whetherthey are metal or ebonite, does notdirectly matter as far as the initialmelting goes. However, if the skisconduct heat well, as metal skiswould, the heat will be lost tooquickly to maintain the water layer.Ebonite skis (and the wooden skisused years ago) conduct poorlyenough to maintain the layer. ll thesnow is well below the melting
point. there will be no water layer,and the skis will have to be waxedto reduce the lrlction.3.46 Like the skis tn FC 3.45, theice skates glide over e thin waterlayer, but unlike the skis the waterlayer is due to pressure melting.The weight of e skater supportedover the two thln blades puts apressure on the toe of 7000 lblsqin. or more. To know the pressureaccurately. you would have tocalculate the weight distributionover the actual points cl contactwith the ice, not the total bottomsurface area of a blade. Othermaterials are unlike water and icein that they do not melt byincreased pressure as ice doesand thus could not be used forskating. Since skiing does notdepend on pressure melting,presumably you could ski on othermaterials such as dry ice.3.4? A sudden warming can meltsome of the snow to provideenough water to lubricate thesliding of the remaining snow- Asudden cooling can be equallydangerous At sunset. for example.the cooling can freeze liquid wateralready present. and the resulting11% expansion by the water cantrigger an avalanche.3.46 when you gresp and firm asnowball, you pressure melt atleast the surface. which thenrefreezes to bond the snowballtogether.3.49 Snow tires are designed toblte into snow to increase thetraction. Studded snow tiresdepend on melting the ice andsnow beneslh esch stud by thepressure from the cars weight.With that weight distributed over asmaller contact area, the stud's
contact area. there is increasedpressure on the ice and moremet ting. lf the snow and ice arebelow 0°F, the increased pressureis insufliclent lo cause meltingSand ts useful ff pressure meltingwill embed it in the snow and icebut, again, that will not happen atvery cold temperatures.3.50 and 3.51 When salt isadded to the water, more heatmust be removed from the mixtureto reach freezing, and thus thefreezing temperature is lowered.Not only must the water moleculesbe slowed sufficiently for icecrystallization to begin but also forthem to overcome the adhesion tothe salt molecules. Salt will alsoraise the bolting temperature ofwater. Because the watermolecules are attracted to the salt.they will have to be moving eventaster than normal in order toescape into the vapor state. Similarlowenng of the freezing point endraising of the boiling point of wateris behind the use of antifreeze incar radiators.3.52 The evaporation cl thewater requires heat, which lsremoved from your body it youstand wet and nude in a breeze. Toremove a water molecule from alayer of water, in other words, toevapcrata some water. energymust be supplied to that moleculeto overcome the attraction to theother water molecules tn the writerlayer. In the meantime, some of thewater molecules already in thevapor state will randomly run intothe water layer and so return to theliquid slate and give up energy. llboth the liquid and vapor are in aclosed system under equilibrium.then as much energy is removedby evaporation as is retumed by
244 Flying clrtul nl |-ihyllcl will answer‘!
condensation. In a breeze,however, the water vapor isconstantly being blown away andthere will then be a net energy lossfrom the water layer. ti the layer lson your sl-iin, the net loss in energywill come Irom your skin, and youwill teel cool. Methyl alcoholevaporates taster than water andwill cool the skin quicker. Theporous canvas water bag is cooledby the evaporation on the bag'ssurlace, especielly it a wind isconstantly blowing across the bag.3.53 The tuel evaporetion (whichis enhanced by tha increase in theair speed when the air is torcedthrough the central aperature pastthe tuel |et} takes energy tor itsphase change Irom the air. As theair cools, it can saiurete in humidityand begin to condense excessmoisture. It the outdoor humidity isbetween 65% and 100% and theoutdoor temperature between 25and 5o’F, then the condensingwater can lreeze on the throttleplate.3.54 The brine {salt watersolution) in the ice blocks is in cellsthat will migrate downwardbecause oi gravity and also in thedirection oi the higher temperatureon the blocli because otprogressive melting andreireezing. Usually the latter is alsodownward since the ice block iseither lloating in the ocean (theocean, which is at ireezingtemperature, is warmer than the elrabove) or on the ground (theground will also be warmer thenthe air). For both eiiects, the brinedrains from the block, whichbecomes potable aher about ayear and has nearty no salt alterseveral years.
To understand the drainage
because oi the temperatureditterence lrom top to bottom onthe block, consider a vertical cell oibrine in the block. The salinity oithe solution will be enough that itstemperature matches the averagetemperature oi the adjacent ice. Atthe lower, warmer end. this salinitywitl be too much (see FC 3.50} andthere will be melting to reduce it. Atthe upper, cooler end. there is toolittle salinity and there will beireezing to increase it. The cell as awhole then moves downward.eventually reaching the bottom oithe blocl-i.3.55 A relatively large amount oiheat is required to vaponze thewater in the pan. ll’ the pan is open,this heat cl vaponzalion isconstantly lost as the water vaporrises in the air currents. The pantop will trap the vapor and thuskeep that heat in the pen.3.56 Other than the onereference descnbing this ettect,apparently nothing has beenpublished on it. Why not tryexperimenting with your ownoven? Will the increased moisturecontent oi the airin the oven meanthat the air heats any taster? lsless heat needed to increase theair‘s temperature by. say. onedegree? Will the circulation ot theair change?3.5? Otten people will preventthe treezing oi their car radiatorsby similarly placing a large lib oiwater near the radiator in thagarege. As the room temperaturecools and approaches ireezing. thewater will act as a heat reservolr torthe room. When ice begins to lormin the tub, a relatively large amountoi energy (latent heat) is released,which will then aid in preventingtunher cooling oi the room.
3.58 The outside air that iscooled during the night will ilow \down into the icehouse during theearly morning as the outsidebegins to warm. This air llowinginto the icehouse will saturate inhumidity because oi the coldertemperature there, condensing outsome oi its moisture. The phasechange trom vapor to liquidreleases a large amount oi heat.There is less heating oi theicehouse it direct sunlight isallowed to warm the air in it toprevent the lntlow ct tresh air andthe consequent condensetion.3.59 The lower, wider end ot thedevice absorbs heat from tha ovenand heats the water in the lowerend oi the hollow interior.Eventually the water is convenedto steam, which requires arelatively large amount of heat torthe phase change to vapor state.The hot steam rises through thetube to the upper end that is in thecooler intenor ot the meat. Therethe water vapor condenses.releasing the (latent) heat it hadabosrbed upon changing to steam.The liquid water then runs downthe tube to begin the cycle again. lThe net heat transler to the inside ‘ol the meat is 100 to 1000 timestaster than the conduction througha solid rod oi the same metalbecause oi the large amount oiheat involved in the phasechanges Irom liquid to vapor andthen back again.3.60 ii a mountain were higherthan a cntical height ot about 30km, the pressure at the base oi the lmountain due to its weight woild Ibe great enough to liqueiy the ‘base, causing the mountain to sinkbelow the critical height. Hence.mounteins must be less than about
.AIlIIIi'H'I 215
30 km high. Because thegravitationon the Martian surlace is less thanthat on the Earth's surlace, Martianmountains have a greater criticalheight.3.61 If the demonstretion comessoon after the tlrst loud soundscome irom the cautcion. the wateris not at th boiling temperature{see FC 1.12) and, althought hot, itshould not be dangerous. Thewater breaks into droplets whenthe performer llings it into theair. Those drops should coolsomewhat by the time they reachthe skin. Ii the performer issweating throughout theperiormance, as I certainly wouldbe, the sweat will protect him iromtha droplets.3.62 There is evaporation irom abody oi water even betore youbegin to heat it. Molecules in theliquid stete having suiiiciently highenergy escape tha liquid. Some oithoss vapor molecules eventuallyreenter the liquid, but there is a netloss As the water is heated. thenumber oi molecules in the vaporstate iust above the liquid surlaceincreases until Iinaliy the pressureoi this water vapor reaches itsmaiumum value, called theseturated vapor pressure. Thecorresponding tempereture iscalled the boiling temperature. Thevalue of the maximum water vaporpressure depends on theatmospheric pressure. In thereduced atmospheric pressure ona mountain top, water boils at alower temperature becausesaturation is reached at a lowervalue. Whether or not the surtaceis rolling with boiling bubblesdepends also on the nucleation oiwater vapor bubbles in the body olthe water. Ii the water is especielly
clean and leit careiullyundisturbed, the water can beheated to above the normal boilingtemperature ior the existingatmospheric pressure. A smallperturbation. perhaps a dustparticle, can then cause anB3ip|OSI\.i‘9 eruption oi boiling.3.63 Splashing and capillaryaction puts relatively thin layers oiwater on the edges ct the puddlesor lakes. As that water evaporates.the dissolved salt is lett behind onthe edges.3.64 The tube connecting thebird's head and base extends intothe base. There is a liquid in thebase that is deep enough tosubmerge the lower end oi thetube. Above the liquid, both in thebase and in the rest oi the tube andthe head, is the vapor irom thatliquid. Those two pockets oi vaporare theretore not connected. Aswater evaporates irom the ielt onthe head. the head and the vaporinside the head cool (see FC 3.52),lowering the pressure oi the vaporin the head. Then there is greaterpressure in the vapor pocket in thebase than in the head and liquid ispushed slowly up the tube towardthe heed. Eventually this makesthe bird so unstable that it tiltsiorward and dunks its head in thewater glass Just when the bird ishorizontal, those two pockets oivapor are connected and equalizein pressure. Willi equal pressures,there is nothing to toroe the liquidup the tube and the instability isremoved. During the jostling ol thedunk, the bird rights itseli, and thenthe whole cycle begins again.
In one study by the HANDcorporation (1457), large birdswere considered tor use intransporting water between would allow the outside
irngation canals in the MiddleEast.3.65 As a water drop approachasa very hot skillet, its bottom portioninstantly vaporizes to provide avapor layer between the skillet andthe remaining water drop. The dropis then heated by radiation throughthe vapor layer. convectioncurrents in the layer. andconduction by the layer. but these ,three processes will take up to 1 or2 min to bnng the drop to boilingtemperature. Thus, the vapor layerprotects the drop tor that long.allowing it to dance and skim overthe skillet surlace.3.66 Superheated water (liquidwater hotter than its boilingtemperature) seeps upward into ageyser‘s cavity and main columnirom heated rock as much as athousand meters below thesurlace. Once the water is in the lcavity, small vapor bubbles iormand then grow as they ascend. Thewater through which the bubblespass ilashes to steam. Theresulting pressure iorces some oithe remaining water to erupt intothe air. This procedure thenrepeats itsell. sometimes, as in thecase oi Old Faithiul, with a deiinitepenodicity.3.67 In the older-style cotieemakers, water was placed in abottom container, and then thecotiee holder was snugly tittedover the top with e rubber gasket-When the water was healad. the ,air and water vapor above thewater expanded and pushed waterup the centrel tube to pour out ontothe coitee. Alter about 5 min. theheat was turned oil. As the air inthe bottom container cooled andcontracted, its lowered pressure
RG6 Flying clruil ol phyllcl tivllll inswcrl
atmospheric pressure to push thewater through the grounds andback into the lower conteiner. Inmany oi the modern percolators.there are several diiierences Thelower end ol the tube is conical andtits over the bottom oi the pot. Thewater trapped in that cone isquickly heated and torced up thetube by the air bubbles that arereleased. Were the tube wider, thebubbles could not do this. Once thewater is spilled onto the coliee.gravity draws it through thegrounds and back to the waterbelow. Each time water spurts upthe tube, the tube and cone aremomentarily tilted. allowing tresh(and cooler} water to ilow underand into the cone.3.68 Steam rises through thepipe and into the radiator where itcondenses and then tlows backdown the pipe. The phase change.rather than a temperature changein the water, releases heat to begiven oil by the radiator.3.69 When I do thisdemonstration with the lead, I wetmy hands iirst. When my lingersenter the molten lead, some of thatwater immediately vaporizes toiorm (at least momentarily) aprotective sheath around mylingers. similar to the protectivevapor layer in FC 3.65. Normalmoisture on the stun [especially it lam scared and sweating) worksalmost as well. Fire walkingprobably involves protection by themoisture on the ieet and maydepend as much on sweatingbetween each toottall as havingcallouses on the ieet. Althoughhaving wet ieet helps, I lind I canwalk on hot coals with no specialpreparation oi my ieet.3.70 Water hammering occurs
when water collects somewhere inthe pipes. When the steam ilowsover the water and suddenly cools.the Pressure is very suddenlyreduced. The water is quicklydrawn into the area oi lowerpressure. striking the pipes with aloud thump. To get rid oi the waterhammering. you should drain thecollected water.3.71 The dull side will rediateand absorb heat better than theshiny side {see FC 3.75).Theretore, having the dull side outmight help cook a potato taster andthen cool it quicker at the table.Since apparently nothing ispublished on this eitect, why notcheck it?3.72 The metal evaporates irom
i the iilament to darken the bulb.Convection currents in the smallamount oi gas in the bulb will carrythose metal molecules upward todarken the top oi the bulb.3.73 When viewed by adark-adapted observer against apertectly dark background, anincandescent blackbody radiatorbecomes visible at about 650 toB00 K, depending on the angle theobject subtends in the observer'siieid oi view.3.74 You might cool yourselimomentanly by opening thereingerator door. but by then thecooling system comes on toattempt to cool the interior againMore heat is released by the motorthan is absorbed by the releasedcool air, so the room will becomeeven hotter. You can be sneaky.however. You can unplug thereingerator as soon as you openthe door. Ol course. then your beerwill not stay cool. and you will haveto drink it all.
3.75 A black surlace will absorbthe radiated heat taster than a lshiny surlace. Thus. the black pie ‘pan will heat the pie taster. Glassabsorbs most oi the thermaltinirared) radiation incident on itand will theretore heat the pietaster than the shiny pie pan.3.76 Archimedes‘ teat wasreconstructed in 1973 by a Greekengineer who had 70 ilat mirrorsleach about 5 It by 3 it) held bysoldiers who iocused the sun'simage on a rowboat about 160 it oilshore. Once the soldiers properlyaimed their mirrors. the rowboatbegun to burn within a lewseconds, eventually beingengulied in flames. Arthur C. 1Clarke independently used theidea in one or his science tictionshort stories ("A Slight Case oiSunstroke"). The home-townspectators at a soccer match wereeach given a shiny souvenirprogram. when one oi the refereescalled an unpopular decision iniavor oi the visiting ream, thehome-town spectators burned thereferee to a crisp by directing thesunlight on him with theirprograms.3.T! The candle converts somecl the water in the boiler to steam,which then pushes the watercolumn back through the tube to ,emerge behind the boat in a iet.Upon leaving the boiler, some otthe steam condenses in the coolertube and contracts, thereby pullingwater back into the tube. However,the key ieature is that the waterentering the tube comes irom ahemisphere oi directions, not iroma single direction. There is a netpropulsion lorward because oi theasymmetry in the let emissionrearward and the inttow irom all
Antiwar-I 241
fp
directions in the rear hemisphere.3.78 How cold an object feelsdepends not only on itstemperature but also its thermalconductivity. The quicker arelatively cool obiect conducts healaway from your linger when youtouch it the colder it will feel.3.79 Clothes are needed in hotclimates to protect the wearer fromthe direct sunlight Dark clothes willabsorb more visible and infreredlight than white clothes, and thuswhite clothes should be wom in hotclimates ll water is plentiful, thenthe clothes should be porous sothat sweating and evaporation cancool the skin However, il water isscarce. then the clothes must beless porous to protect against rapiddehydration of the wearer. InHerbert's sclence fiction classic,Dune (1460), water is so scarcethat the desert people wear suits toseal in all the precious bodymoisture.3.80 The more massive. thickeriron pots and pans should have amore uniform temperature acrosstheir bottoms than the modern thinsteal ones, which will have hotspots directly over the burner.Sticking is otten produced by thehot spots3.81 The Northern Hemispherewinters are cold not because theearth is further from the sun (for itis, in fact. closer} but because thetilt of the eai1h's axis shortens thedays and lowers the sun in the sky.Both reduce the amount ol heatdeposited on the surlace duringthe day. However, the change intemperature will lag behindchanges in these factors by abouta month because the ground andatmosphere take time to cool.
3.82 The side of the astronautlacing the sun ls absorbing thermalradiation, whch heats theastronaut. He is also radiatingthemlal radiation over his entiresurlace area So, tha sunny side ofhis suit will be warm, the shadowside cool. (Actually, the suits haveair conditioning units } Athermometer left in space willwarm until it is absorbing as muchradiation as it ls emitting. At theearth's distance from the sun, thethermometer should read3flIIf0ltlfTlBlG|y room temperature,depending on how much of its areais facing the sun You experiencethe same thing when you lace atire.3.83 The so-celled "greenhouseelfect" is commonlymisunderstood. Greenhouses arenot hot because of any radiationtrapping by the glass, but becausethe cooling by air circulation isdiminished or eliminated. In fact.the glass may reduce the radiationflux into the greenhouse ratherthan increase the radiation insideby trapping. There is trapping ofradiation by the earth'satmosphere, however, because itis more transparent to the shortwavelength solar radiation thanthe tong wavelength radiation. Partof the transmitted short wavelengthradiation ls absorbed by the earth'ssurlace, heating it, after whichlong-wavelength radiation lsemitted by the surlace. Becausethe atmosphere will not transmitthat second radiation well. some ofit will ba trapped in theatmosphere.3.64 ll there is little or no wind,most ol your heat loss is by thermalradiation. Any object with atemperature above absolute zero
‘F 1 1 7"will radiate heat, the hotter it is, themore it radiates. It will elso absorbheat from the surroundings, theamount available depending on thetemperature of the surroundings.Since your body is almost alwayswarmer than your environment,there is a net radiation loss.Outside on a cold day. or facingtoward a window with the cold onthe outside, the absorbed radiationis less because of the reducedradiation from the environment.Consequently, your net radiationloss is more, and you feel coid- Anastronaut space walking without asuit in empty space and far fromthe sun should feet a profoundcoldness since there would be noenvironment to radiate to him.
People can adapt tocontinuously cold conditions byadiusting their diet and the rate atwhich blood flows to their skin.Eskimos have a highar protein dietthan do most people living at lowerlatitudes in order to maintain ahigher basal metabolism to counterthe cold. To protect against rapidheat loss through the skin, thecapillaries carrying blood to theskin contract. If the temperature inthe limbs drops too much. theperson will shiver so that theincreased activity will wanri thelimbs.
Besides radiation. a person canlose heat by conduction (e.g.,through the feet to a cold ground)and by convection, includingevaporation losses discussed InFC 3.52. A lurcoat will help keep aperson warm because the airpockets in the tur are very poorheat conductors. With increasedwind speeds. however. the alrpockets become less effective-The best way to wear e fur coat tominimize heat tosses. especially
243 Flying ch-one ol physics wltli lnnverl
on a windy day, is to wear it insideout so that the wind will not destroythe pockets of insulating stagnantair in the fur.3.85 The metal pipe wallconducts heat well and wouldconstantly be losing a significantamount of heat to the convectioncurrents flowing over the pipes. Byplacing a layer of asbestos aroundthe pipe, the rate at which heat isconducted to the surlace to be lostto convection is decreased,because the asbestos will notconduct as well as the metal wall.3.86 If the thundercloud isseveral miles away, the wind youexperience will blow toward itbecause of the updraft in the trontpart of the cloud. When thethundercloud is closer, the windwill blow away from it because ofthe downdraft of cold air draggeddown by the rain.3.87 The warmth from the fingersuddenly decreases the density ofthe fluid next to where the dish istouched. The nearby denser fluidthen displaces the warmed fluid.which spreads out over the surlaceuntil rt cools. whereupon it sinks.The circulation waves are madeapparent by the aluminum powder.3.88 In the early evening the treeis a reservoir of warm air that willrise from the tree in a convectionplume. The insects are attracted tothe warmer air and perhaps also tothe condensation that may occur inthe plume as the air cools dunttgthe rise.3.69 The sunlight heats thestone on the bottom, and thelighter warm water nses in aconvection plume to the surfaceThe shrimp apparently like thewarm water land possibly any
organic compounds it may carry)but do not like sunlight. Hence theynde the convection current upward lbut steer away from the sunlightand, on reaching the sunlit surface,descend again.3.90 Increased heat flow by theblood to the skin surface andincreased sweating carry off mostof the additional heat But thesecan lead to several minor and alsoserious disorders. The increasedblood flow to the skin maydecrease the ilow to the brain,causing falntness, especially whena person suddenly stands.Nausea, cramps, and circulatoryfailure can result from the saltdepletion caused by the increasedsweating. ll about 2% of the body's lwater weight is sweated away, theperson becomes very thirsty. If thelosses are about 7%. thacirculation can tail. with the person lquickly dying. Overheating in thebody results in the samesymptoms. leading to collapse andpossibly death.3.91 If you want your coffee ashot as possible when class begins,add the cream lu sl before classbecause it will cool the coffee. Thedissolving of the sugar will alsocool the coffee since energy will beused in the dissolving. Stirnng willcool the coffee because it bnngswarmer fluid to the surlace and tothe walls quicker than the normalconvection currents wciiid. A metalspoon wilt absorb heat and will alsocon-duct the heat out of the coffeeto be released to the convectioncurrents in the air or to be radiatedto the room Since black objectsradiate heat more than whiteobiects. white coffee would coolmore slowly. A similarconsideration can be made Ior the
cup being black or white. Therelative importance of these factorshas apparently not beendetermined for coffee. Why notexperiment?3.92 Dye molecules must diffusefrom the nagative through about250 microns to the positive,arriving tn the proper amount oiprocessing time [usually a minutein today's Polaroid pictures). Therate at which the molecules cross agiven distance will depend on howfast they are going which in turndepends on the tempereture. Acolder environment slows thesemoieciiles and thus the diffusion tothe positive.3.93 Cities will be warmer thanthe countryside and even theirsuburbs because of severalfactors. There is less evaporationin the Qty, which would cool thecity by the loss of the latent heat ofvaporization (see FC 3-52). Thepaving and building materials storemore hest than does soil. There isusually less wind in cities becauseof tha taller and more complicatedstructures. Less important factorsare the relatively fast snowremoval in the winter and the heatgeneration by the machines{including cars) in the cities.3.94 The total kinetic energy ofthe room's arr molecules (what iscalled the translational kineticenergy) is proportional to theproduct of the number ofmolecules in the room and thetemperature. With the assumptionthat the arr is an ideal gas, it is alsoproportional to the product of thepressure of the air and the volumeof the room. When you heat the airin the room, the volume of theroom certainly does not change.Less obvious is that neither does
flnlurell 249
the pressure because the room isnot sealed and will always haveleaks to the outside. The room'spressure then must be the outsideatmosphenc pressure. As you healthe room, both pressure andvolume remain constant, and thusso does the total energy ol theroom's air molecules. But this ispossible only because as thetemperature increases, some otthe air molecules are torcedoutside.3.95 The lruit grower will set uppots at the end ot the day alter theground has warmed from thesunshine. The clouds produced bythe smudge pots absorb thethermal radiation emitted by theground and reradiate it to theground. The heat is theretoretrapped between the ground andthe clouds. and the orchard doesnot cool as quickly as it would werethe ground's heat radiated to theatmosphere with no retum. Naturalclouds can do the same thing.3.98 The snow layer is not agood conductor of hest and willhalp maintain the ground's heat byinsulating ll {and the crops} fromthe colder air above the snow.3.97 The tires result Irom thevisible and inlrared radiationemitted by the nuclear-blastlireball. During about the lirstsecond alter the burst, the lireballis so hot [initially about 500,000 K]that most ol the electromagneticradiation lrom it is in the ultraviolet.But ultraviolet light is readilyabsorbed by air and theretore doesnot leave the immediate area ot theburst. As the liraball expands andcools. more ot the electromagneticradiation will be in the visible andintrared because the shill in theemitted radiation will be toward
longer wavelengths- Both oi theseare transmitted by the air. Theirintensity about 2 or 3 s atter theburst will be sutlicient to setmatenals such as wood on tire.‘Virtually anything shading a personIrom the direct light from the burstcan diminish the burning cl thellesh. There were examples inHiroshima and Nagasaki whereuncovered skin was badly burnedwheress adjacent skin shaded bythe person's clothes sutleredessentially no burning.3.93 An impurity can nucleatethe crystal growth, serving as aninitial point ol attraction Ior themolecules.3.99 The hexagonal structure olsnowflakes is determined by thehexagonal bonding ol lhe watermolecules that make up asnowllake. Once the initial crystalis lormed, water vapor moleculeswill diffuse to and collect on thecorners ol the crystal to begin thegrowth outward to torm thebranches. Why one particularpattern is produced instead otanother will depend on the tailingspeed. the temperature, and theavailability 0| the vapor molecules.but not in a known manner. Sincesymmetry is so common insnowflakes. the conditions toradding molecules and branchingmust be the same across the widthol the tlake.3.100 Milk rises between twonearby Cheerios by cepillaryaction. and the surlace tension olthe milk has a horizontalcomponent that will pull theCheerios closer.3.101 The soil must be brokenup in order to retain its moisture. Apacked ground has many small
iopenings that will act as capillarytubes. As the water climbs to thesurlace. it is lost to evaporetion. lCultivated ground has much larger iopenings and thus less capillaryaction.3.102 ll the liquid surface curvesupward on the vertical sides ot acontainer, then the adhesive torcebetween container molecules andliquid molecules is stronger thanbetween liquid molecules. Theopposite is true it the surlacecurves downward on the verticalwalls- Similar consideration ol themolecular iorces explains whethera drop will spread on a partrcularsurlace or will remain a drop.3.103 The atmospheric pressure ‘does not push the sap up the treesas was thought last century. Thetrensport is believed to be due tonegative pressure. As the watermolecules evaporate trorn theleaves. and other molecules move Ionto the teat surlace to take their ‘place, a strong intermoleculartorce pulls the column ol sapupward all the way from the roots-3.104 See FC 3.106.
3.105 The rocks rise because olthe lreeze-thaw cycles that occurin winter. When the groundlreezes. the lreeze line descendsthrough the soil. drawing watervapor upward to the line bydiltusion. When the treeze linereaches a rock. it descends tasterthrough the rock than through thead|acentsoi1, because ol thehigher thermal conductivity of the ~rock Therelore. the bottom of therock lreezes sooner than thenearby soll at the same level. Theearlier lreezing means more watervapor will be drawn there to freeze,and thus the rock will be pushed
250 Flying circus of phyllce with answer:
upward by the expansion ol the icebeneath it more than the adjacentsoil will be pushed upward. Whenthe ground thaws, loose soil next tothe rock lills in beneath it to keep itin its new position. Manytreeze-thaw cycles eventuallybrings the rock to the surtace.3.‘l06 The expansion ol thelreezing water initially just beneaththe pavement cen account tor only11% ot the observed 'lrost heave."The expansion is greatly increasedby the freezing and expansion olwater migrating through the poresin the soil to the lreeze areabeneath the pavement It the top otthe soil is tree. the icecrystallization will push the iceupward to lorm ice columnsprojecting 1 or 2 in. from theground (FC 3.104)3.107 Capillary action drawswater a certain distance upwardinto the wall. The dissolved sellsthat are deposited at the top ot thiscapillary column as the waterevaporates will draw water lunherup the wall by osmotic pressureThe short circuit grounds thepositive area in this region othigher salt concentration toeliminate the osmotic eflect.3.10B Soap bubbles are heldtogether by surlace tension.Because the lluid drains to thebottom ot the bubble, the top willthin quicker and be more likely toburst. The alr pressure inside thebubble is greater than the ambientair pressure because pan ot thesurlace tension is directed towardthe center ot the bubble. thuspushing the surtace inward.3.109 Inverted bubbles,sometimes called anlibubbles,have not been analyzed tri much
detail. Surtace tension pulls theinner water into a sphere and helpsprevent the liquid at the twosurlaces Irom llowing across thealr layer.3.110 ll the llame is too large. thecapillary transport of the tuel to thewick's top will be insutlicient tomaintain the llame. Once the llamediminishes there is lessevaporation Irom the wick, and thetransport provides more tuel thanthe llame consumes. So the flameincreases With a wick ol about 2-5mm, oscillations occur tor wicklengths between about 1.5 mm and5.0 mm, the shorter lengths givingthe higher oscillation lrequenciesbecause the shoner trensportdistance results in a more repidresponse to the llame changes.3.11 1 Because ol the greatincrease in the ratio ot surlace areato volume ol the individual particlesas compared to the onginal lump otmatenal. a llame or spark canquickly bnng the individualparticles to their combustiontemperature- The readily availableair then results in rapid. explosivecombustion.3.1 12 The screen quicklyconducts away the llame‘s heal sothat the llame cannot extendoutside the screen. Flammablegases may still leak inside to thetlame. but the volume then ignitedby the llame is insullicient toexplode.3.113 When mud dries. itcontracts. setting up stresses Overthe surlace and tor some depthbelow the surtace. These stressesrupture the soil- On the averege.the intersection ol two rupture linesshould be at right angles becausethe second ol tha two cracks
lormed should be perpendicular tothe greatest tension in the lirstcreck.3.114 Similar to the mud cracks(FC 3.113). ice cracks torm in thecontrection of lrozen ground duringa sudden cooling.3.115 The exact cause ot thestone nets is not known. althoughthere are several theories. Forexample, lrost heave ot the ground(FC 3.106) may roll an initiallyunilorm distribution ol stonesoutward to lorm a clrcle. Or, it thereoriginally was a bare area in themidst ol stories, that area couldhave absorbed more water thanthe ad|acent area and then pushedthe stones radially outward when itIroze and expanded.3.116 Although this problem ispopular among physics students. Itoverlooks an important tact: abiological system (you, torexample} is not an isolated systemunder thermodynamic equilibnumsince it must constantly haveenergy inputs to maintain itsell.The energy llow through thesystem cen organize the systemand thus reduce its entropy. but theoverall entropy change ct the worldwill increase. The detailedmathematical analysis ol theentropy reduction in a biologicalsystem is lound in currentresearch.4.1 The pressure on the boy'slinger depended only on thedensity ot the sea water and howtar below the sea's surtace thehole was. The overall size ot theocean did not matter.4.2 The lurlher you are below thewater surlace, the more pressurethere is on your lungs. Around adepth ol 3 tt the water pressure is
flnluicrl 25!
large enough to prevent yourinhaling through a tube to thesurlace.4.3 In order to standardize bloodpressure readings, they are allmade level with the heart. ll theywere made. say. at the ankle level,then the reedings would depend onthe heights ol the people. and therestits would be more dillicult tointerpret4.4 On the inside ol the gate istresh water lrom the lakes that teedthe Canal. while on the outside isthe salt water ot the ocean. Whenthe pressures are equalized on thetwo sides ol the gate. and the gateis opened, the tresh water will stillbe higher than the saltwaterbecause ot the greater density otthe salt water. The higher treshwater llows seaward as the levelsequalize. giving the boat e treeride.4.5 Pan ol the oitterence inocean levels at the two Canal endsls due to the ditlerenca in salinity otthe two oceans. The Paclllc tssaltier and theretore its waterdenser. Using identical reasoningas in FC 4.4, the Pacillc erid ot theCanel should be lower than thelighter Atlantic end.4.6 The answer ts simple.perhaps mischievous. Thebuoyancy on tha hourglass mustcertainly be the same in the twocases because its volume dirt notchange. But with the hourglassinverted, it tilts against the side olthe tube, and lriotion holds ll inplace.4-? The stone in the boatdisplaces a volume ol water whoseweight eq.ials the weight ot thestone. Since the stone is denserthan water, it displaces more than
its own volume ot water. When itlies on the pool's bottom. It candisplace only its own volume olwater. Hence. less water isdisplaced when the stone is throwninto the pool, and the pool's levelmusi drop.
In the case ot the sinking boat.the water level remains the sameuntil the boat is lully submerged.and then it drops.4.8 As the lirst water pours inand tilts the lirst loop, some poursover into the second loop. Soonthat loop lills. end there is an aircavity Ietl at the top ot the lirst loop.The water llow then stops until thewater column beneath the tunnelincreases. ll that column issutliciently high, then theprocedure is repeated tor the nextloop. with a limited water column,and several loops. eventually thecolumn is unable to eliminate theair cavities and there is no lurlherwater llow.4.9 The water can be removeduntil there is a centimeter or lesslelt between the ship and the drydock walls. The hydrostaticpressure irom the ship isindependent ol the extent ot waterbelow or to the sides oi the ship- Olcourse, it the water layer becomesvery thin, then the water will climbthe walls by capillary action.4.10 A submarine can descendby taking on water to increase itsmass. Blowing the water beck outwith compressed air decreases themass lor ascension. In order torthe submarine to be stable whilesubmerged, the density ol theseawater must increase with depthat that level. ll the submanne thenmoves upward slightly. a netdownward torce returns it to thept9\l'IOl.lS depth. It it moves
L
downwerd. the net torce is upward.The density depends inversely onthe water tempereture and directlyon tha salinity, both ot whichdecrease with depth. Between 25and 200 m in depth, a submarinecan lind several layers in which thetemperature decreases rapidlyenough with depth to offset thedecrease in salinity and thus toprovide stability-4.11 ll the ratio ol the ber sdensity to the lluid's density isclose to 1 or 0. the bar tloats instable equilibrium as in the lirstliguie. ll the ratio is someintermediate value. then the bartloats in stable equilibrium with itssides at 45° lb the lluid's surlace. Ineach case, the onentalion ot stableequilibrium is determined by theposition tn which the potentialenergy ol the system is least4.12 Fish use their swimbladders to give themselvesneutral buoyancy so that they donot tloat to the top or drop to thebottom ot the see. Suppose a lishswims downward The increasedwater pressure would compress itsgas cavity. Then, because ol thedecrease in the lish's volume, ltwould have less buoyancy andwould have to swim in order toavoid tailing lurlher. Instead, thetish secretes gas into its swimbladder to keep its volumeapproximately constant. So, inspite ot the increased pressure. Itmaintains its seme volume andthus its same buoyancy torce. It itascends, the lish reabsorbs someol lhe gas, again to keep the samebuoyancy torce-4.t3 Two iorces hold thecardboard in place: atmosphericpressure and surlace tension-Once the glass is inverted, the
252 Flplng drcuc of physics uitl
water column descends slightly.leaving the air trapped in the glassat a tower pressure than the airoutside the glass. The pressuredifference between top and bottomol the water column provides aforce to hold the water up againstits own weight. Additional force isprovided by the surface tensionbetween the water and cardboardand between the water and glass.4.14 Gas produced in thevictims‘ bodies buoys them up.4.15 Because the arrangementis unstable. any small perturbationof the water surlace. any smallwave. will grow quickly inamplitude. A bubble develops torise to the tube's top. allowingwater to fall along the sides of thetube. The bubble’s upwardvelocity. and theretore the speed atwhich the glass empties. dependson the square root of thegravitational acceleration (9 Bmils?) and the radius of the upperportion oi the bubble.4.16 Both tlie temperature andthe salinity of the water decreasewith depth. As the cold. fresherwater from the bottom rises. itwarms from the surrounding waterand than is ligtiter than the saltiertop water. Thus. the llow willcontinue. In tact. even without thetube it would continue since therising water wouid exchange heatmuch faster than salt with thesurrounding water.4.17 The instability lorming thefingers is the same as in FC 4.16.The initial motion comes fromsmall perturbations. smell waves,on the surlace between the twolayers of water. The dyad waterloses heat to the undyed water as itdescends. That descending water
,_
will then be denser than theundyed water and will continue itsdescent. Undyed water initiallypushed upward by a small wavewill warm and then be lighter thanthe surrounding dyed water- itsprotrusion upward will thuscontinue-4.16 The interface between thesalt water and the tresh waterundergoes the same Instability esin FC 4.15 and 4.174.19 The volume flow rate (somany cubic meters of lluid passingthrough e cross section of thestream each second] must remainconstant throughout the stream inorder to conserve mass. Since thewater speeds up because it isfalling, the same volume flow raterequires less cross-sectional areathe lurlher down the stream youconsider.4.20 The bail is held in placeagainst gravity by a pressuredifference due to the passage ofthe air |et: the pressure beneaththe ball is greater than that aboveit. The ball deflects most of the |etover its top. The pressure in thatdeltected air is reduced. creating apressure difference between topand bottom of the bail. {See FC4.25 for e similar reduction inpressure.) As a result. there is lifton the ball. Also as a result. the airstream is deflected downward onleaving the bell. Since the ball islikely to be turning. the Magnuseflect that deflects a spinningbaseball (FC 4.39) can contnbutelilt. One possible wrong answer isto attribute the lifl to a reducedpressure in the free air iet rustbecause the air is moving. Such aconclusion is a misuse of theBernoulli principle. The kineticenergy in the air |et comes from
mechanical work in the machine.not from a reduction of pressure inthe air. The pressure in the free letis. in fact. just atmosphericpressure.4.21 The ball is suspended bythe pressure of the air stream on itsbottom side and gets its stabilityaccording to FC 4 2o. The airstream blown into the toy entreinsair inside the lube. causing an airflow from the higher opening to thelower one. As the bail passes thehigher opening, it is merely suckedinto tha tube by the air flow.4.22 The water impact supportsthe bell and also supplies itsstability. Most of the time the ball isoil center, and the impact forces itto spin in a certain direction. Part ofthe water thst adheres to the ball'ssurface is carried around half arevolution. say. and then thrownolf As the water leaves. it pushesbackward on the ball (in otherwords. there is a reaction force onthe bail). thereby holding it in thestream. Even ii the bail leaves thestream. some water is still thrownoff in the neirt hall revolution. andthe ball returns to the stream as eresult. i4.23 Apparently nothing more ‘than a description has been ipublished on this demonsiration.Why not try experimenting with it?What is tha pressure just aboveand just below the egg? Doesturbulence matter? Suppose anegg that would tloat in static waterwere in a narrow. horizontal waterjet. Would the egg move upstreamin the let?4.24 The boundary layer of thestream next to the spoon developsa narrow eddy having reducedpressure. ‘With atmospheric
flnlurctl 253
pressure on the side opposite thespoon and this reduced pressureadjacent to the spoon. the streamis held against the spoon. (Thisphenomenon is called lhe Coandaeffect.) Turning the bottom corneris aided by the "teapot effecl" ofFC 4.1 1 B.4.25 The passage of the air jetreduces the air pressure at themouth of the tube. The watersurlace outside the tube ts atatmospheric pressure. Thus. thepressure difference forces waterup the tube. The real question iswhy there rs reduced pressure dueto the air |et. One wrong answer isto attribute a low pressure to thefree |et. However. as is discussedin the answer to F0 4.20. the free|et has atmospheric pressure. So.the jet must suffer a pressurereduction because of its deflectionby the tube.
Two factors should beconsidered. Some of the air maybe torced up and over the top ofthe tube. The air ariiacent to thetube in this deflected stream wouldmove faster and be reduced inpressure. It the llow is ttrbulent. asis likely. than the stream developseddies above the lube. which alsoreduces tha pressure there. Eitherway. the pressure at the tube's top
l is reduced.4.26 A high speed train producesa high pressure pulse immediately
i in tront of itself and a tow pressurearea in its waiiie. When trains arepassing. the low pressure area
1 between them can suck windowsoutward.4.2? As the air is torced up andover these structures. thepressures at the tops oi thestructures are reduced (see FC4 25] Air can than be pul ed from
the ventilator shall or the pralnedog tunnel.4.28 The acceleration of the airup and over the tront of the car isso great that the insects rupturefrom the force.4.29 Imagine the flag perfectlysmooth and fully spread in a strongwind- A small perturbationdevelops that. on one side oi theflag. forces the air outward slightlyin order to move over the ripple.That air stream must speed up as itcrosses the ripple. The faster airhas less air pressure. and thus theripple grows because of thedifference in air pressure on itsSldB5' the reduced pressure of theair crossing the ripple and thenormal pressure on liiri other sideof the flag. The ripple also movesdown the length of the flag in thedirection of the wind. so the flageventually flaps.4.30 The wing was tilteddownward so that it torced the cardownward and therefore increasedthe traction ol the tires on the road.iMth greater traction. the car couldtake a turn faster. Theaerodynamic torce from the wingwas just like on an airplane (seeFC 4.31). but downward instead ofupward.
The car with fans in the rear alsoreceived a downward force toincrease trsction. The air that wastorced beneath the car had tospeed up because it was beingmade to enter a restncled opening.with greater speed. tha air hadlew air pressure according to theBernoulli pnnciple. Hence. therewas greater air pressure above thecar than below it. and the car waspushed onto the road more. Theweight of the car was effectively
4.31 The air passing the lop ofthe wing moves faster than the airpassing below the wing. Thepressure above the wing is lessthan the pressure below the wing.As a result, a net upward force ison the wing.
Whether or not the Bernoulliprinciple applies to the calculationof this lilt is not always clear in therelerences. The principle is astatement of the conservation ofenergy (here. pressure and kineticenergy) along a stream line in theair flow. Since the air flow around awing is affected by adhesion to thewing and viscosity. both of whichdo work on the air. the principleshouid not be applicable However.it can still be used if the adhesionand viscosity are accounted for bysuperimposing a circulation of air(forward underneath the wing.rearward on top} on the irrotetionalllow or the air passing the wing. Inthe work of Kutta and Joukowskyon lift. such a supeI]:|tJ5ltl0l"l of ecirculation ts made. Above thewing, the circulation speed adds tothe irrotational speed past thewing to give a greater speed.Below the wing the circulationopposes the irrotetional flow. andthe air speed is reduced. ByBernoulli's principle, the pressureabove ti1a wing is less than thatbelow the wing, thus there is liftThe application of the Bernoullipnnciple in obtaining lilt on thewing is therefore somewhat subtle.
The actual iilt on a wing iscalculated in the Kutta-Joukowsi-rytheory by determining themomentum change in the airstream as it is deflected by thesuperimposed circulation.According to Newton's law. theforce necessary to deflect the airstream downward is equal to the liftgr-i - | increased by about 50%.
254 Flying drcul 0| phyolcl uilh lnluicrl
on the wing. Some referenceserroneously descnbe lift on thewing but then show an air streamthat leaves the wing moving inexactly its original direction.4.32 As the pilot attempts to pullout of a dive, the weight of theplane effectively increasesbecause of the centripetalacceleration in the turn upward.The lift on the wings, previouslyinadequate. will now have to beeven larger because of thiseffective increase in weight. Togain greater lift, the plane's airspeed will have to be greater thannormal.4.33 The passing wind producesa "horizontal |ift“ on the sail towardthe convex side. [See FC 4 31.)This force is most efficient andgives the greatest boat speed it theboat is sailing 90° to the wind.4.34 Normally the trisbee sailsthrough the air with its tront edgeupward. thereby gaining litt as awing does {FC 4.31)- In addition.the fnsbee's orientation issomewhat stabilized by its rotation,iust as a gyroscope is stabilized byits rotation.4.35 There are two types ctattempts at man-powered flight-where planea are powered by menand where people {wisely orunwisely] leap from tall structurestiapping their arms and attachedwings. The latter is unlikely to besuccessful for more than 10 or 20ft, with the landing unlikely to besoon forgotten. In contrest.building lightweight aircreft inwhich one or two people paddle forpower to lift and propel the craftseems promising. The first suchflight occurred in 1961, lasting forabout 50 yd. Numerous plane
i designs have appeared since then.Wing spans, for example, haveranged from 60 to 120 ft. Theprimary concern in these designsis to reduce the power necessaryfor lift. Presently, even a goodathlete cannot power a planebeyond about 1oo yd. However.sporting planes of 50 ft wing spanand appropriate wing shape shouldbe feasible for man-powered llightif the plane also takes advantageof thermals and wind currents. Thecraft would then be powered byone or two people only until it issufficiently high that it can actpartially as a sailplane {see FC4.98).4.36 With bottom spin the golf ballgains lift in the same way that aspinning baseball is deflectedsideways. (See FC 4.39.)4.37 The passing wind pushedthe cylinders sideways in the sameway that a spinning baseball isdeflected in FC 4.39. Appropriateonentation ol the ship would resultin the ship moving fonvard throughthe water.4.38 Some ol the wind incidenton the building is forced throughthe opening, having to speed up todo so.4.39 A curve is thrown byspinning the baseball about avertical axis. The passing air thenexerts a horizontal force (called theMagnus effect) that deflects theball. The force on the ball is due tothe unequal pressures on the ball:the side turning into the passing airhas greater pressure than the sideturning with the passing air.
The application of the Bernoulliprinciple is as difficult here as inexplaining the lift on airplane wingin FC 4.31. Again, the principle
should not apply because the airstreams passing the spinning ballexperience both adhesion to theball and viscosity. The side turninginto the passing air decreases thestream's kinetic energy and thus itsspeed- The side tuming with thepassing air increases the air’skinetic energy and thus its speed.The Bemouili pnnciple can beapplied, however. if the effects ofthe adhesion and viscosity areaccounted for by superimposing onthe irrotational flow of air pass theball a circulation of air that turns inthe same sense as the ball's spin.On one side the irrolationalspeed adds to the circulation flow'sspeed, giving a greater speed. Onthe other side, the two speedsoppose each other, giving a lesserspeed. Since the Bernoulliprincple now works (because weno longer have to include extemalforces doing work on the passingair once we supenmpose thecirculation flow], the pressure onthe first side must be less than thepressure on the second side. Thepressure difference deflects theball.
The actual deflection force (thehorizontal lift) can be calculatedwith the Kutta-Jouliowsky theoryas with the airplane wing (FC4.31). Again, some books err intheir description of the ball'sdeflection by giving the ball adeflecting force without giving theair stream a deflection4.40 A reverse affect can beproduced for a slowly spinning,slowly moving, smooth ball. Undercertain conditions, the side of theball spinning with the direction ofthe passing air may remain laminar(smoothly flowing) whereas on theother side there may be turbulentmixing. The pressure in the
flnlwnl 255
turbulence would be less than thepressure on the other side, causingthe ball to dellect in the oppositeway as in FC 4-39. Upon leavingthe ball, the air stream would, ofcourse. be deflected in theopposite sense also.4.41 The vertical forces initiatesmall amplitude waves. As the airpasses over these waves, it isforced upward slightly by the peaksand then flows downward into thetroughs. At the peaks the air speedis greater and thus the pressure isless. The opposite would be true inthe troughs if the flow were ideal.Such an ideal situation, with lowpressure on the peaks and highpressure in the troughs, would nottransfer energy from the wind tothe waves and thus the wavewould not grow. In the nonldealflow the air circulates in a reversedirection in the bottom oi thetrough and thereby shifts the highpressure point closer to thepreceding peak. The pressurevenations are therefore no longerin phase with the water wave and anet amount of energy is trensferredfrom the air to the water. The waterwaves then Qrow4.42 The monster waves are thechance meeting of many oceanwaves ll'l phase. They are not giantwaves that traverse the ocean.Instead, they quickly disappear asthe composite waves go off in theirown directions and leave with theirslightly different speeds.4.43 Wind speeds above about5ml5 produce water surfaceturbulence that then produces airbubbles. Fialts of these bubblesare called whitecaps. The groupvaiooity of ocean waves is abouthall the phase velocity This resultmeans that incivid.ial waves form
_i_ _. .
at the rear of a group of waves,move foreward at about twice thespeed of the group es a whole, andthen dissppear at the front of thegroup. The greatest amplitudeoccurs in the center of the group.So, each wave in turn moveathrough the maximum amplitudeposition. If that amplitude is morethan a cei1ain critical value, thenbreaking and subsequent foamingoccurs. But the foaming will tskeplace only when an individual wavehappens to move through thecenter of the group. Thus. thewhltecaps will appear penodicallydownwind of each other.4.44 A slowly moving boatproduces bow waves of relativelysmall wavelength. Severel of thesewaves will be along the length ofthe ship at any given moment Asthe boat goes faster. thewavelength of the bow wavesincreases until eventually thewavelength IS equal to the boat'slength. Then the bow and sternwaves reinforce each other, andthe ship is esssntialy treppedbetween two crests. one at its bowand the other at its stem. For fasterspeeds the resistance from thewaves increases considerably.requiring much more power fromthe boat. The hydropiane avoidsthis problem by lilting the hull fromthe water. Supports extending intothe water act as airloils do onairplanes: the deflected watercurrents over the moving supportsgive them lift {Sea FC 4.31.) As faras the lilt ts concerned, these boatsare lust airplanes flying throughwater4.45 There are two types ofwater waves: capillary waves.which are govemed pnmarily bysurface tension, and gravity
waves, which are controlled mainlyby gravity. Longer wavelengthwater waves are of the secondtype; shorter wavelengths are ofthe first type. Neither of these canpropagate with speeds below 0.23mfs. lf the beetle skims slower thanthat speed, no wave pattern isproduced. For faster skimming, thebeetle creates both types ofwaves. The capillary waves havegroup velocities greater than thewavespeed, and they are thereforein front of the beetle. The gravitywaves have group velocities lessthan the wavespeed and thus arebehind the beetle. Only thebeetle‘s capillary waves areprominent, but the gravity wavesare visible with close inspection.4.46 were the ship to generatewaves of a single wavelength, thenthe angle of its wake could befound lust as the angle rl is foundfor the shock wave cone left by esupersonic aircraft: ain e = cfvwhere c is the speed of the soundwave and v is the speed of theaircraft. In contrast, the shipgenerates waves of a large rangeot wavelengths that travel atdifferent speeds. From anyparticular position of the ship,these waves are sent outward in alldirections, the longer wavelengthwaves traveling faster than theshoner wavelength waves.However, these wavesdestructively interfere except on acircle that expands forward in theship's direction of motion. Theship's progression leaves a trail ofthese expanding circles ofconstructive interference, the onesfurther back larger than the morerecent ones. These circles developthe V-shaped area in the figuresuch that the angle of this V isindependent of the ship's speed.
255 Flying iclrcul ol phyilcl urllh
Consider a particuar point on thecenter axis directed from the shipbackward through the wake. Thedistance from that point to the shipis always three times the distancefrom the point to the edge of thewake (the outer limit of thespreading circles) along aperpendicular to the central axis.As a result the sine of the angle ofthe V. and thus the angle itself,must always be the same. Insidethe V the expanding cirdes ofconstructive interference producethe particular pattem of crestsshown in the figure.4.47 Apparently there is nopublished aiementary explanationfor the edge waves. The recentpublications suggest that they maybe caused primarily by thenonpropagating oscillations nearthe oscillator rather than the wavespropagated through the besin.4.48 The wave speed dependson the depth of the water, theshallower the watsr is. the slowerthe waves move. If a wavefrontapproaches the shore at someangle, the inshore portion of thewavefront slows before theoffshore portion. As the waveprogressively slows. the wavefrontis swung around until it is close tobeing pareliel to the shore line (orat least the line of shallow water).4.49 The front end cl the board istilted upward (as the nder assumesthe charactenstic surfing stance byleaning backward slightly}. andwater is forced beneath thepassing board. ll the skimming isquick enough, then the boardpasse: before the water beneath itcan be squeezed out. Forexample if the water is 1 in. deep.then the water waves will move atabout 0-5 mfs. Thus, skimming
faster than that speed constantlysupplies fresh water beneath theboard to avoid stalling. The forcesupporting the rider is notbuoyancy, instead, it is the impactforce from the water.4.50 To ride the waves. thesurfer must move with the wavespeed. Normally, in deep water,the wave speed is greater than thespeed of the water particles in thewave. ll the wave is nearlybreaking. the water has almost thesame speed as the wave. and thesurfer needs only a little more inorder to keep up with the wave.The additional speed comes fromthe continuous falling downhill ofthe surfer on the side of the wave.Thus, in order to su if, one needs abeach with waves that are eitherbreaking or almost breaking. Thewater speed is greatest at the crestof the wave. Therefore, the speedof the rear of the board through thewater shouid be less than thespeed of the front of the board.creating an unstable situation. Theshorter the board. the less thisdifference in speeds is a problem4.51 The bow of the moving shipcreates a high pressure area infront oi the ship. The porpoisesnde between that high pressureraglon and the normal waterpressure further ahead of the bow.4.52 The tides are not due to themoon or sun pulling the waterradially outward from the earth.Instead the bulges are caused bythe h. iii.-ontal components of thegravitational forces from the moonor sun collecting the water in thebulgr .'.. §3P'lCB the horizontalcomponents are less baiow themoon's or sun's position in the skyand on the opposite side of theearth, the bulges collect there. \
Were the moon to revolve aboutthe earth always directly above theearth's equator, there would be nodiurnal (once-a-day) tides.However, with the moon's orbit offfrom the earth's equator, some lowlatitude a reas can have a dominantdiumal tide.4.53 The tidal generating forcedepends on the inverse cube ofthe distance to the sun or moon. Asa result, the moon's effectdominates in spite of the fact thatthe sun has a greater gravitationalpull.4.54 To conserve the totalangular momentum of theearth-moon system, the separationbetween the two increases in orderto compensate for the earth's lossof spin.4.55 The wind, barometricpressure vanations, and seismicevents oscillate these bodies ofwater. From the range of oscillationfrequencies in the disturbance, abody oi water picks out its resonantfrequency. Standing waves thendevelop in the body of water. lustas standing sound waves areproduced in an organ pipe excitedwith a range of sound frequencies.4.56 See FC 4.58.4.5! The natural period ofoscillation of the bay is about 13 hi.and so the semidiurnal tide forcesresonant oscillations of the bay,much as sound waves can force anorgan pipe to resonantly oscillate.As a result. the bay s oscllationenergy has bean enhanced. andthe amplitude ol oscillationincreased.4.56 The bore and the sink lumpare both examples of an hydraulic|ump, which is a surface water
Aneurerl 257
wave analagous to an atmosphencshock wave. Normal (sinusoidal)gravity waves can piopagateupstream on a moving stream olwater il the speed oi the water isless than the speed ot the waves.(See the answer to FC 4.45 tor thedistinction between gravity andcapillary waves.) The ratio oi thestream speed to the wave speed iscalled the Froude number. Ii theFroude number is less than 1 , thenthe stream is ' subcritical." ll it ismore than 1. the stream is‘supercritical." The hydraulic |Ul'l'ipis a wave that occurs where thewater llow changes between beingsupercritical and subcritical Thereis a change in height because thewave speed depends on thesquare root oi the water depth. Forexample, tl"l the sink hydraulic jumpthe depth is shallow inside thecircle. the gravity wave speed islow. and the ilow is supercriiicalOutside the circle. the depthincreases. hence the wave speedis more, and the llow is subcritical.In the case oi the bore, the irillowoi tidal water through a channelthat narrows and nses makes thestream supercnticai to any waveinitiated by obstacles in the stream.The bore changes the llow iromsupercritical to si.ibcriiii:al byincreasing the depth oi the waterand thus increasing the speed oithe water waves.4.59 Apparently nothing hasbeen published on thisdemonstration. So. you might liketo eiipenment with it yourseli.4.60 The cause ol beach cuspsis still current research. Althoughrlany theories have beenp stulated, none are generallyaccepted. The larger cusps appear
‘ to be due to np current llows, which,i_ _ __ _.
F’ T” l Uhave lairly regular spacing alongthe beach According to the theory.points (horns) oi the giant cuspsare between the rip currents wherethere is least transport oi thebottom material parallel to theshore. The rounded portion (bays)oi the giant cusps develop wherethe rip currents llow outward to seaand thus where there is |T'l3.'l(lI'T'lUl'l'lmaterial transport. The cause olthe smaller beach cusps is notknown. One oi the more recenttheories descnbes the incidentocean waves creating stsndingwaves oblique to the beach. Thecrests and troughs ol these obliquewaves shape the beach into thecusps.4.61 The rotation oi the earthcauses an apparent torce. theCoriolis torce. to deviate thesurlace ilow irom the direction oithe surtace wind. This deviation isabout 45'“ to the right in theNorthem Hemisphere arid 45“ tothe leil in the SouthernHemisphere. ll the llow is laminar{smooth}. the deviatton increaseswith depth- A plot oi the velocityvectors with depth is called theEkman spiral. To lind the nettransport through the extent oi thisspiral, one must integrate the llowover the depth. The result ol thecalculation indicates that the nettransport is about 90* Irom thedirection oi the surlace wind.4.62 The change oi the Conolislorce with latitude shiits thegeneral circulation oi the oceans tothe west. Since the streamlines inthe west are then more crowded.the current llow there is moreintense.4.63 When the tea is rotatingaround the center oi tho cup, thecentnpetal acceleration lor such
circular motion comes Irom thepressure diiierence between thetea nearer the wall and the teanearer the central axis. Thispressure diiierence also leads toan additional ilow, called thesecondary ilow, that deposits thetea leaves in the center oi the cup.Consider two horizontal suriaoesthrough the tea, the top layer andthe bottom layer. In both layersthere is greater pressure at largerradii trom the center. But in thebottom layer less pressurediiierence is needed to provide thecentripetal acceleration becausethe iriction Irom the cup's bottomprevents the tea irom circling aslast as it does higher up. In bothtop and bottom layers there is apressure diiierence. but thediiierence is greater at the top. Ii asmall parcel oi tea is initially at theouter top part oi the top surlace.not only does it circle the centralaxis. but it also descends along thewait to the bottom because oi thepressure diiierence between theouter top and the outer bottom. Toreplace the lluid lost irom the outertop, there is a ilow oi lluid irom thecentrel bottom upward along thecentral axis and then to the outertop- Thus, while the tea is circling,it is also llowing irom outer top toouter bottom. to inner bottom, thento inner top. and finally to outer topagain. Tea leaves lying on thebottom are captured by thissecondary ilow and deposited ll'lthe center oi the cup where thelluid begins its ascent.4.64 The secondary llow in thepreceding problem is alsoresponsible tor the meandering oirivers. Perpendicular to the ilow olthe stream in an initially slight bendis e secondary llow circulati ig iromouter top to outer bottom. then to
258 Flying clrcun OI phyllcl wlih Inlwen
inner bottom. up to inner top. andthen tinally back to outer top. Thisllow removes material irom theouter stream bed wail and depositsit on the inner bed wall somewhatdownstream. Although a youngstream may slsrt relatively straight.the slight turns in it are enhanced.and the stream begins to meander.4.65 ti the ball is to rise at itsnormal rate. it will have to push thewater above it outward to thesides. But such motion ol the waterwill be against the pressurediiierence that keeps the lluid incircular motion. (The centnpetalacceleration oi the water in thiscircular motion about the centralaxis is provided by the pressurediiierence between the water atlarger and smaller radii: there isgreater pressure on the outside.) Itthe sphere‘s upward speed is toosmall to provide this outwarddisplacement oi the water above it.then the sphere ascends with acolumn oi water that rises at thesame rate as the sphere. In otherwords, the sphere pushes andpulls upward a column oi water itsown diameter in size. The irictionon this column and the greatermass that is moving both increasethe time needed tor the sphere torise.4.66 The dye displaces some oithe water when It enters. Pan oithe water is pushed inward towardthe central axis. But that particularparcel oi water is now moving tooquickly tor its new radius. and thusit tends to press radially outward
l trying to regain its lormer position.The water that is pushed radiallyoutward by the drop linds ilsellunder too much pressure tor thecentripetal acceleration it has, andthus is pushed radially inward
trying to regain its own old position(The radial pressure diiierence isdiscussed in the precedinganswer.) As a result, the dye iscompressed radially. it mixesdownward, but stays in a narrowsheeL4.67 Comments on the directionoi swirl in a draining bathtub areolten as strong as in heatedreligious clashes. some peopleargue that all NorthernHemisphere tubs draincounterclockwise; others insist thatonly about halt do. Shapiro (722)was the lirst to caretully test theswirl direction, although theergumerits appear to havecontinued anyway. Unless extremecare is taken with a carefullydesigned tub, the rotation due tothe Coriolis torce cannot be seen.Non"nal bathtubs and sinks are byno means deaigned to show theCoriolis eiiect. Swirling in themcould be in either sense. being dueto such uncontrolled lactors as theshape ol the tub. the motion due tothe pulling oi the plug. theresidual vorticity Irom the iilling, theair currents above the water, andthe shape and position oi the drain.To show the relatively weakCoriolis torce. you need a verysymmetric tub with a central outletthat can be opened without swirlingthe water. Once the tub is tilled. thewater should sit ior about one ortwo days tor the vorticity irom thetitling to die out There should beno air currents above the water orchange in temperature in the room.both oi which could producemotion that would swamp themotion due to the Conolis eiiect.With these and other precautionstaken, the proper rotation oi thedraining water can linally be seen. i
4.68 The cause, nature. andbehavior ol tornedoes aridwaterspouts are poorlyunderstood. Indeed. the distinctionbetween the two vortices is notclear other than that theWaterspout is over water. isweaker, travals taster. and lastslonger. True tornadoes, the type inthe central plains oi the UnitedSlates, are highly destructive aridaccompany violent storrrs. Thevertical motion appears to beupward through the tunnel.[Dorothy was carried upward in‘The Wizard oi 02".) The tunnelsare visible because oi the watercondensation in its low pressure orbecause ol the dirt. debris. or sprayit accumulates irom the ground.They olten occur in the springwhen the cool. dry air irom thenorth meets the warm. moist airIrom the Gull of Mexico region.However. the mechanism thatgenerates the vorticity is notknown. Thermally induced rotationmay be a cause. Existing rotationalmotion may converge to intensitythe motion. Super thunderstormsmay repeatedly produce electricaldischarges that heat the air soseverely as to generate thevorticity. The irequent occurrenceoi lightning in tornadoes (eitherstroke or bal|—see FC 6.32 to6.35) makes this latter proposalattractive.
4.69 The granular substancepromotes the release ol carbondioxide gas by acting as nuclei torbubble iormation. The bubblesiorm in the center oi the ilow.especially it the granularsubstance is dropped there,beceuse the pressure in the wateris less in the center than lurlherout. {The pressure distribution is
Artlltrcrl Z59
discussed in the answer to FC4.63.) The released bubblesprovide buoyancy to the centralwater, which then nses. Otherwater llows inward at the bottom.resulting in a concentration oiangular momentum in the center.The rotational speed increases,and the swirl forms.4.70 Because oi the greaterdEt‘l5l[y ol the cold milk, the milkstream descends into the hotcotlee. Vortex tubes (vortexcolumns) in the rotating coiteebecome entrelned in the milk andare stretched by the descent. As aresult. the angular speed ol theentrained vortices increeses.perhaps enough to dimple thesurlace. li hot milk is poured intothe coitee. it will not descend or atleast will not descend as quickly- Itthe hot milk is less dense than thecoitee, the entrained vortex tubesare shortened. and the rotationalspeed decreases.4.71, 4.72. and 4.73 The causeand maintenance oi dust devils arenot well understood. Apparentlysuperheated air initially lies inunstable equilibrium near theground- Any small disturbancebreaks this hot air out ol theboundary layer so that it may rise.Once that break is made, the rialnghot air wtll pull other hot air upthrough a chimneyiike eltort [FC3.34). The rotational sense isentirely random and does not showthe preterentiat rotation as dohurricanes. The whirlwindsdeveloped above tires and overLake Michigan are similarphenomena in that there is veryunstable hot air beneath cooler air.4.74 As a drop enters the water,its sides ere retarded by the waterand move slower than its center.
The vortex torms as the tastermoving center descends. andslower moving edges curl upward.The GXQHHSICEI oi the ring as itapproaches! e bottom is similar tothe expansion oi smoke rings in FC4.103.
4.75 Vortices are shed trom botliedges ol the cardboard in the lirstarrangement. In the second, the airis swept along the length oi thecardboard and then finally breaksinto a vortex at the trailing edge4.76 The gas initially coolsbecati to it expands on entering thelube. Near the inlet a vortex iscreated that has greater speedsnear the tube's axis and slowerspeeds cl ter to the tube‘s wall. Asthe ilow spirals along the tube, thespeed distribution over the widthbecomes more unitorm as theinner alr does work on the outer airdue to viscous interaction. As aresult the outer region heats bythe time it reaches the hot air exit.The core oi the vortex ttows towardthe cold air exit, expanding as itpas-~s the inlet and thus cooling.So, the increase in temperature inthe outer layer ot the swirl is due toviscous work in speeding up theouter layer. The decrease intemperature in the core is due toexpansion as it ttows in theoppo= -'e direi ion.4.7? As a bird thmsts downwardwith its wings. it iorces an updraltbeyond the wing that then trailsbeyond the bird. The purpose olthe V tormation is to have anotherbird behind the lirst to takeadvantage ol that trailing updratl.Titus, all but the central bird cansave on energy by using theupdralt lelt by the preceding bird4-78, 11.80, and 4.61 The
‘Ti 7 7 7 7 7 777 777 7 — ——
behavior oi all oi these tailing orrising objects is govemed by thepattern and changes in the tluidllowing past them, but theoreticalor even qualitative explanations oithe results are not availableInstead. ctirrent research hasattempted to correlate the types olbehavior with the Fleynoldsnumber (which is related to thepresence and degree oi turbulencein the llow) or some other suchparameter4.79 The trailing car is propelledtorward by the vortex llow lett bythe leading car and encountersies J air dr-"qr because the air llowhas already been diverged by theleading car The whiplash appearsto occur when the trailing carbegins to pass. Pan oi the airllowing past the leading car on thatside is then torced to pess throughthe relativaly narrow spacebetween the cars. thus speeds up.and theretore is reduced tnpressure. The trslling car then hasgreater pressure behind it than intront on the side closest to theleading cer. The pressurediiierence accelerates the trailingcar momentarily ca it pulls out topa . .. Tr.r- is lJ'!i car shouldexperience a corresponding torcer tnvard.4.60, and 4.B1 See FC 4.79-4.82 The tish swim in a mannerso that, like the birds in FC 4.77,they cart take advantage oi thewakes lelt by their leaders.Coni iler a tish inside the school.As it iwims it leaves a trail oivortices that develop altemately onopptii .ite sides ol an axis extendingdirectly behind the tish. Thavortices turn such that on the axisthe water tlow is In the directionoppoalte the tish s motion Were
260 Flying clrntl 0|’ phy-lice Itrlfh Il'Il'lli‘lttl'I
another llsh to swim directly behindthis particular tish, the trailing tishwould have to expend more energybecause it would be swimmingagainst the llow oi these vortices.However. it the trailing tish were tothe side ol the axis. it would be inthe part oi the vortex llow thatmoved lonivard. Imagine twoleeding tish with a trailing ti shbetween the two body axesextending backwards tront themThe trailing tish would be in thetorward moving pan oi the vorticesirom both the leading tish, and thuswould have to expend less energythan the leading tish in swimming.The purpose oi the school is partlyto decrease the energyexpenditure oi all but the leadingtish by having the trailing tish takeadvantage oi the vortex ttows oithe tish in tront oi them4.83 The wind breaks intovortices as it passes the building.On the windward side the wind issomewhat laminar (smoothlyllowing). whereas on the oppositeside the vortices rrialie the windgusty4.84 The large vertical plates onthe bridge were ultimatelyrespon -ible tor the bndgeoscillations. Such a broad lace tothe wind torced a large amount oiair to divide and ilow aroundthe plate and then across thebridge. The pressure just aboveand iust below the plate haddecreased air pressure because olthis rerouting and con -iquentspeeding up ol the parsing air.Were the plate perleclly symrnetncIn the wind, the decrease trlpressure on top and bottom wouldhave been the same. However. thewind blew at lluctuating angles tothe plate. and thus the pressures
were diiterent irom moment tomoment. This pressure diiierencetlowed across the width oi thebndge and was augmented by theturbulence shed by the windwardplate. As a result oi the pl'BSSl.Il'Bdiiierence between top endbottom. the bridge began tooscillate. Similar oscillations arealso developed in ‘gelioping"telephone wires, where thepressure ditierences and vortexshedding also produce a whistlingirom the wires (FC 1-55).4.85 Clear air turbulence (CAT)appears to be due to What is calledKelvin-Helmholtz instability. As amodel oi the instability, consider adense and at light iluid in a basinwith the lighter lluid on top and withthe two lluid layers sliding overeach other It their relative speed isslow, any small disturbance in theinieriaoe is quickly eliminated. Forgreater speeds, however, aperturbation in the inleriace canresult in an intrusion oi one iluid Inthe other where the intruding lluidthen develops a swirl. Similarvortex development can occur inthe atmosphere where there isstrong vertical wind shear (andthus relative motion ol two layers)and large horizontal temperaturegradients (and thus dilterenoes indEl“lSlllE - oi ad|acent layers). TheCAT is thought to be SWtl'lSdeveloped at the interiaoe4.88 Because there is reducedair pressure on the mountain topsthe air viscosity is tess there. andthus the watch shouid n.in taster.4.BT The mesh introducesturbulence and cavitation in thestream because it narrows theaperture through which the waterp-4:. I‘-'1. The sensation oi solterwater is probably due to the air
bubbles that are iormed_4.88 To my knowledge there hasbeen no systematic research onthis question. although sportsarticles often reter to iast and slowpools. l could guess that thegutters deaigned to absorb surlacewaves would eliminate therellected waves that may interlerewith swimmers. Why not researchthis and other aspects yourseli?4.89 A stream passing over aspillway is similar to an air streampassing an edge (FC 1.56} in thatoscillations are created in thestream. In the tailing water theoscillations set up e standing wavewith live-iourths wavelength iromthe spillway to the ground.Because oi the resonant leeding oienergy irom the pressurevanations induced by the edge tothe oscillations oi the ialtmgstream, those oscillations can growto a signilicant amplitude. Thisstanding wave may be related tothe earth's vibratlors near a watertall (FC 2.65}.4.90 As the air passes the outeredge oi the parachute, vortices areshed. Since the sheddingalternates from one side to theother. and since they each havereduced air pressure. the chuteexperiences tower pressure lirst onone side, then on the other Thisalternating oi pressure begins toswing the parachute. II theoscillation trequency is ciose to theresonant pendulum trequency oithe parachute and its load, theoscillation can be as large as 60°The central hole allows some oithe incident air to continue alongthe central axis oi the parachuteand break up the vortices on thelop side- Stock cars can toleratethe oscillations even less than
Answers 261
parachutists, so the parachutes onthe cars have even more directllow areas to lurlher reduce thevortices.4.91 The explanation ol the boatdrilling taster than the stream isstill missing details about the waterllow and momentum transport nearthe boat. However. the higher boatspeed is partially iustilied by asimple analysis ol the loroes on theboat. lts weight is directly down,but the buoyancy is at an angle tothe vertical. because the river isllowing downhill. Thus. there is acomponent ol the boat's weightthat is parallel to the stream'ssurtace. This component isbalanced by the drag irom thewater. An equivalent volume olwatar in the boat's place wouldeiipenence drag also. But becauseof turbulent lTl|ll<ll"tg in such avolume ol water. it would meetgreater resisianoe than the solidboat does at the same speed. As aresult, the speed at whch the dragcancels the parallel component otthe weight is greater lor the boatthan tor an equivalent volume oiwater.4.92 A solid well creates strongvortices that swirl the snow. Afence. on the other hand, createsmilder vortices. ll the air speed inthese lance vortices is less thanthat needed to suspend the snow.then the snow is deposited on theleeward side ol the lence_4.93 In order tor an obstacle tocapture the snow. the snow has tobe brought nearby. The windbeginsto diverge tensor hundredsol meters in tront ol a large house,thus diverting the snow too earlytor it to be deposited at the house.A smaller obstacle. such as a pole,diverts the air much less. and the
SHOW Cfll"l QBI l"lE3t'.
4.94 The trailing edge is sharp sothat the boundary layer on the topol the wing does not separateprematurely. Such a seprationwould result in turbulent mixing atthe rear ol the wing, which wouldput the airplane in stall because itdestroys the till.4.95 The aerodynamics ot askier are. ol course, toocompliceted tor an exacttheoretical solution, so the choioeol a particular stance withouteiiperimentai data is largely lust aguess.4.96 The air drag on the ballcomes irom two lactors: thepressure diiierence between trontand back sides ot the ball. and theiriction between the air and theball. With a smooth ball thebotindary layer ot air on the ballseparates trom the ball withoutentering the rear side much. Alterseparation, the air developsvortices and leaves the tear inreduced pressure Since there ishigher pressure on the tront slde.the pressure diiierence retards theball. A rougher surlace delays theseparation ol the boundary layer.As a result. there is less pressurereduction on the rear side. lesspressure dl'llBfEI1CE between lronland rear. and therefore less dragdue to the pressure dillerenoe Thedimpled goll ball goes lurlher.4.97 There are two generalaspects to a bird's ability to tly. Ilawings act as airloils (FC 4.31], andthe bird can soar {FC 4.98). Butwhen it llaps its wings to propelitsell. the thrust comes not Irompushing backward on the air, buttrom the leathers twirling in the airand acting as propailers. Perhaps
a plucked bird could soar but itcould not propal itsall.4.98 Birds and sailplanes cansoar by two techniques. They canlly into wind that is deviatedupward by some obstacle such ashills and water waves Morepractical lor distance llying.however, is tor them to tly intorising bubbles ol hot air. Once liltedby such a bubble. they can thenglide downward until they lind yetanother rising bubble. The bubblesare not tall oolumns ol hot air.Instead. they are ring vortioes thatare developed as hot air in theboundary layer ol air on the groundbreaks loose from the ground. Thecirculation in the ring is upward inthe center and downward on theoutside (an upside down version clthe vortices in FC 4.74). A bird cansoar by circling around in the risingportion.4.99 All kites act essentially asairloils in that they toroe the air todiverge and there ls less pressureon the top than on the bottom togive tilt to the kite {see FC 4.31).The ditlerent bridling techniquesdistnbute the stress from thehandling string and also giveStability to the lilte. For example.the last three techniques shown inthe liguie will give a stabler llightthan the lirst technique Thebridling can also be used to ad|ustthe kite s angle ol attach. that is. iteangle with respect to the winddirection. In a light wind, the kiteshould be at more ol an angle tothe wind so as to diverge more airto get the proper lilt. With strongerwinds. the kite should be at less olan angle since less wind needs tobe diverted. A kite tail has twopurposes other than |ust being tunto watch. Its air drag stabilizes the
262 Flying circus of pllyllcl with lnluiurl
kite. thus making the kite lesssubiect to gusty winds. And,second. the drag helps adjust thekite to the angle of attack proper tothe prevailing wind4.100 Cloud streets are due tolongitudinal vortex rows, that is,rows ol vortices whose axes olrotation are horizontal and in thedirection ol the wind. Where thecirculation is upward between twoadjacent rows. the air cools byexpansion and condenses outsome ol its moisture to lorm acloud {see FC 3 23]. No cloud islormed where there is downwardmotion between two adjacentrows. The vortices are produced bya thermal circulation in whichwarmer air nses end cooler airdescends. similar to the Bemardcirculation cells ol FC 4.101. Thehorizontal wind stretches thesevortices so that they becomehonzontal vortex rows-4.101 ll the bottom lluid issulticenlly hotter than the top lluid.the lluid ls unstable and convectioncurrents ol rising hotter lluid anddescending cooler lluid candevelop into these patterns. Forexample, the hot lluid can rise inthe intenor ol a hexagon while coollluid descends on the boundarywith other hexagons. For a giventemperature dillerence and a givenlluid, theory can determine thosepattems (rolls or hexagons) thatare steady-stale solutions ol thellow. Pan ol the visible appearanceol the cells on the collee is due totiny drops suspended |usl abovethe areas ol rising collee. Acharged comb disturbs thesedrops and partially destroys thecellular appearance4.102 The dune streets are dueto the same type ol horizontal
vortex row tormation in the air thatis responsible tor the cloud streetsln FC 4.100. Where two adjacentrows have ascending air, sandcollects in a dune street Wheretwo ad|acent rows havedescending air. there is no dune.Since the dominant winds in all theworld's deserts are north or south,the streets run north and south.
Similar rows develop on thesurlace ol the ocean because olsimilar vortex rows in a layer olwater beneath the surlace. Wheretwo ad|acent rows havedescending water. matenal suchas seaweed collects. There is acorresponding absence ot materialwhere two ad|acent rows haveascending water. Although thedependence ot these vonex rowson the direction and strength cl thewind is well established. theiractual production mechanism isnot known.4.103 To explain the expansionoi a ring as it approaches a wall,Imagine a mirror-image ringapproaching lrom inside the wall atthe same time. The parts ol eachnng's llow that are perpendicular tothe wall cancel. The pans ol theirllow that are near the wall andparallel to it add. As a result, thering expands parallel to the wall asit gets closer to the wall. Cit course,there really is no second ring insidethe wall, but the air llow caused bythe presence of the wall is thesame as it there were amirror-image ring.
lri spite ol the descriptions olmultiple passages ol smoke nngsin the literature, the trick may beimpossible. Until 1972 thosedescriptions were common insome textbooks, but thenMaxwotthy (B50) carelullyinvestigated the ellect with water
rings. ll the rings initially havealmost equal speeds, then the rearone merely becomes entrained ll"lthe leading one to lorm a singlevortex ring that does not separate.However. it the rear one initiallyhas a much greater speed than theleading one. the composite ringbecomes unstable and throws thelon"ner rear ring torward, leavingthe tormer leader behind- Thelormer rear ring then has the sameor a somewhat greater speed.making a luture encounter lbetween the rings unlikely. It iMaxworthy's descriptions arecomplete, then themultiple-passage descriptions arean example ol where textbookshave continued to use anillustration that no one botheredverilying.4.104 On an initially ltat sandtloor. the wind picks up and thendrops sand grains, which thencause other grains to hop up. Theresult is to build deposits ol sandthat in tum modify the wind toluither enhance the depositsFlipples develop with a wavelengthabout equal to the averagedistance a sand grain hops whenstruck by other sand grains.
Sand waves on stream bedsmay be built in a similar way, orthey may result from the llow oivortex rows (see FC 4.100 and4.102). In the latter case. the sandripples are onented along thedirection ol motion ol the streamsllow.4.105 Contrary to much popularbeiiel, the lluid is not pushed overthe siphon by air pressure, as isdisproven by the tact that siphonscan operate in a vacuum. Thetorce that pulls the lluid over thesiphon is its own intermolecular
Answer: 263
torce. When the siphon worlis,there is more lluid on the outletaide than on the inlet side, and theresulting imbalance oi weightcauses the lluid to llow up. over,and then down the aiphon. As thelluid travels up the inlet side. itspressure is reduced the lurlher upit goes. It the siphon is highenough, the lluid pressure iseventually reduced to the pointwhere bubbles [oi air or othergases] begin to lorm Such bubbletormation limits the height oi thesiphon because it breaks theintermolecular bonding betweenthe lluid molecules and destroysthe siphoning. Siphons work beherat atmospheric pressure than invacuum, because the pressure onthe two ends oi the siphonlncreese the lluid pressure at allpoints in the siphon. Thus. withatmosphenc pressure outside thesiphon, the height at which bubbletormation occurs is increased.4.106 The wind (which ilowsdown and to the leit in the diagram}picks up sand grains on thewindward side oi the dune andthen dumps them as it spills ontothe leeward side. Although slow.the net transport ot the sandresults lt't the dune tormationmoving downwrnd.4.107 All modern toilets have asiphon between the toilet bowl andthe plumbing to the sewer. Aswater is put into the bowl, the waterlevel iri it and the inlet side oi thesiphon rises Evaritually waterspills over Irom the inlet side to theoutlet side ol the siphon and thesiphoning begins. {You can ilush atoilet by |ust pour ng a bucket oiwater inlo it.) The siphoning ilowand the general swirling oi thewater pouring into the bowl remove
r-* ~ , lthe waste The extre hole at thebottom oi many bowls is a water |etthat entrairis the lluid irom the bowland increases the speed and vigoroi the siphoning.4.108 As an oil drop is releasedirom a car, air resistance stretchesit out. intlates it like a chei s hat,and then bursts the center oi thatinllaled Shape. When the oil stnkesthe road, it is doughnut shaped.4.109 These lines are smallndges pushed up by the viscousiorces oi the stream llowingbeneath surlace iilms te.g., an oiliilm).4.110 Nothing beyond adescription oi the clear band hasbeen published. You might tryexpenrnenting with dilterenl iluidsand solutions to understand thisettect4.111 The orl torms a very thiniilm over the water The surtacetension ot such a iilm is notconstant, instead lt changes asthe iilm stretches and contracts.Waves paSS|I1g over the iilmalternately stretch and contract thefilm and so produce an altematingtangential drag on the water belowthe iilm. This drag increases theenergy loss oi the wave to such anextent that the wave clamps outquickly. leaving the iilm-coveredarea calm4.112 Oil lilms on the watersurlace collect and then damp outsmall waves to give streaks orpatches oi calm water. [See thepreceding answer ) Apparently theoil comes irom diatoms that haveoil tor assistance in tloiation and tortood. ll the wind is strong, the oilpatches arrange 'iiei'nselves inrows as ls discussed in the answerto FC 4.102
4.113 Both the crown and thecentral breakup oi the central ietare due to an amplification oiunstable waves on the water. Inthe crown case the wave is aroundthe rim.4.1 14 The surlace tension oi thewater holds the water in a thin layerand BVBt'llU-Elly pulls it bad-r to thecentral suppoit beneath the disc.4.115 ll the two water ]B|S areexactly identical. then the verticalcomponents oi their momenta arecanceled in the collision, and thepressure developed at the point oiimpact sends the thin water layerout honzonlally Breakup occurswhen small holes develop and arethen enlarged by the watei’ssurtace tension.4.11 B Surtace ten s on holds thestreams together.4.117 The surlace iilm on whichthe pepper grains reside contractsas the soap iilm develops and thenspreads across the surface.4.118 The tum ol the streamaround tha edge oi the can isstable bet use of the pressurediiierence across the width oi thestream An ideal incompressiblelluid in a circular path has greatervelocitres at smaller radii. Thus. bythe Bernoulli principle. there is lesslluid pressure at smaller radii. Herethe atmosplieric pressure outsidethe stream ls greater than the iluidpressure near the edge andtheretore holds the stream to theedgi" At some point on the side olthe I -n the stream detachesbecause il is unslabie to smallperturbations4.119 Previous to Loewentha|'swork the tears '|Ort't'llflg abovestrong alcoholic drinks were
261 Flying clrcul ol |iI'||,illl:l with lnluierl
thought to be due to surlacetension pulling the solution upwardalong the glass where then thealcohol would evaporate to leave|ust water. However. Lowenthaldemonstrated that the watercollecting at the top oi the climbingiilm was condensation from theroom air. Furthermore. the toroeresponsible tor the iilm‘s climbingwas not surlace tension pulling theiilm up but a pressure thatdeveloped in the lluid next to theglass surtace4.120 There are several tiredesigns to decrease the probabilityoi aquaplaning. The tread canchannel the water at the rear oi thecontact area outward and erect ii.Other. shorter channals can eiectwater to the sides. Finally, smallholes in the tire can essentially blotup a water layer as they makecontact with the road in the trontpart oi the contact area. in each oithese techniques the emphasis ison removing the water quickly toavoid aquaplaning.4.121 Tlii support tor the drop.is not lully understood but isthought to be an electricalrepulsion between the watermolecules in the drop and those ll'Ithe main body oi water. A watermolecule has a positive side wherethe two hydrogen atoms arelocated and a negative side wherethe oxygen atom is- It the drop sbottom surtace and the surtace oithe main body oi water iustbeneath the drop present the semecharged side to each other. thenthose two surfaces will electricallyrepulse each other. Anothersupport mecl - rnism is Efl't]JlOy1\.l ilthe main body oi water issuperheated. In that case theevaporation oi the bottom surlace
oi the drop provides a continuousvapor layer to support the drop(lust as is described in the answerto FC 3 65).4.122 The .oup llow reversal isan example oi elastic recovery by aviscoelaslic lluid. when the souphas almost come in rest boiauseol iriction irom the sidus oi the pan.the top surlace brielly continues tomove alter the lower soup hasstopped- The < vrtai It layer is thanpulled back by an elastic torcebetween it and the li -. rer soup. andthe swirl is momentarily reversed.Oscillations around the Gql.il|lbi'lU[T'lposition would continue except thatthe soup is viscous enough todamp out the 0.-~itlations almostimmediately4.123 Although this eflect, calledthe Kaye eileci, der onds on theelastic nature ct the lluid, its causeis not well understood Collyer andFisher suggest that the leap maybe due to a rapid change in the\ It-COSIIY oi the i-Jieam iii it stnkesthe heap on the main body of lluid.The iluids that display the Kayeetlecl are apparently‘lhEiEil'-ll1li'l|'\tI‘lQ orlv i, that is, theirviscosity decreases when the lluidis sheared (FC 4.126]. Ourlng itstall the stream is unsheared andhas a relatively high \nbu'J5l|yUpon sinking the heap, however,the rapid changes in velocity willcreate large shearing lI'l the lluid.thereby reducing its viscosity.Being elastic also, the stream thenrellects irom the heap.4.124 As the i l.‘»CO6|€lSllC lluidrotates. tha shearing oi its layerscre- ites sire-. -.-1 ; that act around|he circumierenw-i ot the - rcularpath Oi the iillld, iclrldllig ‘U \20i'\UflClthe lluid to the i - nter oi rotation.These stresses are not created in
normal (Newtonian) iluids. Theirresult in this demonstration ls topush the lluid to the center oirotation and up the rod.4.125 The compression on thetailing stream causes the stream tobuckle. Since the stream cannotbreak under these conditions, thebuckling makes the bottom oi thestream circle around as more lluidtails than can be absorbed into themain body oi the lluid.4.126 A tundamental explanationoi how the viscosity oi a lluid isdecreased when the lluid is undersheanng stress is not currentlyavailable. Most suggestionsinvolve a change in tha molecularcontiguration because oi thesh . lI‘ll'|Q. For example. the longmolecules may be stretched alongthe ilow lines created by thesheanng. As a result. the viscosityis decreased. Once the shearing isremoved, the molecules regaintheir previous orientations, and theviscosity increases4.12? The internal stresses inthe viscoalastic lluid are ralievadwhen the lluid emerges, therebyiorcing the expansion at the tube'smouth. One model oi this relial andconsequent expansion considersthe molecules as being stretchedwhen torced through the tube.When they emerge they contractand consequently swell the lluid4.128 and 4.129 Both oi thesedemonslrations are examples oialastic recovery by a lluid. Thesilicone putty is highly viscous. butthe viscosity is lower tor slowsheanng rates. At high sheanngrates it iraclures.4.130 The viscosity cl quicksandincreases with shearing, so tryingto pull yourseli out oi the stuti
Anlurcrl 265
quickly is impossible; the more youshear the quicksand, the more itwill hold to you. Move slowly so asto keep the viscosity as low aspossible. The eyes oi trappedanimals mey bulge because ot thelarge hydrostatic pressure on thelower pan ol the body due to thedensity ol the quicksand. [Asand-water mixture is denser thangust water.)4.131 ll the cylinder is rotatedslowly. then the dye is pulled alonga thin layer and spiraled inwardwith each turn Provided thereversal is mede betore moleculardiltusion (thermal motion ot themolecules} can smear the dye. thespiral is unwound almost exactlyby rotating the cylinder back anequal number oi turns.5.1 In order tor there to be a clearimage on your retina. the eye mustretract the light rays. About twothirds ot the retraction occurs at thesurlace ot the eye. ll water is onthe eye. nearly all ot that retractionis lost because the retractive indexoi the eye matenal isapproximately the same as that olwater. Ii you wear goggles. there isa layer oi air in tront oi the eyes togive you normal retraction. The tishthat sees in both water and airsimultaneously has two retinas andan egg-shaped eye lens. In orderto compensate tor the reducedretraction tor the submergedportion oi the eye. the eye lens hasmore curvature tor the rays comingirom the underwater scenes.5.2 The man would be invisible ilhis index oi retraction matched theair’s index. which is slightly greaterthan exactly t. the index oiretraction lor vacuum. A greaterindex would result in someretraction oi the rays coming irom
scenes behind the man. musmaking his presence noticeable bythe distortion oi the images.especially when he walked. Inorder lor the man to see. he has toabsorb some oi the incident light.Such absorption would have to beslight enough that the man doesnot appear as a shadowy iigure. Inshort. his index ol retraction woi.ldhave to have a real pan that isapproximately equal to 1.0 and animaginary pan that is great enoughthat he would absorb enough lightto see but not so much that thesubtraction oi the tight would benoticeable.5.3 Water rises along the side oithe pencil by capillary action,curving the water surtace next tothe pencil. The curved surtaceretracts light into what wouldotherwise have been a shadowregon ol the pencil to give thewhite gap.5.4 The coin s image is lirstvisible on the water's top sunaoebecause the rays irom the coin arereilected lrom the back surtace oithe container, directed to the top.and than are retracted out to beseen. ll you put your wet hand onthe back. you destroy that initialreltection there. A dry hand hasmuch less ellect because it hasrelatively lew Contact points withthe glass. A wet hand lills thespaces between the contact pointswith water. Since the indices otwater and glass are about thesame. this titling oi the spaceseliectively Increases the contactarea oi the hand with the oontainerto about 100%. Much ot the lightrays lrom the coin that tall on thisarea are theretore absorbed aridlost. As a result the image on thetop surtace disappears
5.5 Light rays irom thesubmerged ot:i|ect are retracted atthe water-air surtace. bendingtoward the surlace as they emergeand. as a result. appear toonginate lrom a place higher thanthe true position oi the submergedobrect For normal viewing (eyeson a horizontel line} the horizontaldistance is not distorted. ll you turnyour head so that your eyes arealong a vertical line. then the raysreaching one eye have beenretracted at a dilterenl angle to thewater surtace than the raysreaching the other eye. As youmentally extrapolate the rays backto lind the apparent position ot thesubmerged obiect. you place it notonly higher than its true depth butalso closer.5.6 Hays passing the lirst planeot glass will be partially reilectedlrom the inside surtace ot thesecond plane. Normally this panialt'BllECi|OI1 is insignilicant becausemost ot the light continues throughthe second pane to be seen.However. it the external airpressure diliers lrom the airpressure between the two panes.then the panes are not parallel.and pan oi the internally reilectedlight can produce a taint butnoticeable ghost image Considera ray irom an ob|ect outdoorsentering the lirst pane initiallyhonzonlally. Most oi that light goesthrough the second pane andenters the room. ll this is the onlylight seen. it gives an undistonedimage oi the ob|ect. However. panoi the light is reilected by the insideot the second pane, returned to thelirst pane. reilected again. returnedto the second pane. and linatlytransmitted into the room toprovide a second. lainter image llthe two panes are not parallel. this
266 Flying CIICI-II of physics urltlt anlwlrrc
second image is displaced lromthe true image.5.7 through 5.11 All oi theseproblems [except tor the storyabout the bird in FC 5.9} areexamples oi mirages and dependon the variations with height in thereiraclive index oi the air near theeanh's surlace. That indexdepends pnmarily on thetemperature ol the air. Looming(which is an example ol what lscalled a supenor mirage) can occurwhen the air temperatureincreases with height Theobserved light rays have originated
; lrom a distant ob|ect. say a5 mountain, at an upward angle to
the honzon. They are thenretracted enough by the increasein reiraclive index (due to thetemperature increase with height}that they are bant over tor you tosee. An observer mentallyextrapolates straight back alongthe observed rays and places theimage above where the ob|ectreally is. In other words. the imagelooms above the obtect and is anexample oi a "superior" mirage.
The oasis mirage is an "inleriormirage in that the image is belowthe true position ol the object. Inthat case the object is the sky.Light rays irom the blue sky areretracted by the ground layer oi alrin which the temperaturedecreases with height. The raysare bent up to the observer. whothen mentally extrapolates straightback along the rays to believe thatthere is a body oi blue water on theground somewhere ahead. Theshimmering due to variations in theretraction by the hot air gives theillusion oi llowing water. Thepalican could not have seen such amirage because the light rays lromthe sky could never be so retracted
as to return at such a large angle tothe ground.
The Fata Morgana is a morecomplicated mirage in that thetemperature proiila producing itdoes not change linearly withheight The temperature increaseswith height. but at someintermediate height the rate atwhich it increases is less Such atemperature proiile. but with amore noticeable drop-olt at theintemiediate height. can result in athree-image mirage.5.12 Most one-way mirrorsdepend on one side (say the roomin which a criminal is beingquestioned) being more brightly litthan the other side {where a vieweris}. Some oi the light incident onthe glass lrom the criminaI‘s side isreilected by the tront and backsurfaces ol the glass. Ii the otherside is relativaly dark. then thecnminat sees only the reilectedlight and thinks the glass is amirror. The viewer. on the otherhand. receives ample lighttransmitted through the glass andcan clearly see the criminal. Themirror ellect is enhanced it theviewer's side oi the glass is coatedwith a very thin layer oi metal thatwould increase the amount oireilected light to the criminal butstill allow anough light tor theviewer.5.13 Even though the moon is inthe eanh's shadow. sunlight canstill illuminate it it the sunlight isretracted into the shadow area bypassing through the eanh'satmosphere on the edges ol theeanh. However. such retractionremoves the blue end oi the visiblespectrum tor the same reason thatthe sky is blue (FC 5.59) andleaves only the red end oi the
spectrum- Hence. the sunlight thatis refracted suiiicientiy to illuminatethe moon is red. The same colorsubtraction is responsible ior thered skies during sunrises andsunsets (FC 5.58}5.14 Although mirages arenormally due to retraction oi light(see FC 5.7}. this particular illusionappears to have been a miragedue to rellection. The girl probablysaw a rellection oi hersell on thethin mist. Nothing more than thissuggested cause has beenpublished on reilection miragesand their physical possibility canonly be guessed at now.5.15 There is no one equationgiving the number oi imagespossible in the two mirrors as aiunction oi the angle between themirrors and the angular location otthe ob|ect with respect to themirrors. The most complete workdone on the problem is that byChai (989).5.16 The green ilash is due tothe separation oi the colors in thesunlight by the earth's atmosphere.similar to the dispersion ol light bya prism. As a ray irom the sunenters the earth's atmosphere. it isretracted such that it is slightlycloser to being venical than betore.As a result. the sun appears to besomewhat higher in the sky than itreally is. The shoner wavelengthsol light (the blue end ol thespectrum} are retracted more thanthe longer wavalengths [the redend). and. as a result, there shouldbe a blue image oi the sun slightlyhigher than a red image. withimages oi intermediate colorssomewhere in between. However.the blue is lost by atmosphencscattenng [see FC 5.59) and thehighest image is the next color.
Anlllicrl 261
green. As a result, green is the lastcolor seen iust as the image ol thesun dips below the horizon.5.17 The unmixed sugar createsa vanatron in the relractive Indexwith depth with the maximum beingat the bottom where there is moresugar. As the laser beam entersthis solution, let us say initially at aslight downward tilt, the beam iscontinuously retracted to s greatertilt as it encounters progressivelygreater values ol the relractiveindeit. Eventually it retlects lromthe bottom surlace As it movesupward it again encounters acontinuously changing reiracliveindex and again is continuouslyretracted. This same type olretraction. but with sound insteadof Ilglll, is discussed in the answersto FC l 29 arid l 38.5.18 The light rays lrom the sunare retracted by the atmosphereThe closer the sun is to thehonzon, the more this retraction isConsider the sun when its loweredge appears to be on the horizon.Were it not Ior the retraction. thesun would just then actually haveits lower edge a lltlle more thanhall a degree below the horizonThe upper edge, in the meantime,appears to be slightly less thenhall a degree lrom where it wouldbe il there were no retraction. As aresult, the vertical width ol the sunappears to be somewhat less thanit would be with the sun overhead[actually about 6 arc minutesshort]_ The horizontal width sullersvery little ShClI19l"ilt1Q due toretraction (about hall an arcsecond} Thus, when the sun is onthe horizon it appears to be anellipse. {Please don't conluse thisrelreclion ellect with the optl zilillusion ol FC 5134}
5.19 The blue ribbon is duo tothe rellection ol lhe blue sky by thewaves on the horizon According tothe answer to FC 5.20, the averagecontnbution to the rellecled light bythe horizon waves comes lrom thesky about 30“ up lrom the honzon.During much ol the day that portionol the sky is a deeper blue than therest ol the sky, and theretore theribbon should be a deeper blue.Tre ri-t'eclion pQ|fll'lZB5 the lightparallel the w- ii- (see FC 5.49}.5.20 Ci rtairily tl ~- ii ives do notall have a =|O|JB ol I5 but theaverage contribiit i -n ol the lightscattered by the waves on thehonzon comes lrom the sky about30° up lrom the horizon So. theoverall ellect ~ the -ame as it allwavv - did have I5‘ - lopes. Waveswith small "topes ¢|fG moreproli iDle than in .. .- !S with largerslopes, but they reflect only a smallpart ot the = -,i Wave< withsomewhat larger slopes are lessprobable, but they reflect largerportioir- of the sky at greaterangles to the horizon. Waves withrelatively large I i ipes are soimprobable that they t.-Jntnbutealmost nothing The overall ellectls that the part ol the sky at 30lrom the horizon is m- ml stronglyrellecled by the waves on thehorizon and that purti0l'lS ol the skyat smaller angler. have much lessrellection and are not seen5.21 The tilt ol the random waveson the water spreads the rellecledimage ol the light -aurce (sun,mi: "n, or artili * ill light]. Thespread to the --I-It and right is lessthan the spread between theobserver llfld the horizon becauseol the geometry invr!-.-ed Inrel-1 ing tight to the olr -erver. Theratio ol the width to the length ol
the bnght area is sin ti where H isthe angle ol elevation of the lightsource. The dark tnangle abovethe horizon is a contrast ellect. Byblocking olt the luminous area lromyour liald ol view, you eliminatethat illusion.5.22 The cloth can glisten it it hasa regular pattern ol threadsrunning parallel to each other togive a lurrowed surlace Whensuch a cloth is viewed at certainangles the rellection of incidentlight is relativaly large. At otherangles. the reflection is less. So, itthe cloth is moved around in thelight, sometimes it retlects well,sometimes not. tn other words, itglistens_ The orientation giving themost rellection is when a tineperpendicular to the lurrowsbisects the angle between theincident light ray and the light rayrellecled to the observer's eyes5.23 The eye produces a realimage ol the nail on the retina thatis inverted from the nafl‘sorientetion. The nail looks rightside up, however, because thebrain ellectively inverts the realimage in its interpretation ol thescene. The nail also puts a shadowon the retina whose orientation isthe same as the nail. But since thebrain inverts the scene on theretina, that shadow appears to beupside down-5.24 The optimum hote radius isapproxiately \ 0.6 ill’ where A isthe wavelength ol the light and I isthe distance lrom the hole to thescreen or film. Larger holes giveless resolution in the photographSmaller holes produce diltractionpatterns. [Dillraction is aninterterence ellect due to the wavenature ol light Similar drllraction,
_ \ but with sound rnsteadol light is in
7
258 Flying |:l|-cue ul pltyilcl with lnluizll
FC 1.42 and 1.43.} The pinhotecamera doas suller chromaticaberration because the optimumdistance to the lilm lor a givenpinhole depends inversely on thewavelength ol light, which varieslrom about 0.40 microns (blue) to0.65 microns (red).5.25 The images are pinholeimages mede by the tiny holes inthe leaves. They are alwayspresent during the day but areusually lost in the overall glare ollight. During an eclipse that glare isreduced somewhat.5.26 Light talling on the dewdrops is strongly rellecled backalong the path to the sun, that is.retrorellected. Part ol the rellectionis at the tront surlace ol the drop:pan is at the back surlace at thepoint on the axis through your eyesand the sun. Light incident at otherangles on the drops can also enterthe drop to rellect on the backside.5.2? Hellectors that return thelight to its source, even it the lightsource is not on the rellector'scentral axis, are calledretrorellectors. They can bespheres (FC 5.26], triangularprisms, or incorporate mirrors andlenses. A perlecl retroretlectorwould be practically useless sincethe eye is rarely exactly at the lightsource. But most retrorellectorsare sullroiently impertect that thecone of light returned toward thesource is wider than the cone otlight intercepted by the reflector. Asimple retroretlector is a corner otthree mutually perpendicularmirrors. A light ray entering thecomer lrom any direction willrellect ott all three mirrors insuccession and then be returnedopposite ris initial direction.
5.28 The drops locus the light,placing an image ol the sun on theleaves, which burns the leaves.5.29 Chance orientations ol thewater waves rellect light to youreyes The illu-.ion that there aresti mils ol light fE!dl'lII'lQ lrom thehead ol your shadow ls due to therequired wave orientation tor therellection to reach you and theconstantly changing wave pattern.5.30 Cfli and ott--r animalshave retrorellecting eyes that arenoticeable in Otl"lBt‘il'r'lI.c. darksurroundings The eyeincorporates a lens and a curvedmirror that returns the light in acone which then passes the sourceol light. In the case ol carnivores,there is a layer ol zinc cysteinecrystals behind the retina thatprovides the high rellectance.5.31 The horizontal line marksthe height at which tailing snowmelts. The snow rellects more lightabove the line than the water dropsdo below the line5.32 Light doi.-- emerge in alarge range ol angti 1 lrom a waterdrop, but the most inv nse lightemerges at the rainuuw angles (inray theory you can say that there isthe densest clustering ol theemerging rays at the angle].Since the dilterenl visible‘M iveiengths suller dilterenlamounts ol retraction (blue isretracted more than iecli. the exactaigle .r: w- i ch the _mer.ing light isbrightest is slightly dilterenl toreach color. Henca. at ttie rainbowangle the colors are not only brightbut also slightly = eparated so thatthey can be di itrnguished. (Alsosee the answer to FC ii 44.)How -rer.the di -ilfldt Lt 5nseparating the colors is not
prismatic. The lirst clue to its truenature is in the tormation ol thesupernumereries (FC 5.34).
The color sequence in thesecondary bow (which is higher inthe sl-iy than the pnmary bow andsomewhat rarer) is reversedbecause the participating light raysreflect twice inside the drop. As aresult, they emerge at a dilterenlangle than the rays participating inthe pnmery falt'lbDW_ Since theblue is retracted more than the red,the drops contnbuting the blue tothe secondary rainbow must be ata slightly greater angular elevationthan the drops contributing the red.The exact opposite is lt‘LtB lor theprimary rainbow because only onerellection is involved there. Thus,the color sequence is reversed.
More than two rainbows havebeen seen in the lab. [Forexample, see my paper in theAmer. J. Physics, 44, 421(l976).] A lew people havereported seeing the third orderrainbow (corresponding to threeinternal rellectionsl when the sunis low and below some darkclouds In general the higher orderrainbows are not seen becausethey are dimmer than the glarereilected lrom the surlace ol thedrops, the glare transmittedthrough the drop with no internalreflections, or the background skylight5.33 The uneven distribution olthe red is due to the verticalflattening ol the lalling drops by theair llow around them. Since thehorizontal cross sections ol thedrops remain circular, the colors onthe vertical legs are the expectedrainbow colors because the lighttraverses the drops through such acircular cross section On the lop olthe arc the light must go through a
Anlwerl 269
llatlened cross section, whichdisplaces the red inward anddownward in one's view ol thebow. As a result the contribution olred is dirntnished. Smaller dropsare less allected by the air tlow andtherefore can contribule to all partsot the rainbow.5.34 A correct calculation ol therainbow intensities and colordistribution abandons thetechnique ol tracing light raysthrough the drops in lavor oltreating the light as a wave. Even itthe incident light wave is a planewave, the emerging light wave isnot. As a result the emerging llghtcreates an interterence pattern.The maior peaks (the brightestareas) in the pattern are iual thebnght colors in the ususi rainbow.so nothing substantial has beenchanged lrom the previous rayapproach. Some subtle etlects arenoticed. however. The actualangular locations ol the colors arenow more accurate The change incolors with change in drop size islinally accounted tor (FC 5 44}. But
~ rnore important, the interference otthe emerging waves explains theoccasional taint bows lust belowthe pr-Kmary bow and iust above thesecondary bow. These extra bowsare the other peaks tn theinterference pattern, They areseen less otten only because theyare less intense than the maiorpeaks in the pattern and becausetheir visibility depends onunitormity of drop size.5.35 From all cl the sky in thedirection ol the rainbows there lsthe general background skybrightness and some glare lromthe rellection ol sunlight lrom the ioutside surtace ol the drops. Below 1
, the primary rainbow there is also
light rellecled once inside thedrops. The brightest ol this light lsat the pnmary rainbow angle. butother such singly rellecled light canexit any drops at a lower angle inthe sky than the primary bow.However. such singly rellecledlight cannot exit lrom drops at agreater angle than the pnmarybow. A similar but reversed caseholds tor the light rellecled twiceinside the drop. The brightest otthis twice rellecled light exits at theangle cl the secondary rainbow.Other twice rellecled light can exitlrom drops at greater angles in thesky, but none can exit lrom dropsat lesser angles. S0. in addition tothe backgraind light and glare,there is an additional light belowthe primary bow and above thesecondary bow but not betweenthe bows. That band belwean thebows is theretore relatively dark.5.36 The rainbow is polanzedparallel to the bow at any givenpoint because ol the retraction andl'Bl|ECl|Ol1 ol the light by the waterdrops.5.37 The lunar rainbows are rarenot only because moonlight ismuch weaker than sunlight. butalso because ol the weather andthe time the moon is in the properposition and condttion tor making arainbow The time ol day with thehighest lrequency olthundershowers is late atternoonand earty evening (FC 3.4 ti. Thusthe moon has less opportunity olmaking rainbows. Also, theintensity ot the moonlight changesas the moon changes phase,making the chances ol a rainboweven slimmer5.36 The drops contnbuting tothe rainbows are not at any
observer. Only their angle lrom theline extending lrom the sun andthrough the obsenrer matters. Thedrops can be anywhere lrom a lewyards to several miles distant lromthe observer. ll the only dropsparticipating are lust a lew yardsaway, such as with a nearbygarden sprinkler, then each eyesees its own rainbow displacedlrom the other.5.39 The rainbow pillar is a leg olthe primary rellection rainbow. Thenormal primary bow is lormed fromthe direct sunlight. Near a body olwater light rellecled lrom the watercan lorm another rainbow in thesky. Although the geometryrequired tor such a reflectionrainbow is necassarily the same astor the normal rainbow, itsorientation in the sky rs dilterenllrom the normal rainbow becauseot the rellection. were the wholerellection rainbow visible, it wouldhave its center higher ‘n the sky.Thus, near the horizon its leg is ata steeper angle to the ground thanthe leg ol the normal rainbow.Some intensity ol the sunlight islost on reflection lrom the body otwater. so the rellection rainbow isweaker and rarer than the normalrainbow.5.41] In contrast to the precedingphenomenon, the rellecledrainbows are merely the mirrorimages of the normal rainbows.Although Minnaert [954] describesthe two arcs as being identical,Humphreys [164] correctly showsthat the rellecled bow appearsllatter because less ol the arc isseen than for the normal rainbowabove it The dilterence inappearance stems lrom therequirement ol scattenng angles illight emerging lrom water drops isp panicular distance lrom the 1
210 Flying clrcul 0| phyllcl wlth answer!
to ccntnbute a rainbow that thenrellects lrom the water surlace toyour eyes. The water dropsmeeting suclt angle requirements
i are at a lower angular elevation in1 the sky than those giving the direct
rainbow.
‘ 5.41 The normal dewbow is iusti a rainbow lrom the water drops on
the grass. The primary rainbow isroughly 42° lrom an axis runningthrough the sun and the observer'seyes (FC 5.32} and would be acomplete circle it the ground didnot interfere with the suspension otwater drops in the lield ot view. llthe ground is covered with waterdrops. however, then the part olthe rainbow below the horizon canbe seen- The angle ol 42“ stillholds, but because the drops arelimited to a horizontal plane ratherthan lilting all ol the space in trontol the viewer, the shape appears tobe hyperbolic- In the nonnatdewbow the incident light isessentially parallel rays lrom thesun. The street light givesdiverging rays. and although theangle ot about 42° is still requiredtor the bow, the position ol thedrops contributing to the bow takeson the initially strange shapebecause ol the diverging range olincident light rays available-5.42 The sun dogs are due to theretraction ol light by tatlinghexagonal ice crystals that havetheir central axis [which is parallelto the six faces) vertical. Althoughthe crystals retract light into a largerange ol angles. the bnghtest olthe emerging light is at the anglethat least deviates the sunlightlrom its onginal direction, Thatangle ol least deviation is about22° it the sun, the ice crystal, andthe observer are all in a horizontal
plane. The observer then sees thebright llght lrom the crystals 22° toeach slde ol the sun. As the sunrises, however. the crystaI's axis isno longer perpendicular to the lightrays and the angle between thesun dogs and the sun increasessomewhat. Eventually the sun is sohigh that the brightness iseliminated. The sun dogs arecolorlul because the ice separatesthe colors in the same way as doesa prism.5.43 The 22° halo is produced bythe same type ol retraction lromtalling ice crystals as tn FC 5.42except that the central axes ol thecontributing crystals are randomlyoriented in a plane perpendicularto a ray ol incident suntight. Thus,at any point 22° lrom the sun thereare some crystals that happen tobe oriented property to give brightlight The cotlection ol thesecontributing crystals lorms thehalo. Cotors are again due to aprismlike separation ol the colors.Since blue is retracted the rneut olthe vlsible cotors. it is on theoutside ol the halo.5.44 An explanation ol rainbowsinvolving iust the ray theory andprismatic separation ol colors (FC5 32} cannot account lor whiterainbows. The interlerence theoryot rainbows used in FC 5.34 isneeded. The colors in the normalrainbow are the lT|El|Of peaks in theinterterence cl the light emerginglrom the water drops at therainbow angles. As drops smallerthan a millimeter in diameter areconsidered, the widths ot thosepeaks increase and eventuallyovertap sulliciently to etiminate anydistinguishable colors. The lightexiting at the rainbow angle is stillrelatively bright but now has no
color and thus gives a whiterainbow.5.45 Ftetlection lrom the outsidesurfaces ol latling hexagonal icecrystals give the pillars ol lightabove and below the sun, Thecrystals can be short along theircentral axis as compared to theirwidth, in which case they ere calledplates. Or they can be longer thantheir width, in which case they arecalled needles or pencils. Both cangive sun pillars. For exampleconsider the plates. The air llowaround them iorces them to behonzontal to maximize thalr airdrag. ll the plates are higher in anobserver's lield ol view than is thesun, sunlight retlects lrom thebottom ot the plates and gives theobserver a relatively bright area inthat ponion of the sky above thesun. ll the plates are lower in thelield ol view. rellection is oll the topsurtace.5.46 Fteceni work by Greenler(1034. 1065) provides computersimulations ot the 22‘ halo and thesun pillar. To untangle all ol theobserved and conjectured arcs, acomplete simulation ol lightscattered lrom tailing icecrystals—t:ioth plates and pencils(FC 5,45), and both onented andspinning—is needed lor the wholesky and tor all positions ol the sun.Some oi the present. althoughperhaps controversial anderroneous. explanations tor a lewarcs and halos are the lollowing(the letters reler to Figure 5.46):(a) and (bl 22“ halo and its sundogs: See FC 5.43.(cl 46“ halo" the retraction ol lightto make this halo is similar to thatin the 22° halo with one exception.The ray passes through a 90“corner. rather than a 60° corner as
Answer! 27!.
ii
with the smaller halo. by passingthrough one ol the and laces andone ol the six side laces ol thecrystal. Again, the brightest light iswith the geometry giving leastdeviation to the rays. The light soscattered by appropriately orientedice crystals glves the 46" halotd) Circumzenith halo: suntightenters and exits through twoad|acent laces that areperpendicular to each other. Tocreate the halo. the sun must betower than 32° lrom the horizon(et Parhelic circle: light isrellecled lrom the vertical sides ofthe tailing crystals.(ti Sun dogs to the 46° halo.these very rare bright patches aredue to the same scattering as the46° halo but are limited to thosecrystals having their central axishonzontal.(I) Lowitz arcs. to produce thesearcs, hexagonal ice crystal platesmust spin about an axis that lies inthe plane of the plate. Lightentering one ol the hexagonalsides then exits through another.The maximum brightness ot thisretracted light is tor the geometryleast deviating the incident ray.and the arc is the light lrom acollection ol the crystals meetingthis requirement5.4? Crown llasn is clue to themirrortike rellection ol light lromfalling hexagonal ice crystal plates(They are also responsible tor thesun pillars in FC 5.45.} The etectnclield in the thundercloud makesalectric dipoles ol these crystalplates (r.e., makes one sidepositive and the other negative)and the dipotes align themselves inthe lield Norrr .illy the ola I15 tallwith that broad side down so as tomaximize lhe arr l'r* i-.tance. Butthe etectnc lield ol a lightning
stroke momentarily changes thisonentation and l'lETlL.:: the relativebrightne--; lrom a panicular part olthe cloud. ll the change in etectnclield propagates through the cloud.then the brightness could also.5.48 One ol the lirst suggestionswas to cover the I wadlights withpolanzed tillers oriented 90° to thepolarizing litters plar r-d over thewindshield. Willi this orientationthe dnver would not see the lightlrom an approaching car becausethe polarized light lrom itsheadlights would not pass the tillerin lronl ol him. Such a situationwould also be dangerous.Orientations somewhat dilterenllrom the 90° would be better sothat some ot the oncomingheadlight could be seen. One olthe drawbacks to the -.-zheme(perhaps a latal one) is that thelitters alt -r. orb rrrne oi the lightlrom the surroundings. as torexample. the light lrom astreetlight. So the overall viewwould be darker Anotherdrawback is that the tilt ol thewindshield would matter and thuswould have to be st i "idardrzed.5.!-I9 Direct sunlight isunpolarized, that is. the oscillationsol its electric lield areperpendicular to the direction oltravel but along no pdf'llCl.lli':lT axis.The retlec‘ irn ol sunlight lrom asurlace will polarize the rellecledlight parallel to the surlace. that rs.the electnclield oscillations are stillperpendicular to the direction oltravel but are prelererltlallyonented parallel to thr surlaceThe intent ol th x p .i-rationdepends on the matenal and therncidi-1tar.;~ ol the I-. ht ll youare e'-.i '1] 1.,-..| .1’ vrrrnoon:.-ii.il‘l,lOr l" J"{!\' '.‘=. '-.3 ' rEllE.'Cl8El
lrom the road is strongly polanzedparallel to the road. Polarizedsunglasses reduce this glare byblocking that sense ol polarizationand passing light with verticalpolarization. On a microscopicscale, this blocking means that thelong molecules in the tillers areoriented horizontally and willabsorb tight whose polanzation(and thus electrical oscillations)are etso honzontal. Much ol theglare is thus aliminatecl, but thegeneral illumination ot thesurroundings is not as reduced
A tlshermari can reduce theglare ol sunlight rellecled lrom thetop surtace ot the water and stillsee the light rellecled lrom the tish.Ol the unpolarized incident light.the parallel polanzation has beenprelerentialty rellecled- The lightentenng the water then must beprelerentially polarized in theopposite sen“.-s=—-perpendicular toboth the direction ol travel and tothe parallel polarization. Oncerellecled lrorn the lish. this light willbe able to pass through thelisherman‘s sunglasses. Thus, theman sees the tish and not thesurtace glare. This explanation isnot completely correct it the tish lsmore than about 5 IL deep.because therealter the scatteringot the light by small particlessuspended in the water polanzesthe light horizontally (FC 5.55].5.50 The polarization oi thesunlight scattered by theatmospheric particles is derivedfrom the same scattering physicsas ln the popular explanation torthe blueness ol the sky (FC5 59). The unpotarrzed incidentsunlight osoil ates the electrons inthe arr molecules (nitrogen,oxygi- i, r-i :.], which reradiate thelight. Consider, tor example a sun
272 Flying clrcul crl phyilcl with answer!
on the honzon and a scattenngatom directly overhead. Since thedirect suntight is unpolarized, theelectrons in the atom can oscillatealong any axis in e planeperpendicular to the direction ottravel ot the sunlight You canconsider such oscillations as beingeither ol two cases: where theelectrons osc llate vertically orwhere they oscillate horizontally asyou would view this overheadatom. The vertical oscillations donot radiate light vertically so you donot see that contnbution. Insteadyou see only the light radiated bythe horizontal oscillations. Suchlight is potarized along the samesense as the electron oscillations.north-south it the sun ls due west.In other words. the light scatteredlrom that part ol the sky ispolarized. Similar considerationscan be made for the rest ol the skyand tor any elevation ol the sun.Clouds are not polarized becauseol the multiple scattering cl thelight traversing lhem. Multiplescattering is also the cause ol theneutral points in the sky'spolanzation pattern.5.51 The ice is double retracting,that is. a beam entering the Ice issplit into two beams eachexperiencing dilterenl indices olretraction and havingperpendicular senses olpotarization. Instead ol thearrangement in the problem. lirstconsider ice between twopolarizing litters. Light passing thefirst tiller entera the ice. is split intotwo beams. which then propagatethrough the ice at ditlerent ellectivespeeds [because ol the dilleiencein the reiraclive indices theyexperience). When they emerge.the two beams may be in or out otphase depending on the
i
wavelength ol the light, the lengthot the crystal. and the diiierence oithe reiraclive indices The sense otpolarization ot the emerging beamwill depend on this phaseditterence. Suppose that when.eay, the yellow ot an Initially whitebeam emerges that its sense otpolarization l‘|appBl'lS to beperpendicular to the second tiIter‘spolarization sense. The secondlitter will theretore block the yellowlight, and an observer will see theother colors in the visible range inthe light from that litter. In theproblem there are no potarlzinglitters. but the sky providespolanzed light and the rellection olthe light lrom the water poolprovides the second polarizingsalecliorl.5.52 The cellophane can beconsidered as having two ap8ClHlaxes. Light polanzed along one otthese axes will experience acertain rndex ol retraction. Lightpotarized along the other willexperience a drllerent index olretraction. it the incident light lspolarized along a direction lyingbetween these two specialcellophane axes. then the light iseltectively split into the twopolarization senses of thecellophane and propagatesthrough the cellophane at dilterenleltective speeds because of theirdiiierence in the reiraclive index.Upon emerging. these twopolarization senses ol the light areout ot phase. The result is that thenet polarization sense ol the lig ht tsrotated by the caltophane.Normally two perpendicularpolanzing tillers will not transmitlight. But with the cellophaneinserted between them. thepolanzation sense ot the lightpassing through the lirst lilter is
rotated by the cellophane. Thenpart ot the lights potarizationsense happens to lie along thepolarization axls ot the secondtilter. and some ol the light getsthrough the second tiller.
The tood wrap does not havesuch apBClBl axes until It isstretched. The stretchinguntangles the spaghetti ot the longmotecules, onents the moleculesalong the direction ol stretching,and thus makes lhem polarizinglitters. Light whose siectric lieldoscillates perpendicular to theseoriented long motecijes passthrough the wrap, whereas the lighthaving its etectnc lield parallel tothe molecules does not pass asreadily.5.53 The spots indicate thestress points in the bonding ol theglass ptatas and thus behave likethe stretched tood wrap in thepreceding problem.5.54 The sense ol polarization ofthe light entenng the syrup isrotated by the haticsi structure oithe syrup molecules. The rotationdepends not only on the type olsyrup but also on the wavelengthol the light. the blue and ol thevisible range being rotated moreper unit length ot syrup than thered end. What colors are seenthrough the second tiller dependson which ot lhe oolors that litterhappens to block when the lightemerges from the syrup. Forexample. suppose the second litterblod<s the sense ot potarizationthat yellow light happens to havewhen it emerges lrom a particularcontainer ol syrup- Then anobserver will see not the white otthe initial light. but the other colorsin the visible range besides yellow.5.55 The polarization detection
Answer: 213
I.
-‘~
lies tn the ultraviolet detectors ct \the insect eyes. There. therhabdoms. which act as lightguides in the photoreceptors. aretwisted: some one way. the othersthe other way. The direction tormaximum sensitivity of thepolanzation ot the incident lightditlers tor these two senses oltwisting by about 40". Thus. tworhabdoms acting together coulddetermine the polarization sense olthe incident light. Thatcleteirnination. along with anintensity detennination by anultraviolet detector insensitive tothe polarization. orients the insectwith respect to the sky5.56 A dichroic crystal can beconsidered as having twopolarization axes. It the incidentlight is polarized parallel to one ctthese axes. their the crystal isclear. It the light happBl1S to bepolarized parallel to the other axis.then the crystal IS dark blue. Byorienting the crystal and observingits color. the Vikings could detectthe polarization ct the sky. Withexperience they could inter theposition of the sun. even it the sunwas below the horizon. Cloudcover. however, destroys thepolarization ol the sky light andwould make the crystal useless.5.57 A blue absorbing pigment inthe macula lutea (the depression inthe eye's rear) absorbs according ito the polarization cl the incidentlight. For example. blue verticallypolanzed light is absorbedhorizontally to leave a honzontalyellow hourglass (yellow is blue'scomplementary color).5.58 and 5.59 The basic colordetermination ol the sky is in thewavelength dependence ol the
scattenng ol sunlight by theatmospheric molecules accordingto the Rayleigh scattering model.The electric lield ol the incidentsunlight oscillates the electrons inthese molecules. which in turnreiiate light The overall ellect is toscatter the sunlight. Light withshorter wavelengths (the blue endcl the visible range) is deviatedmore lrom its original direction thanis light with longer wavelengths (thered end). When the sun is near thehorizon the sky above an obsenieris theretore largely blue. The skymore than 90“ lrom the sun is lessblue because it is illuminated withsunlight which must traverse along path through the atmosphereand is theretore somewhatdepleted in the blue. The sky nearthe sun on the horizon is ied oryellow because it too is illuminatedwith light whose long traversal olthe atmosphere depletes the blue.Dust lrom a variety ol sources(e.g.. volcanos. torestlires} can notonly scatter additional light. but canalso display a ditlerent wavelengthdependence than the Rayleighscattering. Sunsets and sunrisesalter a major volcanic eruption canbe bnlliarit {and also teed to theblue sun and moon ot FC5.84). The particular hues seen inany particular sunset are due to acombination ol the normalRayleigh scattenng and the dustscattenng.5.60 The purple light is due todust at an altitude cl about 20 kmin the atmosphere. Some cl thesunlight passes through a layer ctthe dust. comes out underneaththe layer. and then because thelayer is curved around a sphericalearth. reentars the layer. Its lirstpassage through the layer scattersout most ot the short wavelength
(blue and green) light. so the lightreentering the layer is red. Some olthis reentering light is thenscattered by the dust to anobserver. That observer alsorecaives blue light lrom sunlightscattered by the atmoaphereabove the dust layer. (In otherwords. the blue light ot FC 5.59.)The combination ol red light due tothe dust and the normal blue tightgives an overall purple tor theobserver. The second purple lightis believed to be due to a seconddust layer at an altitude cl To to 90km.
5.61 The enhanced zenithblueness comes as a surprise.According to the Rayleighscattering ot FC 5.59. the zenithsky should be blue-green and thenyellow as the sun sets Themissing element in a simpleRayleigh scattering picture is theabsorption by the atmosphericozone in the red end ct the visiblespectrum. with the red endremoved. the blue end is lelt andappears richer. The geometryfavoring such a blue enhancementoccurs when the sun is about 6‘below the horizon and the lightscatters lrom directly overhead theobserver. The blue is lurlherincreased by dust in theatmosphere because the dustabsorbs more ol the red and yellowlrom the direct sunlight than theblue (see FC 5.64).5.62 Next to the earth's shadowthe sky is illuminated with sunlightlrom which all ol the shortwavelength (blues and greens)have been subtracted (FC 5.58)5.53 The paniculate matter(industrial pollution. smog) withradii smaller than about 0.2 micronscatters the blue tight out ot the
214 Flylng clrcun 0| |:i'l'||,illcn uilth
light reaching the distant observer.5.64 The sky is bnght because clthe scattering ot sunlight by the airmolecules. But there is a problem-For every molecule scattenng lightto an obsenrer there is. on theaverage. another molecule on theline ol sight and hall a wavelengthcloser to the observer. The tightscattered lrom these twomolecules arrive exactly out oiphase at the observer andtheretore cancel each other. Sincethe argument can be repeated torany portion oi the sky exceptdirectly toward the sun. the skyshould be completely dark eirceplin that special direction and excepttor the stars and planets- Theargument has a slight llaw.however. Although the moleculescan be paired this way on theaverage. they cannot becontinuously paired because oi thefluctuations in the distribution oithe molecules. Were there nolluctuations. the sky would be dark.5.65 Apparently nothing beyonda description oi the ellect has beenpublished. The yellow glasses maybe oi advantage it the haze iscomposed ol relatively smallpanicles. smaller than about 0.2micron in radius. Such smallparticles scatter the shortwavelengths ct light (the blue end)more than the long wavelengths(the red end). Thus the reds andyellows may illuminate the groundin a more direct beam whereas theblues and greens. having sutteredmore scattering in the haze. aremore dillused. By eliminating theblues and greens. an observermight be able to see more ol ashedow oi an obiect in the lield ctview.5.66 Instead oi being easier to
l
see. stars are harder to seethrough a shalt. Although most oithe sky is blocked oll. the skysurrounding the star's image is still|ust as bnght as without the shalt.The shalt certainly cannot makethe star itsell bnghter.EJtpBfll'l'lBI'll3t work on viewing asmall luminous test area in a largesurrounding dark area indicate thatthe threshold in distinguishing thetest area is decreased it thelumination oi the surrounding areais increased until it is about thesame as the test area. Instead oibeing more easily seen. stars aretheretore harder to see through ashalt because their threshold oivisibility is increased when the skyis blocked oll.5.67 It the water is pure anddeep. it is blue due to the surtacerellection of light lrom the blue sky.Shatlower water has greater greenbecause of rellection lrom thebottom. Contamination can acid avariety oi hues to the waterbecause oi selective absorption or.in the case oi micron-size particlesuspensions. because oi thescattering ot the light. This latterellect is similar to the scattering inFC 5.87 and 5.88.5.68 The greenish tinge is addedby the rellection lrom greenvegetation. A similar upwelling oilight edding features to an overcastsky is responsible tor the sky mapsoi FC 5.72.5.69 The illumination oi the"dark" part oi the moon (i.e.. thepan oi the moon ll'l a shadow lromthe direct suntight) is due toearthshine. the tight rellecled lromthe earth's atmosphere andsurface.5.70 The scattering ot light oll
objects much smaller than thewavelength ot visible tight lollowsthe Rayleigh scattenng model inFC 5.59. The water drops In theclouds are usually larger andmerely retlect the sunlight lromtheir outside surlaces. No colorseparation results lrom suchrellection. and the scattered lightremains white. (An exception is inFC 5.73.) Very dense clouds areblack because little oi the sunlight
i is able to penetrate them. beingeither absorbed by the water orrellecled upward.5.71 Sunlight scatters lrom watermolecules as lrom any othermolecule in the atmosphere. andso individual water moleculescontribute to the sky brightness(FC 5.58). The scattering lromwater drops is greater than lrom anequal number oi individualmolecules because ol their closespacing in the drop where adjacentmolecules are about 1000 timescloser than the wavelength oivisible light. Consider two suchadgacent molecules. When thesunlight oscillates their electronsthe oscillations are in phasebecause the electrons sampleessentially the same pan ot the
. incident light wave. The electrictietos radiated by those electronsare also in phase andconstructively add to give twice theelectric lield as lrom a singe atom.The intensity oi the radiated light isthe square oi the amplitude oi theradiated electric tiald and theretoremust be tour times that lrom asingle atom. It these two moleculesare well separated (much morethan the wavelength oi the light).there is no average constructiveinterference and the radiatedintensity is only the sum oi theintensity lrom each. that is. only
finlurllrl 215
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twice the intansity from a singleatom The clouds are brightbecause of the constructiveinterference of the closely spacedwater molecules in the waterdrops.5.72 The maps are ton-ned fromthe selective rellection of sunlight jfrom the ioe and water surtace and ithen from the clouds. For example,the direct suntight is reflected morefrom the solid ice than lrom thewater. Since both rellect well. thedifference in the rellections can beseen on the bottom of the clouds.5.73 The mother-of-pearl cloudsare composed of smell dropswhose radii {(1.1 to 3.0 microns) arenear or somewhat larger than thewavelength of visible light. Suchdrops scatter light according to theMie model rather than the Flayleigh imodel of FC 5.59 for smaller dropsor the simple reflection lrom largerdrops The diffraction of the lightaround the drops depends not only ‘on the drop radius but also on thewavelength of the incidant light andis theretore responsible for thebeautiful oolors. The clouds can beviewed up to two hours altersunset because ol their high ~altitude: they are still illuminated torthat tong alter a ground observerhas entered twilight.5.74 The interference fringesresult lrom the scattenng of thelight by the dust particles on the \lronl surtace cit the mirror.Consider two rays. One isscattered by a dust particle bsforeentering the minor and beingreilected in the normal way. Theother ls first rellecled in the normalway and then is scattered by theseme dust particle on leaving theglass. Since the paths taken byeach were slightly different, the
rays can have a variety of possiblephase differences when observedtogether. depending on the angleof the rays and the wavelength(color) of the light. Thus, the lightshining on the dusty mirrorproduces an Interference pattemfor the observer, with the ooiorssepareted because of thewavelength dependence in thephase difference of interferingrays.5.75 The light beam dime notonly because of the spreading ofthe beam but also because of theattenuation of the beam by thescattering of the atmosphere.(Were there no scattering, thebeam would be invisible.) Theattenuation exponentiallydiminishes the beam's intensity.giving a rather abrupt end to thebeam.5.76 Both the zodiacd light andthe gegenschein are due to thescattering of sunlight lrominterplanetary dust. probablydenved from the astroidal belt. Thedust giving the Zodlacd light liesinside the earth's orbit and isvisible only under the specialcircumstances descnbed in theproblem. The gagenscihein issunlight backscaltered from dustoutside the earth's orbit.5.77 The windshield wiper rubscircular groves of gummy dirt onthe windshield that then rellect lightto the driver. The bnghtestreflection occurs when the inctdantlight ray is perpendicular to atangent to the grooves. Theooilection of these bnghterreflections lorms the streak of lightalong a radius of the curve throughwhich the wiper moves.5.78 The brown is primaniy due
to selective absorption by thenitrogen dioxide in the hazes.5.79 The glory results from lightbackscattered to its source bysmall particles whose radii arenear or somewhat larger than thewavelength of visible light. Thescattering is described by the Mietheory rather than the Fiayleightheory for smaller particles (suchas in FC 5.59] or by the normalrellection and refraction models forlarger particles. The light that isreturned in the direction of the lightsource enters a drop on an edgeand exits from the edge on theopposite side of the drop aftersuffering both a reflection withinthe drop and a skimming elorig thedrop's surtace. That skimming,which is described es being asurtace wave. is not part of thestandard ray optics used inmodeling a rainbow (FC 5.32). Thereturn anges for different incidentcolors are slightly dilterenl andthereby produce the distinctcolored rings around the shadow oithe observers head. Since theangles involved in a panicularpattern depend on the size of thedrops, the colors are lost it thedrops in the cloud have a largerange of sizes5.£ilJ The solar and lunar coronaare the diffraction pattems of thelight from the small water drops Inthe line of sight. The dillrection ishandled best with the Mie theoryas in (FC 5.79) but can beapproximated with theconventional ditfraction of lightaround a small sphere (as in FC5 96 and 5.98). In the latterinterpretation, the tight rayspassing opposite sides of a waterdrop interlere with each other onthe other side of the sphere lo
276 Flying clrcul of phyiulu with answers
‘I
create bnght and dark ringscorresponding to constructive anddestructive interference. Theangular positions of the bright anddark rings depend on the drop sizeand the wavelength oi the light. llthe drops are unifom-i in size. thanrings of dilterenl colors can bedistinguished. the longerwavelengths (red) on the outsideand the shorter wavelengths (blue)on the inside of a nng.5.51 The frosty glass coronaresults lrom the scattenng of lightas in the preceding problem butwith a lew changes. Instead ofbeing randomly spaced spheres,the drops are now fairly uniformlyspaced, flat drops.5.B2 The Bishop's Hing ls adiffraction pattern from smallparticles. usually dust iromvolcanic eruptions, in whichsettling has sortad the suspendedparticles to a uniform size. As in FC5.79 the Mie theory of scattering isneeded to calculate the intensity ofthe scattering pattern for theseparticles whose radii are about thewavelength of visible light.5.83 Colored rings can be seensurrounding street lights even if thenight is perfectly clear. Similar tothe corona in the previousproblems. these corona result lromdiffraction of light around smallobgects which are about thewavelength of visible light in size.The difference in this corona is thatthe obiects are inside the eyeSome of the possible diltractingobiecis responsible for theseenloptic halos are the radial tibersin the crystalline lens or the mumsparticles on the comeal surtace.Similar enloptic diffraction pattemsare in FC 5.95.
5.84 In contrast to the Ftayleighscattenng in FC 5.59, the bluemoons are due to the scattering oilight by atmosphenc aerosolswhose radii range from 0.4 to 0.9micron (which oontains thewavelength range of visible light).Particles in this size range scatterthe tong wavelength end (red) ofthe visible range more than theshort wavelength end (blue). As aresult. a normally white moon seenthrough such an aerosol will havethe red end of the spectrumscattered out, leaving the observerwith the blue end and thus a bluemoon. These aerosols areoccasionally produced by volcaniceruption or combustion as in largeforest fires. The selection of thissize range can result from theparticles settling in the atmosphereor from condensation increasingthe size of small nuclei until theyare within this size renge.5.85 In spite oi several studies,the value of yellow fog lights is notclear. Ii the particles are smallerthan about 0.2 micron in radius, theblue will be scattered more thanthe red end of the visible spectmm.Yellow light would therefore betterpenetrate the fog because it has alonger wavelength than blue andgreen. However, for the particularsize range described in FC 584,the result could be the exactopposite. For evan larger particlesas in a true fog. the yellow wouldbe of no advantage. One problemin these general coriciusions is thatthe absorption of the light by aparticular type of suspendedparticle could be important.5.68 The blue results from thescattering of light from very smallparticles, smaller than thewavelength of visible light They
can be macromolecules (largemolecules) of terpenes released bythe vegetation. Or they can beparticles released from the tips ofthe vegetation (e.g., the tips of aleaf) where the electric lield isrelatively high (FC 6.33) and brushdischarge (FC 6.46) might occur.The scattenng is adequatelymodeled by Fiayleigh scattering{FC 5.59) in which the blue isscattered more from the directsunlight than are the other colors Ifthe particles are closer to being thesize of the wavelength of tight, thanthe Mie scattering theory is neededto predict the exact scatteringintensities and color.5.87 In order for you to see yourown shadow in the shallow water,you must be able to distinguish thelight reilected from the top surtaceof the water. In clear water thatrelatively feeble light is lost in thelight reflected from the water'sbottom. With mud in the way, thebottom light is partially or totallyeliminated, allowing you todistinguish the light and dark areasfrom the surface rellection. To seethe shadows of other people, theremust be more elimination of thebottom light.
The colorful edges on shadowsresult from the scattering of light bysmall particles suspanded in thewater. They, like the atmosphericparticles of FC 5.59 and the otherparticles in FC 5.88-5.90. scatterthe shorter wavelengths [blue].Consider viewing a shadow nearyour own shadow. The near side isblue because this paniclescattenng is distinguishableagainst the dark background of theshedow. The far side of theshadow is red because light fromthat side has had the bluecomponent removed by the
Ancuicn 211
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St;-filtering
5.68-5.90 In each of thesecases. light is scattered from verysmall particles. As in theargumants for the blue sky (FC5.59). the Flayleigh theory ofscattering is applicable for particlessmaller than the wavelength ofvisible light. In such cases bluelight is scattered more than redlight Thus, the suspended milkglobules and the smoke particlesappear to be blue when seen whilelooking from the light source orfrom the sides, but appear to bered or yellow when seen whilelooking toward the light source. (Inthe campfire smoke case, thesmoke is first seen because of skylight coming from behind theviewer and then later seenbecause of sky light in front of theviewer.) If the particles are near thewavelength of visible light orsomewhat larger. then the Mietheory of scattering is needed(The Mie theory is used in FC 5.73for direct baciiscatier-) Whencigarette smoke is inhaled,condensation in the mouthincresses the drop radii such thatthey are comparable to thewavelength of light, and yellow ispreferentially scattered instead ofblue.5.91 The colors in a soap or oilfilm are due to the same type ofthin film interference that isresponsible for the blue Morphowing in FC 5.94. Bnefly, lightreflected from the first surlace ofthe film interferes with the tight
‘ reilected from the second surface.Whether the interference isconstnictive or destructivedepands on the wavelength of thelight. the refractive index of thefilm, and the path length of the light
inside the film. If the film is lessthan about one fourth thewavelength of light and has air onboth sides. as with a soap lilm heldon a vertical wire hoop, theinterference is destructive and thefilm appears dark to an observeron the same side of the lilm as thelight source. As one considersprogressively thicker films, theinterference gives progressivelylonger wavelength colors for thoseexperiencing constructiveinterference in rellection. ll a thinsoap film is held vertically andilluminated with white light, the topponion may be thin enough to bedark Further down the film are thecolored bands corresponding tothe constructive interference. But.mysteriously enough. iust belowthe dark portion is a white strip. Forthe film thickness there, partiallyconstructive interference comesfrom the entire range of visible lightand therefore gives the observer awhite light reflection (Bayman andEaton, personal communication].5.92 The source of these ringshave apparently not beeninvestigated but they seem likely tobe the enloptic halos of FC 5.83caused by mucus particles or smallwater drops on the surface of theeye.5.93 Liquid crystal, which is amatenal somewhere betweenbeing a liquid and being a solid,comes in three basic types.depending on its moleculararrangement. The smectic typehas its molecules aligned in thesame direction and in parallellayers. The nematic type hassimilar alignment in a singledirection but lacks the layering.The third type, the cholesteric one,is responsible for the colors in the
liquid crystal toys now being sold inthe United Slates. This typecontains layers of molecules inwhich the molecules of any onelayer are aligned in the samedirection parallel to the plane- Thealignment direction shifts fromlayer to layer such that a vectorgiving the alignment would rotatein a helical path as one considereddeeper and deeper layers. Thepitch of this helical path deterrrlnesthe wavelength of the light stronglyreflected by the cholesteric liquidcrystal. Other wavelengths merelypass through the crystal. Byapplying pressure to the crystal(the toy comes packaged in aflexible plastic container) or bychanging the temperature of thecrystal, one can alter the pitchangle and therefore vary the colorselectively reflected by the crystal.5.94 The nch blue from the lopsurface of a Morpho butterfly wingis due to thin film interference oflight from thin terraces that liealmostparallel to the wing and on asupport structure sprouting almostperpendicular to the wing. Of thewhite light sinking such a thinterrace. part is rellecled (call it rayA) and part is transmitted into theterrace. Of the latter. part (call it B)is reflected from the bottomsurface of the terrace and emergesupward along with A. Hays A and Bcan interfere with each otherconstructively or destruclivelydepending on their phasedifference. That phase differencedepends on the wavelength of thefight, the thickness of the terrace.the reiraclive index of the terrace,and the angles ol the light enteringand leaving the terrace. For lightincident perpendicularly to theterrace. the wavelengthcorresponding to blue light will
278 Flying dict-II OI physics with anlwflrl
produce emerging rays A and B ll"'lphase so that they construclivatyinterfere. Hays A and B of all of theother colors of the incident whitelight more or less destructlvelyinterfere and do not contributenoticeable light to the observer. Asa resultthe observer sees blue. Asthe observer changes either theangle of view or the angle otincident light, the path length of thelight inside the terrace changes,thereby varying the phaseditference between rays A and B.The wavelength giving maximumconstructive interference changesas a result, and a stightly dilterentblue hue is seen.5.95 The dark lines betweenyour lingers are the dark lnnges ofthe diffraction of light through thespace between lhe tingers. Thelight passing through pan of theslit. say adjacent to a linger.interferes destruclively with lightpassing through a different part otthe slit, say further from that linger,to give a dark line at the observer.5.96 The eye floaters are thediffraction pattems ot light passingsphencal blood calls floating ]ust intront of the loves on the retina.{The lovea is a pit of denselypacked cones directly opposite theopening of the eye.} Blood cellsloosened by old age or violentblows to the head swell to spheresby osmotic pressure whan theylloat in the watery matter in tront otthe retina.5.97 It the photograph isexposed |ust nght. it might record5pik6S ot the stars because ot theirtwinkling [PC 5.102). Spikes canalso be present because of thediffraction of the star light by thestraight sections ot the camera'seperture. These apertures are not
perfectly round but are composedof many straight edges so that theeperture width is adjustable. Thehuman pupll is not perfectly roundeither. and diffraction around thestraight edges creates spiked starsthere too. The spikes must alwaysappear in pairs.5.98 The interference ringsshown in Figure 5.98 are thediffraction pattern of the light by thesphere. Light passlng one side ofthe sphere interferes with lightpassing the other side to givebright and dark rings on a distantscreen The center of the pattern isequidistent lrom the two sides. andthe light rays from the two sidesarrive in phase to give constructiveinterference.5.99 and 5.100 The cause ofshadow bands is not we'llunderstood. Probably the bestcurrent explanation is that they areinterlerence patterns or light thattraverses air cells of varyingdensities. Such cells in the upperatmosphere could be naturallyoccurring turbulent cells.5.101 The lake acts as a singlesiit. and the observer flies throughthe maxima and minlma ot itsdiffraction pattern.5.102 Stars twinkle because theair is turbulent. which ultimately isdue to uneven heat distributions inthe atmosphere. Small turbulentcells. several centimeters or moreacross, are constantly present toretract the passing starlight tirstone way, then another- This smallshimmy is noticeable with the smallstar images but less noticeablewith the larger images of the moonand the planets-5.103 The ultraviolet light isabsorbed by the organic molecules
in the pigments and alters theirmolecular bonding, eventuallyeliminating most of the colorproperties of the pigment. Thisultraviolet fading of colors wasdiscovered to be one ot the mostserious threats to paintings hung inmodern museums that had begunto install common fluorescentlamps for uniform illumination. Thelamps also emitted eppreoableultraviolet light. Now. either thelamps or the paintings are filteredto remove the ultraviolet light. orthe museum has returned toincandescent bulbs.5.104 Light has momentum andcan therefore exert a torce. Thelaser used in this type ofexpenment provides an intensebeam ot light that exerts sufficienttorce on the sphere to raise it. Thestability is due to the retraction oflight by the sphere. The laser lightis most Intense in the center of thebeam. Consider a spheresomewhat ott osnter but still in thebeam. Light entering the spherenear the beam's edge retracts intothe sphere, propagates across thesphere. and than retracts out of thesphere toward the center of thebeam. That light beam hassuffered a net delleclion, andtheretore must exert a force on thesphere- Light entering on the sldenear the beam's center sufferssimilar detlection but toward thaedge of the beam. Both deflectionsprovide lift lo the sphere. Both alsoprovide sideways iorces. But thelight deflected toward the center isless intense than the light deflectedtoward the edge. Thus, the netsideways torce is toward thecenter. If the sphere wanders fromthe center. this net sideways forcebrings it back.
Anlwarl 219
5.105 The dark and bnght bandsare the diffraction pattern from thescreen. You can see similar butmore colorful pattems by viewing alight through an umbreI|e's fabric.5.106 The range ovar which astar radiates light depends on itssurtace temperature (to the fourthpower when expressed in Kelvindegrees}. The higher thetemperature ot the star. the lowerthe wavelength at which the peakof its radiation occurs. A cool starmay have an insignificant amountof redialion in the visible range. Asone considers progressively hotterstars. the redialion range entersthe visible range from the red end.Thus, a star may have only red orred-yellow radiation in the visible itits temperature is lust nght. Ahotter star could have its peak intha center of the visible and thenemit all the colors approximatelyuniformly. Such a star would bewhite. as is the sun. A still hotterster could have its peak in theultraviolet and emit more blue lightthan the other colors in the visibleand therefore appear somewhatblue.5.107 As yet the lightsassociated with tornadoes are notexplained- In fact. tomadoesthemsalvas have not beenexplained (FC 4.68). Most likelythe light results from the electricaldischarges present in thatomadoes5-106 The light is from moleculesexcited by charge differences onthe crystal planes as the crystalsare fractured in the pounding andscrapping of the stirring.5.109 Solar ultraviolet tight isresponsible for both tanning andsunburning. If you are exposed to
large or lengthy dosas of ultravioletlight. both tha d9Il"ltlS andepiderrns otthe exposed skln maybe damaged. As a result thecapillary vessels dilate and bnngmore blood to the skin suiface,both reddening and warming theskin. Shorter exposures to theultraviolet llghl tans light-coloredsliin by lirst oxidizing a ptgmanlnormally without color and than byactivating (perhaps indirectly bydeactivating an inhibitor)tyrosinase. This activationincrassas the amount ot melanin. abrown or black pigment Themelanin protects the nuclei of skincells by tomitng a layer over thecalls which litters out theultraviolet
Sunian and antisunourn lotionscome in three main types. Some{with zinc oxide or titanium oxide)screen all the ultraviolet and visiblelight and provide no tanning but doproteclsensitive skin. Others (e.g..benzophenones} absorb all ol theultraviolet arid also provide notanning. The third group(containing substances such asaminobenzoic acid] provides bothtanning and protection againstsunburn by selective absorption-Tlie ultraviolet wavelengths extendfrom about 0.28 microns to about0.40 microns Shorter wavelengthsdo not pass through theatmosphere. and longerwavelengths are in the visible. Oithis range. the wavelengthsbetween 0.29 and 0.32 micronsare the most efficient insunburning. whereas thewavelengths between about 0.31and 0.40 microns are the mostefficient in sunlanning. The point ofthe third class of lotions is to tillerout the wavelengths below about0.31 microns.
1: 7 W" ' ' ' ' 7' HSunburn and tanning are less
likety in the moming or lateafternoon because the sunlightmust traverse a greater paththrough the atmosphere and moreof the ultraviolet tight is absorbed-Glass also absorbs the ultravioletwavelengths- Sunburn is morelikely on high mountains becauseof the shoner pathlength of thetight through the atmosphere. It lsmore likley at the beach becauseof the ultraviolet reflections fromthe sand.5.110 and 5-111 In each oftheseluminescent cases two materialsare responsible for the lightproduction. These materials aregiven the general namas otIucitenn and lucilerase. but whatthey are differs among theorganisms. The tuciferase is justan enzyme, a biological catalyst torthe reactions in the lightproduction. Marine creatures canbe luminescent in three ways.They may have cells designedspecifically tor that purpose,perhaps even edvanced enough toresemble lanterns- They mightinstead issue luminescent clouds.Or they actually may not beluminescent themselves but playhost to luminescent bactana. Thedinoltagetlales turn the sea red,yellow. or brown during the day bytheir natural color. but at night theyglow blue whan disturbed. Someintemal clock regulates that light.Dlnoflagallates kept undercontinuous dim light still will havetheir maximum light output about 1A.M. when disturbed. Such rhythmmay last for several weeks underthe dim light. Fireflies set ofl aseries of chemical reactions toproduce llght Their converson otenergy to light is 100% efficient inthat one photon is emitted for each
230 I-‘lying cllcul of pllyllcl with IIIIIIIITI
lucllerin molecule oxidized in thechemical reactions. The light is saidto be "cold" light because, incontrast to Incandescent bulbs.candle lire, red-hot pokers, and soon, the liretly light does not resultlrom high temperatures and rapidthermal agitation ot the molecules.Bacterial light, which is responsible
r tor much ct the luminescencereported tor tood, rs a part oi thenatural process ol that bacteria inobtaining energy Irom nutrients.5.112 This type ot glass containssmall crystals that react to theillumination. For example, it thecrystals are silver bromide, then
y the fight translorms the silver ions‘ to silver atoms that then darken the
glass. The silver atoms are stilltrapped near the bromide,however. so as soon as the light isdimmed. the two recombine, andthe darkening is reversed.5.113 The black-light posterlluoresces by absorbing ultravioletlight and then radiating visible light.Under an ultraviolet light the posterseemingly glows without anystimulus. Whiter-than-white soapsdo almost the same thing. Theyoonverl the natural ultraviolet toblue tight and thus add to thevisible light radiated by thematerials containing the soapproduct. In the advertising iargon,the resulting "white" [meaningvisible] light is more than thenatural visible light5.114 Electrons emitted by an
I electrode collide with an atom olmercury vapor, exciting one ot thecuter electrons in the atom. Thatexcited atom quickly deerricltes toreturn the electron to its lormerenergy level. As a result ot thedeeircitation, the atom emitsultraviolet light that is absorbed by
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phosphor crystals coating theinside of the tube. The deexcitetlonol the crystals results in the visiblelight we see- The crystals shouldemit some light for at least twocycles oi the I20 cycles a secondat which the maximum dischargeoccurs (the rates can differ with thecountry). ll the crystals deexcltedinstantaneously atter beingexcited, than the tube would havean intolerable flashing.5.115 The Speckle is aninterlerenoe pattern of incidentparallel rays (spatially coherentlight) scattering lrom the very smallstructures on the dilluse scatterer.Spatially coherent means that thephase oi the light emitted by oneportion oi the light source IScorrelated with the phase ol thelight emitted by another ponion.Such a correlation is needed tomaintain a stationary lnlerterencepattern. To some extent directsunlight is spatially coherent andcan produce these specklepatterns. The apparent motion ofthe pattem when the observermoves is due to the parallaxpresent because the observer'seyes are not focused on thescattering surlace. For example, itthe scatterer is several metersaway lrom the observer and if theobserver is nearsighted, than theobservers eyes are locused intront ot the scatterer. As theobsenrefs head moves to the lelt,tor example, parallax causes thespeckle pattern to eppear to moveto the right.5.116 In each ol these two caseshumming creates a strobosoopicimage ot the TV screen or rotatingdisc on the retina. -Each source haspenodic changes in eppearance.The disc turns. The TV has a
recurring image because oi theline-by-line, horizontal sweep olthe electron beam er-rcitlng thescreen. A correct hummingtrequency oscillates the head, andthus the eye, appropnateiy to bringthe recurnng image beck to thesame place on the retina. Theimage than looks lrozen. It thehumming is not at such alrequency, then the head and eyeoscillations are out ot synch withthe TV or disc, and the recurringimage appears to migrate. Forexample, it the humming is at afrequency slightly too high Ior atrozen image. then the pattern onthe disc will eppear to movebackwards against the sense otrotation cl the disc.5.11‘! The elliptical motion of thependulum is seen because the eyecovered with the darkened litterexperiences a delay by severalmilliseconds in its perception cl thependulum‘s position. In the brain'sinterpretation ot the pendulumpositions perceived by the twoeyes, the pandutum is placedeither doser or lurlher away thanits true position. Thus, thependulum swing is interpreted asbaing two dimensional rather thanone dimensional- For example,suppose the pendulum is swingingto the right while viewed with thetett eye having the darkened tiller.The right eye perceives the trueposition ot the pendulum, whereasthe tett eye perceives it as where itwas several millisecondspreviously. You mentallyextrapolate the light rays lromthese two positions backward untilthey converge so that they mattesense as having come lrom asingle ob|ect. This extrapolationmeans the pendulum will eppear tobe further away than It really Ie.
Anlurun BB I
When the pandulum swings backto the tett. a similar lag inperception occurs tor the coveredeye. and the brain interprets thependulum as being closer than itreally is- Overall, the pendulumeppears to swing in an ellipse as inthe right-most sketch ol Figure5.117 The cause ot the visuallatency is not well understood. Oneanalogue tor the visual system is asenes oi deiay tine tillers in whichthe time resolution oi the system isimproved by an increasedleedback signal when the eye issub|ected to greater illumination. Adecrease in lllUlTlll"lEl|OI1 reducesthe feedback and thereby worsensthe time resolution.5.116 The entire screen oi theTV is not continuously lit. but isconstantly swept honzonlally linebyline with the electron beam inthe TV lube The sweeping lightcan act as a stroboscope in lightingthe top. causing you to see atrozen image ol the top surlace. oran image that turns one way oranother. all depending on how thesweep lrequancy compares withthe roteticn rate ol the top.5.119 Flods [which are primarilyused in low levels oi illumination)are packed the densest comparedto the cones (which are tor greaterlevels ol illumination) toward theperiphery ol the retina. Staringdirectly at a star places its imageon the lovea. in which there are norods. Jumping your eyes awaylrom the star sweeps the star'simage across the greater packingoi rods and enhances theperception cl the star5.120 Blue arcs are stilt underresearch. Although their cause ispoorly understood. they appear toresult lrom neurones excited by
J~ _ — ' 7
F l lthose axons directly stimulated.Suppose a stimulating light excitesa panicular set oi photoreoeptorsthat are linked to a particular set olganglion axons. That set oi axonscan then excite other nearbyneurones. which then stimulate thephotoreoeptors to which they arelinked. The result is an apparentarc cl stimulation stretching awaylrom and around the tovea {thecentral pitlike region on the retina]with one end on the point underdirect stimulation. The cause oi theblueness has not been discovered.5.121 Apparently the productionmechanism tor phosphenes is notunderstood at alt. because therehas been almost no workpublished on modeling thephenomenon The physical sourcehas not even bean identifiedconclusively although someresearch hes shown directetectncat stimulation cl theoccipital lobe at the rear ol thebrain can result in phospheneimages.5.122 All the lamps should turnon at the same time because thelag oi electricity is imperceptible.However, tha street lamps at anintersection appear to turn onsooner because they collectivelyprovide more tight to the observerand theretore suller less visuallatency (FC 5117) than the streetlamps between the intersections.
5.123 and 5.125 The elaborate
retina creates distinct shadows onthe retina but those shadows arerarely seen because the brainignores any constant image lromthe eye. The vessels remain tixedwith respect to the retina. theirshadows remain constant. andthus you do not "see' the
network ot blood vessels on the
shadows Exceptions occur in twocases. Upon lirst opening youreyes in the moming. the suddencasting oi these shadows is achange and thus will ba seenbrielly until the brain tades out theinlorrnaticn as being lrom aconstant image. The otherexception is that the blood celtscarned by the retinal capillariescan cest shadows that are seenbecause the cells lerk their waythrough the capillaries. These cellshadows are the ierky specks inyour lield oi view when you stare ata lealureless illuminated area.5.124 The cause at thesegeometric designs is not wellunderstood and is currently beingresearched. They could develop atthe retina or in the neuralpathways They could also depandon the interaction oi theintcrmation cl one eye with that ctthe other eye. One type oi pattern.roughly geometric but lackingprecision and complexity. appearsto be dependent on monocularvision. The more complex patterns.on the other hand. appear to resultin part lrom binocular vision.5.125 See FC 5.1245.126 Vision in bright light is bythe cones on the retina. whereas inlow illumination vision is by therods These do not have the samespectral response. The peakresponse oi the cones is in theyellow {corresponding to awavelength of light ol about 0.56micron} with a much lowerresponse in the blue. The rodsrespond best in the green{wavelength oi about 0 50 microntor peak response} and have amuch lower response in the red. It lyou observe red and blue while theroom illumination dims lrom being
282 Fl|,rl|.'|_|| circus 0| pliyllcs with nnlwero
initially bnght. your vision shittslrom using the cones to the rods.and the relative response to theblues and reds changesdrastically.5.127 The bnght and dark bands.Mach bands. are ltlusionary. Theycan be photographed in the sensethat an observer sees the illusionas readily in a photograph ol ashadow edge as with a realshadow edge. The current theorytorthe band production involves aninhibitory eflect in the neuralnetwork oi photoreoeptors beingstimulated by the incident lightnear the shadow edge. tn short.
\ the signal oi a tinng photoreceptorinhibits the signal oi a neighboringphotoreceptor also beingstimulated. Consider a shadowedge on the retina. On one side,say the tett. the retina received aunitorm bnght illumination. On theother side, the nght one. the
~ illumination is unitorrnly dimmer. Ina short intermediate region. theillumination drops lrom the brightlevel to the dim level. On the bnghtside ct this intermediate region abright Mach band eppearswhereas a dark one appears onthe dim side. In the unitom-ity litregion all ot the photoreoeptors areinhibited by their neighbors So.
\ the signal tevel Irom this area isless than would be expected itthere were no inhibition. Aphotoreceptor on the edge ot theintermediate region is lessinhibited because on one side. inthe intermediate region. there isless illumination. Hence a brightband is perceived there. Aphotoreceptor on the other edge ctthe intermediate region. that is.bordering the unilormly dim area.is more inhibited than the receptorsin the dim area because ct the
i
illumination in the intermediateregion. Hence. a dark band isperceived there.
or5.128 The Land eltect IS n wellunderstood in its complete processbut is currently modeled bysupposing that there are threetypes ct cones on the retina thatare distinguished by where in the\llSlblB range their peak responselies: one type each tor theshort-wavelength.rniddle-wavelength. andlong-wavelength ranges. whenyou observe a ootor scene. eachset cl cones somehow measuresthe rellectance ot light lrom thescene in those three wavelengthranges. compares thosereltectances. and then createsyour color sensations. Colorresults lrom the black-and-whiteslides described in FC 5.128because the rellaclanceinlormation at two dilterenlwavelengths is apparentlysulticient to trigger colorresponses. Hence. the colors youperceive may be almostindependent ot the wavelengththe tight you receive5.129 The colored adges ol thelight source are due to theChfOt'TlBllC abberation ol the eye Inthe arrangement cl Figure 5.129.the linger blocks the right side ofthe viewing eye such that theobserved light rays lrom thewindow enter the eye only on the
k
ct
tett side ct the eye. Upon enteringthe eye, the red rays are retractslightly less than the blue rays.Although the aberration is normallynot noticeable. the partial bloc ingoi the eye with the linger allows theviewer to distinguish the dilterenlimages oi the window edge fordilterenl colors Consider light
ed
radiated lrom the right side oi the \window and entenng the tett side ol ithe eye. The small diiierence in *retraction tor red and blue lightresults in the red image oi thewindow edge being slightly to thelelt oi the blue image on the retinaThe blue image is lost in the whitelight coming lrom the windowsomewhat away lrom the edge.Thus. the observer sees a reddishwindow edge- A similar separationol colors occurs tor the tett side ctthe window. but this time the redimage happens to he lost in thewhite light lrom the rest cl thewindow. and the viewer is tett witha bluish edge5.130 Previous to currentresearch. the colors were thoughtto result from the ditierance intimes needed to turn on the colorresponses in the visual pathwayatter the observer vieweddarkness. In particular. thetheories concluded that red turnedon slightly sooner than blue. andthus the leading edge oi the whitearea was red. However. recentresearch indicates no suchdiiierence in turn-on times tor thedilterenl colors- One ot the currenttheones about the color responseto the disc is that the pattern oi itsintensity variations either mimics or ‘creates a photoreceptor iinngpattern that mimics the brain'scolor coding. In other words. theproper pattern cl intensity changessends a Morse-code-like signal tothe brein telling the brain it sees apanicular color Ior that panicularcode. As in FC 5.128. seeing reddoes not necessarily mean thatyou are viewing light with awavelength oi about 0.6 microns.Color perception appears to be tarmore intricate.
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5.131 Whereas the blues andgreens Irom the lluorescsnt lampsturn oll during part oi the cycle inthe 120 cycle-per-secondstimulation ot the lamp. the yellowsand reds til the lamp has muchred) do not. As a result. a spinningblack-and-white disc or a spinningcoin will rellect colors to theobserver that change with time.The diiierence in the color durationcomes lrom the three types olemissions presant in the lamp'soutput. The short-lived blues andgreens come primarily lrom themercury emission lines {whichhave very short liletimes} and aphosphorescence also with a shortllletime. The yellows come mostlyfrom a long-lived fluorescenceirom the same phosphor.5.132 The picture on a TVscreen is not created whole out isquickly produced by the electronbeam in the TV tube movinghorizontally line by line downwarduntil the bottom oi the screen isreached. The sweep is so last thatyou don't perceive it. Ii you swingyour eyes to the right. eachhorizontal sweep leaves an imageon the retina tor about 75 msec orso. Because your eyes moveduring the beam's line sweep. thelasting image oi a particular line isslightly to the right oi the line justbelow it because the top one wasmade slightly sooner. The overalltasting image oi the screen istheretore tilted as shown in Figure5.132. Multiple images areobserved because during the tullswing oi your head the alectrongun has tilled the sciean severaltimes, each lull image giving youan image to carry brielly oti to theright5.133 Most oi the stereoscopic
d— — _ — __
illusions depend on imitatingnormal binocular vision that givesdepth in our normal viewing. In thestereoscope (the device nowbought only tor children but thatonce provided much eveningentertainment tor ail} contains twophotographs shot with camerapositions separated by a lewcentimeters and with anappropnate angle adjustment tomimic our normal viewing. Whenyou examine the photographs withthe stereoscope. the dilterenllmeges are iused to make a singleimage with apparent depth.Three-dimensional moviesdepended on providing a similarshitt in perspective tor each eye.For example, the two images mightbe projeclad, one in blue and theother in red. The audience wouldthen wear glasses with bluecellophane over one eye and redcellophane over the other. Againthe two images ere lused toprovide a sings one with depth.Dillerent polarizations oi theproiected tight could be usedinstead oi the dilterenl colors. Theglasses would then have the Ieltside passing a dilterenlpolanzation than the right side.Three-dimensional postcardsemploy a single picture but providedilierant images tor the tell andnght eye by a grid oi prisms oriurrows in a plastic sheetoverlaying the photograph.Because ol the tilted sui-laces olthe plastic overlay, the tett eyereceives a dilterenl perspective olthe photograph than does the righteye. resulting in depth when thetwo are lused.
The illusion that the red letterson a blue background are in trontoi the background appears to bedue to chromatic aberration oi the
eye. With the object viewed so thatits light rays enter at some angle tothe central axis oi the eye. the bluerays are retracted more than thered rays. This diiierence meansthat only one oi the colors can bebrought to locus on the retina. Theimage in the other color will be ablur to one side ol the sharp image.For example. consider viewingequidistant red and blue points ona card somewhere in iront oi youreyes. Suppose the red point is inlocus. its image lies lurlher trornthe center oi the head than doesthe blue blur lrom the blue point.Such a displacement in normalbinocular viewing is interpreted asindicating the red point is closerthan the blue point.5.134 Exactly why the illusion isseen is not clear. even alter muchdebate in the literature on thasubject. The enlargement hesnothing to do with atmosphencconditions (indeed. retractiondecreases the size oi the moon, asdiscussed in FC 5.18). Instead. theillusion appears to depend on thespace between the moon and thehorizon. For a very large space,corresponding to a large angularelevation ol the moon, the moonappears to be its proper angularsize ol 0.5 arc degree. As themoon descends and the spacebetween it and the horizon {or theob|ects on the horizon) decreases.the rnoon appears to grow.5.135 The rays are actuallyparallel. Their apparent meeting atsome point in the distance is anillusion. A similar illusion can beseen by standing in the middle oi avery long, straight train track- llyoupretend not to know about thedistant track, it will eppear toconverge at some point on the
231 Flying circus 0| physics with answers
horizon.5.130 it you bisect the rnoon withalong stick. it will cut through thesun lust as it should. But withoutsuch a reference. the mentallyextrapolated line bisecllng themoon will miss the sun. The illusion
i results from your perception of thesky as an overhead sphericaldome.5.137 The apparent bending olthe searchlight beam is an illusionthat depends on the illusion ot thesky being an overhead dorne iustas in the previous problem.Holding a straight edge along yourview of the beam will convince youthe beam is really straight.5.138 Apparently an explanationof why the illusion occurs is notavailable. It is a surpnsing illusion
1 in that previous to its publisheddescnption. an elevated objectequidistant with a similar levelobiect was thought to alwaysappear lo be more distant.5.139 Whiteout can come in twodilterenl cases. A ground blizzard
limit visibility to iust a lew feet. Withsuch restricted visibility, a personcan become lost in the swirlingsnow altar walking just a lew feet.Another type oi whiteout is theelimination oi visual clues when
i the ground is covered with snowand the sky is tilled with white
I clouds. The lighting becomes sol diffused that no shadows are cast,* and both the snow and the clouds
appear to vanish. One might thenhave the impression of walking orskiing over a vast white emptiness.Permanent blindness might elsoresult from constant viewing ofsnowlields under intense tigttbecause the visible and ultraviolet
may whip up ell the loose snow to 1
light can destroy part of the visualprocess- tW. C- Burkitt. personalcommunication.)5.140 For an example. consideran astronaut viewing the earthfrom an oibit about B00 km (500mi) above the surtace. ll he usesonly his eyes rather than atelescope. signs of intelligent tileare very dillicult to detect. His eyesare ctiflreclion-limited in theirresolution, that is. the limit on howsmall an ob|ect he can resolve isimposed by the diffraction oi lightthrough the circular opening to theeye. (Some animals are limited intheir resolution because of thephotoreceptor spacing on theirretinas. An image smelter than thatapacing cannot be resolved.) For atypical human eye the emallestobject that can be resolvedoccupies about 0.0005 radian inthe field oi view. This limit meansthat the astronaut can just barelyresolve obiects ol about onekilometer on the earth's surtace.Very lew man-made leatures canbe recognized with suchresolution. Pnmarily the tellteiesigns ot intelligent lite aregeometric structures. such as longstraight superhlghways. In anexamination oi thousands otphotos from the Tiros and Nimbusmeteorological satellites havingresolution limits ot about 0.2 to 2.0km. only a highway and anorthogonat grid oi some Canadianloggers were recognized.5.141 A point source of light in adark room appears as a light streakin the Christmas tree ball becausethe eye can accept reilected lightrays in a significant range oiangles. Mentally extrapolatingthose rays back into the bell givesthe impression that the light
originates from a line source.‘ When the room lights are tumed
on. the pupil size gets cut in halland that acceptance range isdecreased enough that theapparent line source is shrunk to epoint.5.142 The Moire patterns appearaccording to how elements in thetwo overlaying gnds. cloth, and soon. fall in step. For example. thecomb and its rellection willperiodically have teeth exactlyoverlapping, partially overlapping.and then not overlapping at all. Theresulting Moire pattem appears tobe an enlargement oi the teeth inthe comb. or at least anenlargement ol the same type olperiodic stnicture-6.1 Floughly speaking, theettects ol current through thehuman body are the following:
less than 0-01 amp-tingling orimperceptible0.02amp—painful and cannot letgo (see FC 6.3)0.03 emp—breathing disturbed0.0? arnp—breathing verydillicult0.1 amp-death due tofibrillationmore then 0.2 amp—nofibrillation. but severe burningand no breathing
The intermedate range of 0.1 to0.2 amp is strangely enough themost lethal range for commonsituations. because this level olcurrent initiates fibrillation of theheart. which is an uncontrolled.spastic twitching of the heart. Theresulting disruption ol blood flowquickly results in death. Above 0.2amp the heart is merely stopped.and normel first aid procedure canrestart it But another. controlled
flnlwcrl 285
electrical shock is the only way tostop fibrillation. Hence, the 0.1 to0 2 amp range is more deadly thanlarger currents.
The current passing through avictim is usually determined by theskin resistance, which ranges fromabout 1000 ohms for wet skin toabout 500,000 ohms for dry skinThe internal resistance is smaller,being between 100 and 500 ohms.Touching voltsges higher thanabout 240 V usually results incurrent puncturing the skin. Often aperson grabs a wire that hassufficient current to contract hishand muscles onto the wire. Thatlevel is initially not lethal, but theskin resistance drops with timeuntil the lethal level ol 0.1 amp isfinally achieved. It you lind
l someone “frozen ' to a live wi re butstill alive. you should remove thatperson as quickly as possiblewithout endangering yourseli. oreventually the person will die.5.2 An electric potential liesbetween the two metals wherethey contact, owing to thedifference in the enargy levels ofthe conduction alectrons on themetals. when the frog leg touchedthe railing, a complete circuitthrough the railing, support, andleg was made. and electricity[those conduction electrons)
l flowed through the circuit- Thecurrent excited the muscles in theleg, iorcing the leg to contract.6.3 The wire does not captureyour hand with an electrical force.Instead. the current through thehand muscles causes the handmuscles to contract, clamping yourhand around the wire- Eleclnciansworking with live or potentially livewires often use the back oi their
i hands or lingers to move the wires.
If the touch does draw current, themuscle contraction than throws thehand away lrom the wire.6.4 when activated by a nervesignal, the biological cells calledelectroplaques suddenly allow anion l|ow—a currant—across theirmembranes. The electric fish havea series of the cells lrom head totail, and the combined electricpotential frorn each dunng the ionflow [about 0.15 V between theinterior and exterior of the cells)creates a voltage diiierencebetween head and tail. Many suchseries of cells are "wired inparallel in the lish to providesufficient amperage to ilowexternally from its head to tail tostun or kill its food or onomy. Forexample. the Torpedo nobillene(a saltwater giant ray) has about1000 electroplaques in senas andabout 2000 series in parallel. wereell the electroplaques placed insenes. not only would the tish berather long. but also the currentthrough the series would be largeenougi to destroy the cells. Byusing a parsiial wiring of the series.the current through each cell iskept low without sacrificing theexternal cunent Fresh-waterelectric fish have greater numbersof electroplaques in seriesbecause they need morehead-to-tail voltage to force thesame current through the higherresistance ol tresh water.6.5 The microwaves areabsorbed by the meat. mostly bythe water in the meat, within adepth of one to several centimeterslrom tha surface. The rate ofabsorption with depth depends onthe frequency oi the microwaves:the lower the frequency, thegreater the depth Most microwave
ovens operate at a frequency of2450 MHz, which penetrates andheats primarily the first twocentimeters of meat. A microwaveoven is designed to bathe the meatwith microwaves lrom essentiallyall directions. Provided the meat isnot too large, the amount ofradiation reaching the center ol themeat lrom all directions could begreater than the amount absorbedin the first centimeter on any oneside. As a result, the center wouldabsorb more than the outside layerol meat and would cook sooner.However, the result could be iustthe opposite if lt'ie piece ol meat islarge, or if the oven does not bathethe meat. or it the operatingfrequency is high and thus thepenetration depth is smellcompared to the size of the meal6.5 The electrons move throughthe circuit at a relatively slowspeed of 10-“ mfs, but thesignal—~the change in the etectncfield along the wire-moves atnearly the speed of light. It is thesignal rather than the actualelectrons lrom the wire in theswitch that must reach the light.The slgnel may reach the filamentin the bulb in as little as ananosecond [10-9 s). hardlyenough time to bother with.However, the filament must first beheated by the cxirrent through itbefore it can emit light. To emitvisible light, the filament should beseveral thousand degrees Kelvin,and that temperature is typicallyreached 0.01 to 0.1 s atter theswitch is thrown.6.7 When the two materials (e.g.,shoes and rug or cat's fur andglass) touch, electrons lrom one olthe materiels tunnel through theelectrical potential barriers on the
286 Flylng circus ul physics uillh nnnuiern
surlace to the other material. Forexample. when glass touches cat'slur. electrons tunnel lrom the glasssurtace to the lur's surlaca. Sinceneither are good conductors. thistunneling occurs only where thematerisis actually touch To obtainmore trenslerred electrons, morepans ot the materials should be putin contact. Rubbing the surfacestogether is the most convenientway ot putting more parts oi thematerials in contact to obtain agreater transler ol electrons. Thematenal losing the electrons is leftpositively charged: the othermatenal becomes negativelycharged. It the air is damp. theexcess charge drains quickly to theairborne water drops- Smokeparticles could also remove thecharge. Without such discharge.normal contact ot materials canproduce fairly high potentials. Forexample. sliding across a car seatand stepping outside can leaveyou 15 RV higher then groundpotential.6.8 The apparatus must bearranged such that the waterstreams tailing lrom the nozzlesbreak into drops at about the levelot the top cans. Initially. when thewater lirst begins to tall. one can ischarged negatively slightly morethan the other can. which can ismore negative is shear chance.because the initial chargediiierence is due to the charging byeither cosmic rays or the earth'snatural radioactivity. Suppose. torillustration. that the bottom-lelt canin Figure 6.8 is more negative.Then the top-right can will also bemore negative than the top-tett canbecause ol the wiring. Theright-hand stream is polarized as ittalls through the top can. It thedrops develop iust then. the drops
will be positive. the negativecharge in the stream beingrepelled by the can around thestream. Since those drops tall intothe bottom-nght can. that canbecomes more positive thanbetore Although the initial voltagediiierence betwean the bottomcans is trivial. some homemadeKelvin dro-ppers develop apotential diiierence oi as much as15 kV.6.9 The liquid stream breakupwas lirst explained by Fiayleigh.who showed that disturbances tothe emerging stream would resultin waves around the stream axis.these waves growing exponentiallyin amplitude until the streamdisintegrated. Once broken up. thewater pulls together by surtacetension to lorm drops. The breakupcan be avoided or delayed by thepresence ot a charged rodbecause ol the resulting inducedcharge separation in the stream.For example, il the rod is positive.then the stream side nearest therod is negative and that sideturtherest trorn the rod is positivebecause the rod's electric tisid hastorced electrons to llow across thestream to be nearer the rod. Withsuch a charge separation. thestream is less likely to break intodrops. Suppose there is aseparation into drops. Considertwo treshly produced drops lyingalong a line redlally extended lromthe rod. Because ot the inducedseparation ol charge in the drops.their adjacent side would beoppositely charged. and the twodrops would attract each other-Thus. the drops do not iorm in thelirst place. ll the rod is highlycharged, then the stream's nearside is so attracted to the rod thatthe stream is bent lrom its normal
traiectory.6.10 The charging ol wiretences. airplanes. and similarmetallic objects by blowing snow isthe result of the same type otelectron transler as in FC 6.7. Themetallic objects receive electronsirom the snow particles andbecome negatively charged.6.11 The tape separationappears to cause a separation oicharge. the adhesive layer carryingaway a dilterenl charge than thetop surlace ol the tape to which ithad iust been attached. The glowis an electrical discharge betweenthe two surlaces ot tape that havejust been separated.6.12 The sugar is charged as inFC 6.10 and 6.7 when it is sitted-Since the felling sugar grains thenhave like charge. they repel eachother. and some ol the sugar ispushed to the side.6.13 Contact between the tiresand the roed leaves the tiresnegatively charged. As the tiresrotate and become unitomilycharged. the negative electrons inthe metal body and lrame arerepelled by the tires, leaving thebody area near the tires positivelycharged. Sparking between aparticular part ol the car and somenearby grounded or oppositelycharged body is then possible. Thesparking would be merely anuisance except in the case olgasoline trucks where gasolinetumes may be ignited. Years agochains were dragged lrom thetruck's body and on the ground inthe beliet that the chains wouldcontinuously discharge the truck.The chain would drain some ot theelectrons lrom the tn.ick's body, butthat would not leave the truck
Anew:-re 287
neutral and thus sale because itwould then be positively chargedand hence still susceptible tosparking.6.14 Details oi the chargeseparation in the splashing oiwater are not presently weltunderstood. ln the nineteenthcentury, however. Lenard showedthat the larger drops lloating in theair near the splashing werepositively charged. whereas thesmaller drops were negativelycharged. Since the larger dropssettle more quickly than thesmaller ones. the air is tett withnegatively charged drops and arather large electric lield.6.15 Apparently the ellect oicharge on a human being is riotlully verilied. much less explained8.16 Tl'le basic toroe preventingyou lrom tailing through yourshoes. the tloor. and the ground isthe electrical repulsion betweenthe atoms in each set ot adjacentsurlaces. {Also see FC 7.24.)6.1? Four types ot toroes mayhold a powder together. If theparticles are less than about 50microns. van der Wears toroe (anattractive toroe between atoms}may be important. Electrostaticattraction oi unlike charges on thepowder grains can also hold thegrains together. ll the powder isdamp. then the water can bond thegrains by essentially a surtacetension type oi torce. [But it there istoo much water, the powderbecomes lust a slush.) And linally,it the particles are irregular inshape. their interlocking holdsthem together. Current researchon powders and crumb tormationattempts to explain the bulkcohesion oi certain powders in
microscopic scale.6.18 Static electricity on theplestic wrap causes the wrap tocling to itselt and to most toodcontainers. For example. it thelayer oi plastic next to a metal wallhas an excess ol electrons. then itrepels the electrons In the metal.The araa next to the wrap is thuslelt positive and attracts the wrap.Since the wrap is not a goodconductor ot electricity. its staticcharge does not readily drain to themetal. As a result, the plasticclings. Soma ol the static chargeoriginates when the plastic roll isbeing manulactured. Indeed,avoiding static charge during theproduction would ba dillicult. Morecharge separation can occur whenyou pill the plastic oll the roll: ataster pull produces more charge.Humid air or a wet container drainsthe static charge and thus reducesthe cling.6.19 The ink in the dollar billcontains magnetic salts. probablytron salts. that are attracted to oneot the magnet's poles.6.20 The lluid in the leveler isdiamagnetic_ that is. when it isplaced in a magnetic lield. itproduces a magnetic lield in theopposite sense. The lluid isrepulsed lrom the magnet. therebyforcing the bubble toward themagnet.6.21 A changing current in thecoll creates an accompanyingchanging magnetic tisid in whichtha ring lies. That lield in turncreates a current in the nng suchthat the magnetic lield ol thelnduoed current is opposed to themagnetic lield oi the coil. ‘Theseoond magneticlield supports thering in the lirst magnetic lield. ll
change oi current in the collinduces a larger current in the ringand thus a larger magnetic fieldthat may be sulticient to send thering upward.6.22 The alternating magneticlield induces currents in both thelixed sheet and the disc. Withoutthe lixed sheet. the pen oi the discover the magnet would lully havesuch induced currents, whose llowwould be in such a direction thatthe magnetic tield created by thellow would cause rapulsion ol thedisc by the magnetic lield lromthe magnet. Without the lixedsheet. the disc would theretore berepulsed by the magnet. With thesheet in place. however. theinduced currents in it and in theunshaded portion ot the disc attracteach other (the magnetic lield oione oi the currents iorces the othercurrent ctoserl. and the disc iscontinuously rotated.6.23 The changing magneticlield from the rotating magnetinduces currents in the aluminumdisc. These currents in turn set uptheir own magnetic lield. Theinteraction of the two lields createsa torque on the disc. causing it toturn in the same sense as therotating magnet.6.24 Why not build this simpledevice to see it it is truly workable’?ll the magnetic lield is strongenough to start the ball up theinclined plane, won't it be strongenough to prevent the ball lromslicing down the ramp undemeaththe plane?6.25 The penetration depth oiradio waves through theionosphere depends on thelrequency of the waves. Theionosphere is transparent to the
_terms oi these iorces on the . current is switchedon the sudden
258 Flylng circus ol physics with unaware
relatively high lrequency wavesused in TV and FM radiotransmissions. However. the lowerlrequency waves used in AM radiotransmissions are reilected lrornthe ionosphere. Thus. to receive apanicular TV or FM program. thereceiver must be near thetransmitter to receive either adirect signal or at least a signalrellecled lrom the environment(buildings. etc.). In the AM case.the receiver can be distant since itcan use the signal reilected lromthe ionosphere Occasionally thehigher lrequency signals arerellecled lroni the ionosphere andcan be received at surprisingdistances. Such retlectrons arelikely due to the increasedionization in the ionosphere dunngmeteor showers or dunng what iscelled sporadic-E conditions. Thelatter increase in ionization is notcurrently understood very well. butmay be linked to increasedradiation lrom the sun. Therollecting level oi AM signals risesat night because the lack orsunlight decreases the ionizationot the molecules on the lower sideoi the ionosphere. With e higherrellecling level. the AM signalstravel lurlher around the curve clthe eanh. To avoid anunmanageable mess ol signals.the FCC requires most stations tocut their power or to leave the airdunng the night6.26 The receiving circuitresonates at a panicular lrequencythat depends on the magnitudes oithe capacitance [ol the capacitor}and the inductance {oi the coil). Byvarying the contact on the coil. theinductance can be altered. thuschenging the lrequency at whichthe circuit responds. The incomingsignal is sinusoidal. Since the
average power absorbed lrom esinusoidal signal is zero. thelistener would hear nothing werethe signei not changed. Theoontact between the metal'whisl<ef' and the crystal allowsthe current to llow li"l one directiononly. Thus. the signal is reclltred.because hell the sinusoidal (saythe negative part) is removed. Withonly halt the sinusoidal wave in thecircuit. the average powerabsorbed ls no longer zero. andthe listener can hear the signal.6.27 The airplane rellects the TVsignal to your antenna slrglttiy laterthan the direct signal is received.The direct signel places an imageon the screen; the later rellecledsignei places another. lalnterimage to the right on the screen--aghost image—that changes as theairplane continues to move. Theghost is to the nght because theelectron gun producing the screenimage scans lrom your Ielt to yourright.6.28 The AM transmitters havevertical antennas It the radio waveis directly received by the car'santenna the electric lield in thatwave is polanzed along the sensebl the transmitting antenna. inother words. vertically To gain themaximum signal strength. thereceiving antenna should also bevertical.6.29 in the FM region theappearance ol the same signal atmultiple places across the dial isdue to the nonlinear re ' ponse olthe receiver in the presence ol every strong signal. the ellect iscalled crc:. ii modulation. in the AMregion. a signal can beoverwhelmed by a stronger onenormally at a dilterenl lrequency itthe receiver is near the transmitter
oi the second sig nel. Both thetransmitter and the receiver wont ina rather narrow lrequency range.However. neither is exactly at asingle lrequency. For example. atransmitter may be primarily at11.000 kHz. but it may also betransmitting a lreciion oi its powerat 11.500 kHz. A distant receiverwould not sulticiently amplify thisvery weak signal at 1 1.500 kHz tor itto be heard. ll a nearby receiver istuned to another station whoseprimary lrequency is at 11.500. itmay also receive and sutlicientlyamplrly the undesirable signal lromthe lirst station.6.30 Low-energy solar electrons[with energies in the hundreds oielectron volts) are swept into theplasma tail on the anlisolar side oithe eanh. are somehow increasedin energy (to several thousandelectron volts). and then aredirected into the atmosphere nearthe poles by the earth'slield lines. Those lines enter andleave the earth at the magneticpoles. which are oltset somewhatlrom the geophysical poles aboutwhich the earth spins. Theenergized solar electrons enter theatmosphere in an oval around themagnetic poles and excite nitrogenmolecules and oxygen atoms bycollision. Green light is emitted bydeexcitrng atomic oxygen ataltitudes lrom 100 to 150 km.Higher atomic oxygen produces astrong red light. Fled light alsocomes lrom deexciting molecularnitrogen. These colors areobsenied in the ovals around themagnetic poles along thegeomagnetic latitudes around 70°.With the north geomagnetic pole inCanada. this arrangement placesauroras over southern Cenada andnorthern United States. The same
Answer! 289
1:
geophysical latitude over Siberia isat a tower gsomagnetic latitudeand has tewer auroras6.31 Lightning sends outelectromagnetic pulses that arelirst heard directly as clicks on thedetectors. Part of the pulse wavestravel upward. Those wavestraveling upward are concentratedinto a beam in the ionosphere andare then bent over such that thebeam travels along one oi themagnetic lield tines oi the earthWhen the beam reaches theopposite pole raglon, it is reilectedby the stronger magnetic lields andreturns along atield line to near thepoint oi origin. But not all oi thebeam travels at the same speed:the higher lrequency componentstravel taster. When the returningbeam is detected. the higherlrequencies are heard lirst. andthen progressively lowerlrequencies arrive Instead oi theonginal click being repeated. thiselectromagnetic echo lasts longerand descends in pitch.6.32 In a normal lightning strokethe charge distribution in the cloudis the iollowing: small amount oipositive charge at the base. largeamount ol nagative chaige in thelower middle. and large amount oipositive charge in the top. Thestroke bagins with a dischargebetween the base and the lowermiddle, bringing electrons down tothe base. This discharge proceedsirom the base downward by a' stepped leeder_ ' which jumps inlengths oi 50 m, pauses about 50as, and then jumps again. Eachtime. negative charge drains iromthe cloud to the bottom ol thechannel. Only the lower tip oi theleader is visible. but the motion isso rapid at this stage and the
following stages oi the stroke. thatthe whole process appears to beluminous. The leader is crookedbecause the path ot thedescending channel is deviated bypockets ol positive charge in theair. It a pocket is sutliciently strong,the leader may even be turnedhorizontal
When the leader is near theground, the electric lield nearsharp points is suiiiciently high thatelectrical breakdown occurs and apositive return stroke starts upwardto meet the leader. The point olmeeting is highly luminous as thenegative leader is neutralized andits electrons are brought to ground.This region ol high luminosity andcurrent propagates up the leaderchannel UI'ill| it reaches the cloud,but the obsenier cannot resolvethe rapid motion and seas acontinuously luminous channel.The leaders trip down takes about20 ms. whereas the return stroketakes only 100 as. The light comesirom the center ol the leaderchannel. probably irom a core nowider than a lew centimeters.6.33 The earth's electric lield,which lies between the negativelycharged surlace and the positivelycharged upper atmosphere, shouldbe discharged in 5 min or lessbecause ol the constant ionizationoi air molecules by cosmic raysand the eanh's naturalradioactivity. Some ol the electronsirom the ionization move to theupper atmosphere where at analtitude ol about 50 km theconductivity is so good that theatmosphere is essentially asphencal conductor. The risingelecii'ons will neutralize thispositive conductor. Similarly. someoi the positive ions irom theionization descend to the negative
ground to neutralize it Becausethe worldwide current resultingirom the ionization is about isooamps, both the ground and theupper atmosphere should bedischarged in a lew minutes. Theyare not, because the worldwidelightning activity is constantlyrecharging the earth withelectrons.
There may be a 200-Vdiiierence between the heights olyour ieet and nose. but your bodyis such a relatively good conductorthat all oi it is at essentially thesame potential. Hence. noSigl'iillC<':lI'l| voltage diiierence existsacross your body.6.34 The cloud-to-air stroketerminates in a pocket oi positivecharge in the air. The ribbonlightning occurs when the wind isstrong enough to move the ionizedchannel noticeably betweenstrokes when more than iust theleader and return strokes runbetween the cloud and ground.Bead lightning is not wellunderstood. it may sometimesoccur when the stroke is partiallyobscured by rein so that theobserver is not blinded by the llashThen. as the luminosity dies away,those portions of the stroke runningalong the observer's line ol sight willlast slightly longer because ot thegreater amount ol light when such aportton is viewed on end. However.the bright beads may also occur tordilterenl, and as yet unknown,TBHSDFIS.
6.35 The nature oi ball lightningis still current research, and anyexplanation given here may besoon proven wrong. Probably thebest explanation to date is that theball is a plasma ball that is tedenergy lrom externalelectromagnetic waves. Some
290 Flylng circus ol phpolcl with nnouie-re
electrical activity oi athunderstorm, lightning. or pointdischarge initiates ionization oi theair or oi a vapor gas {it somethingsuch as a metei conductor hasbeen struck). The ionized gasremains integral because oi itsoverall electrical neutrality. butgrows to some equilibrium sizebecause it absorbs energy iromnatural radio waves. Such wavesare known to be generated eitherat the clouds or at the grounddunng intense eiectncal storms.The environment oi the ballimposes constraints on the radiowaves. creating standing waves.and the ball absorbs energy iroman antinode in such a standingwave. An external source otenergy like this is appealing,because the relatively long-livingluminosity oi the balls is otherwisevery dillicult to explain. ii the light isonly irom en internal source oienergy, and ii a nuclear iireball isscaled down lo the size oi balllightning in order to put an upperlimit on such internal energy, thebail woitd glow tor no more thanabout 0.01 s instead oi thereported several seconds.6.36 The H-bomb lightningstrokes may have resulted irom thecharge produced when gammarays lrom the burst scatteredelectrons irom the air molecules.The leaders tor the strokesapparently propagated upwardlrom the instrumentation structuresnear the surtace. Similar upwardpropagating leaders, whichcontrast with the downwardleaders oi nomal lightning (FC6.32), have been seen startingirom tall structures such as theEt'nptre State Building. Since theleaders run upward, so does thebranching.
6.37 The hot lava hitting theseawater sends positively chargedsteam upward Alter sutticientcharge separation has occurred.the clouds oi steam dischargeback to the ocean, allowingelectrons to ilow upward throughthe ionization column. The upwardilow oi electrons is opposite thesituation with normal lightning (FC6.32).6.38 Earthquake lightning is notwelt understood. Fleoently it hasbeen attributed to piezoelectnclields created when seismic wavespropagate through either thesurtace or low-tying rocks. (In thepiezoelectric ellect, electric fieldsare created in a matenal when thematenal is placed under stress.The diamond used in modernrecord players is an example oi apiezoelectric crystal whose electriclields are created by the stressirom the bumps in the recordgrooves.) Supposedly such electriclields would be large enough tocause atmospheric discharges onthe surlaces. However, details andprool oi this model are currentlylacking-6.39 The pointed wire was toprovide a suilictently high electriclield that enough current would beattracted to allow Franklin to do hisexperiments (The sharper theobject, the greater the electric iieldis around it ) The silk ribbon wasinsulation between himselt and thewet conducting twine. The keyprovided several sharp points torvisible discharge oi the electroncurrent descending the twine.Otten Franklin is pictured doingthis expenrnent during a lightningstorm. He was never that stupid. Alightning stnke to the kite wouldhave destroyed the kite. the twine.
and possibly Franklin, regardlessoi a trivial piece oi silk. In actuality,Franklin ilew his kite betore the tullstomi arrived.6.40 The purpose oi the lightningrod is to provide a sate route toground tor the descending current.The sharp point has a high etectnclield around it and can initiate theupward traveling channel thatmeets the downward travelingleader stroke (FC 6.32). Oncecontact is made, the electroncurrent ttows lrom the ionizationchannai and through the rod to theground in which the rod is buried.The possibility oi the stroke hittingthe structure to which the rod isattached is thereby reduced. Thelightning rod cannot appreciablydischarge a passing cloud to avoidlightning because such dischargeis too slow. The radioactive sourceproposed tor the rods would haveno ellect and probably would proveto be dangerous ti a lightning strikeruptured the source.6.41 ti the tree is thoroughly wet,the current descends through thewater sheath and leaves the treeunharmed. ii not, the current mayenter the tree to descend throughthe sap. The rapid heating andexpansion oi the sap then blowsthe tree apart. Oak is moresusceptible to explosions thanmany other trees because it hasrough ban<. It the lightning strikeoccurs early in the rainstorm, itmay lind only the top part oi an oakwet, whereas a smooth bark treewould be wet to the ground. Theoak would be blown apan, and thesmooth bark tree tett untouched.Forest tires are initiated bylightning strokes in which there is acontinuous current running throughthe lightning channel between the
Anlurere 291
main strokes. that is, between thefirst return stroke and the lollowingones. Since the continuous currentis not always present, not alllightning strokes to trees would setthe trees on tire.6.42 The high lrequency currentoi a lightning strike does notpenetrate the metal walls of a car,airplane. and the like. but stays onan outside layer oi the metal.Barnng a puncture to the tuel andthe consequent explosion, theoccupants in such a metalenclosure will probably riot evenknow that they have been hit6.43 At times the water dropletsin the clouds are partiallysuspended by the local etectnclields. A lightning stroke occurringthen may decrease those lields.causing an enhanced tall oi thodroplets-~a rain gush. As theetectnc lields regain their strength,the precipitation decreases.6.44 ‘l'he rapid evaporation andexpansion of the moisture on yourskin blows your clothes and shoesoil. You may be otheiwiseunharmed it little oi the currententered your body-6.45 Alter reaching the ground,the lightning current spreads outand runs partially horizontal. ii acow stands as in Figure 6.45. anappreciable amount Of the groundcurrent enters the tront legs andexits irom the rear tags,electrocuting the cow ll you arecaught outside during athunderstorm. you should not liedown It a strike hits nearby. theresulting electncel potentialbetween your head and your ieetmay draw enough oi the groundcurrents to kill you. Since you alsoshould not stand up. the best
position is to squat. That way youkeep your head low whileminimizing the contact area withthe ground. With minimal contactarea, the possible electricalpotential irom one side oi thecontact area to the other is least.and you will draw the least groundCUtfBl'll.
6.46 and 6.48 Ground-level St.Elmo's lire and the Andes glow areboth examples oi corona dischargein which the electric lieldsurrounding obiects, usuallypointed ob|ects, is sutticiently highthat electncal dl'I harge can 0oi:- irThe Andes glow is an especiallystrong type oi corona. not lullyunderstood yet. St Elmo's tire canalso occur on aircraft tlying throughrain or snow because oi thecharging discussed in FC 6.?6.i0, and 6.146.47 ll a massive current entersa victim s body, the person willlikely die because oi intemal burns.But the lightning may not penetratethe body it the person l5 wet Then,most oi the oirrent descendsthrough the water sheath on thebody. (Wei trees struck by lightningmay be completely unharmed. SeeFC 6 41.} In this case, the victim'sbreathing end heart may bestopped by the electrical shock, butqutclc application oi ariiticialrespiration can revive the person.Many times a lightning victim doesnot suller a direct hit. but is hit by aside-sr ash lrom the ob|ectsuilenng the direct hit or is tailed bythe ground currents ot the hit (FC6.45]. One relerence sugg-i als thatmost people dying lrom lightningdo so only because rescuersprematurely give them up tor dead.Hence. common tirst aid toretectnc shock should always be
given a lightntng victim6.48 See FC 6.466.49 The pinwheel does notmove because oi somethingthrown oil or pulled on. butbecauss oi the ionization oi the elrnext to the point. Once the air isionized in the high electric lield oithose points. the ions and the pointhave the same sign oi charge andthus repel each other. Theionization and consequentrepulsion occurs regardless oiwhether the pinwheel is chargednegatively or positively.6.50 The alternating high voltageinduces an altemating current innearby metal obiects. which thenmay be discharged by an unwaryperson grounding part oi theob|ect.7.1 As lascinating as thepossibility ot communicating withan extraterrestnal civilization ls.one should remain somewhatskeptical about the occasionalltood ol tlying saucer"sightings-at least skepticalenough to retain the fundamentalphysics man has developed. Manyoi the sightings would have toviolate these basic laws it theywere truly sightings ot machines.The gravity shielding scheme isuntenable. ll, as in H. G. Wells‘story. a ship could be shieldedirom the eanh's gravity but stillexposed to the moon's gravity. theresulting acceleration would beridiculously small. about a I'l'll||lOl'llhoi the acceleration oi a lreelytailing body near the earth ssurtace. Besides. there isabsolutely no evidence torantigravity or gravity shielding, andsuch ettects might even betheoretically inconsistent with
292 Flying circus ol |-thyeilcc rtvlllI IIIIBIUOII
modern piiyeica7.3 Numerous arguments havebeen published to resolve theparadox. ranging trom limiting theextent oi the universe to a linileradius. to red-shitting the light Iromvery distant stars so severely that itis essentially nonexistent. [Thered-shill is the Doppler shill oi lightlrom a source moving away lromthe observer and is similar to theDoppler shiti in sound (FC 1 Ei5\ IProbably the best argument is arecent one {1587}. The sky is notablaze with light because a theorythat assumes that ail the stars inthe universe are lit simultaneouslymust be wrong. The typical lifetimeol a star can be taken as about10"’ years. Although this timeseems very long. it is not whencompared to the time about 107*‘years necessary lor the universe toreach thermodynamic equilibrium."In other words. this means that theluminous emissions lrom stars aremuch too toable to till in theirliletime the vast empty spacesbetween stars with radiation ol anysigniticant amount. '7.4 The nature oi noctitricentclouds is sun controversial. butthey are probably due to thecondensation and lreezing oi wateron dust particles at themesopause. which is a relativelylow temperature region near thealtitude oi 90 km. The dust couldbe cosmic dust {star dust). cometdust thrown oil during a comet'spassage by the sun. or dust lromthe astroidal belt. The clouds canbe seen only during sunsetbecause they are so ialnt Theycan be seen then only becausethey are so high that they are stillilluminated by the setting sun whenthe ground observer has entered
twilight. The wavy structure is dueto the passage oi atmosphencgravity waves. periodic variationsin the density and temperature oithe air.7.5 I have no answer to thisquestion, and the literature is oi nohelp in resolving the controversy.Expenments to show the statisticalsuccess oi water witches isunconvincing and marginal andleaves the reader a believer only ithe or she were already a believer.Unless someone publishes a verycareful experiment in which thesignal is ctearly shown. waterwitching will remain controversial.For example. it the water witchsubconsciously detects a veryweek electromagnehc noise signalirom running water. then thatsignal will have to be detectable onsensitive instruments and thencorrelated with the water witch'ssucce< -i.7.6 The snow waves areprobably the progressive loweringoi snow that lays over a structurallyweak layer oi hoartrosi. a situationthat is also responsible tor someat. -i zitches (FC 3.47].7.8 The original. purelytongue-in-cheek calculations byDavid Stone (1424) indicated thatsuch a iump by the Chinese wouldproduce an earthquake with aFlichler scale magnitude oi 4.5.The |ump would suraly devastatepart oi China. But il the groundwave is resonantly amplified.destruction elsewhere would alsobe possible To make resonance,the Chinese would have to jumpevery 53 or 54 min. the time aground wave requires to circle theearth. To protect itsell. the targetnation would have to organizeiumps whose waves would cancel
the Chinese-generated waves.Since the target nation would havea smaller population. the jumpswould have to be lromproportionally greater heights. Onewnter to Time magazine arguedthat any iumps mist be with stitfknees in order to impart thegreatest energy to the waves. Thediiierence between stitl- andloose-knead iumplng is not clear tome. since the energy mipartedmust be the gravitational potentialenergy in both cases. But were hisargument correct. he points outthat a resonant wave ‘would not begenerated . because the onlyweapon derived from the actionswould be the ear-shatlenngscream lrom 750 million badlymaimed Chnese" (14251.7.9 The protein molecules in theegg white are initially in aspagheltilike mess- Beating orheating the egg whites untangiesthose long molecules. and theythen can attract each othersuilicienlly to give a lirmerstmcture.7.10 Apparently no completeexplanation tor the compressionpoint has been published. althoughone could guess that it ls causedby the llow ot the adhesive tayerbeneath the tape toward theseparation point7.11 through 7.13 These threephenomena are really the same. I'llexplain the lirst one end leave theother two tor you- OsborneFleynolds explained the whiteningot beach sand in 1885 when hepointed out that the sandexpended when stepped on. Priorto the pressure. the sand grainswere as closely packed aspossible. Under the shearing lromthe iootstep. the clisturbance to the
Answer! 293
grains could only result in lesselticient packing. In other words.the sand was torced to occupymore volume because oi thesheanng. Whereas the ssnd levelsuddenly rose. the water levelcould change only throughcapillary action. and that tooksome time. Thus. just alter theiootstep. the sand beneath the loothad risen above the water andwas. lor a little while. dry and white.7.14 Fleceni publicationsindicate that the radiation level inhigh altitude iets is not ol muchconcem. Flediation irom the sunoco.irs principally during solarllares. and those are beingmonitored. The more senousdanger was thought to he in theheavy nuclei irom our galaxy thatcould produce 1000 rads near theend ol their traiectory ii they stop inhumen flesh. This rate should becompared with the limit oi 100 radsper week tor radiation workers.However, the heavy nuclei tlux atthe llight altitudes is only a lewpercent ol that in space and isthought not to be a senousproblem alter alt. (Improperlyshielded astronauts will have moreto worry about-) Although theprimary cosmic particles areapparently sale tor airplanepassengers. still uncertain is theellect ol the secondary neutrons.low-energy protons. and alphaparticles produced by the primarypanicles.7.15 The ilashes observed byastronauts and by researcherssitting in the beams ol acceleratedparticles are likely produced by avanety oi mechanisms Either thecosmic ray panictes or theman-made beams might be able toproduce light by Cerenkov
radiation in the eye. directexcitation oi the retina. andlluorescence oi the lens.(Cerenkov radiation is thatradiation accompanying a particlewhose velocity in a materialexceeds the velocity ol light in thatmaterial. The radiation iorms abow wave with lhe particle at thevertex. similar to the bow wavelormed in the shock wave oi asupersonic airplane.] Some oi thelight ilashes are probablyconnected with the phosphenesdiscussed in FC 5.121.7.16 The ability oi using X-ray.inlrered. and ultraviolet light toexpose multiple layers ol paintingslies in the dilterenl responses oithe ditlerent paints and othermaterials used in the paintings Forexample. inlrared analysis ol "TheMarriage ol Amoilini" by van Eyckexposed an original sketch olArnollini's right hand that was donein charcoal on the white chalkbackground. That sketch wasbu ned beneath the iinal painting oithe hand. In the infraredphotograph the charcoaled handappeared because it greatlyabsorbed the inlrared whereas thewhile chalk did not; the hand thusappeared dark in the photograph-Under ultraviolet light. dilterenlpaints tluoresce differently. andalterations to original paintings canbe detected in a similar manner.7.1? Part ol the energy irom theparticte and electromagneticradiation emitted by the initial burstis absorbed by the air in theimmediate vicinity oi the burst.Those air molecules are highlyexoted or ionized. and theresulting deexcitation andreoombination yields visible light.About halt oi the initial burst energy
‘F " ' i lis released as mechanical energy[and develops a shock wave}.about a third emerges aselectromagnetic energy (infraredvisible. UV. X rays. and gammarays) and the rest is given toparticles. The shock wave rapidlycompresses the air. heating it toincandescence. The temperatureol the iirebatl's surface about 104s alter burst can be 3 x 105 K orgreater. The iireball expands andcools. and eventually the shookwave breaks away lrom the balland thus no longer causesincandescence.7.18 Although Herbert did nothave this ll"‘l mind. there is ananalogy in physics. Ii a metal plateis swung into a magnetic lield.such as a metal pendulum swungbetween the pole laces oi ahorseshoe magnet. the kineticenergy oi the plate is lost to Jouleheating in the metal. This toss isdue to the currents created in theplate by the change in themagnetic lield experienced by theplate swinging through the magnet.For example. the lield lirstincreases as the plate nears thepole laces. and then decreases asthe plate swings away. Thecurrents created in the plate heatthe plate in the same way thatelectric currents heat the coils lI'l anelectric oven. The original kineticenergy oi the moving plate iseventually dissipated as thisheating. and the plate stops.7.19 Modem work on inctiondiscrodits the old theory about itoriginating entirely lrom surtaceinegulanties and instead points tothe adhesion between the surlaces(due to molecular attraction} asbeing the main cause ol iriction. inspite ot this work. many physics
291 Flylng drcul 0| pliyllcl nil
\ textbooks still regard lriclion asbeing due only to hills and valleysin the suriaces jamming together.7.20 Pure lead is sott; it can becut with a lingernail. When theCathedral's root heated dunng aWashington summer day. it mighthave reached temperatures near80°C. high enough that the leadbecame malleable enough to ilowunder its own weight. Less pureteed would be less malleable. andthe root was remade with an elloyoi 94% lead and 6% antimony. TheEuropean structures did not havesuch a problem because their leadwas unpure to begin with andbecause their summar days werenot as hot.7.21 Cracks begin at small.perhaps invisible detects that lormwhen the matenal is lirst labricaledor that develop later under thewear and tear oi use. These cracksgreatly weaken the materialstructure. because theyconcentrate an applied torce onthe vertex ot the crack. Suchconcentration means that a torcenormally too small to rip thematerial apart it there were nocracks. can now propagate thecrack through the ob|ect. Somecracks expand because otcorrosion. Foreign molecules mayenter the crack. break the bondingot the matena|'s molecules at thecrack's vertex. and then react withthese molecules. Ii the resultingnew molecular structure occupiesmore volume than the originalstructure. the new structure priesthe crack open.7.22 The corrosion begins whenelectrons released by the wet nickeltunnel through the oxide layer onthe chromium surlace to reach an
oxygen species. As a result. thenickel is slowly dissolved at thedetect site. But the rate ot thereactions is controlled by theelectron llow. ll only a lew detectsare in the bumper. the electronscome lrom only those lew places.the nickel there is relatively quicklydissolved. and the iron layer is soonexposed and becomes rusty. Itthere are many (small) detects.then lewer electrons come lromeach, and the dissolving ol thenickel and exposing and rusting otthe iron at each detect are muchslower. giving a longer lite to thebumper.
surtace does not depend ontransleiring material lrom the hillsto the valleys on the surtace or onhearing the surlace The lirst doesnot occur. and the latter may beundesirabte it the surlace issulticiently heated as to developwaves. Polishing removes mater:lrom the hills on the surlace Undera heavy load, larger pieces olmaterial are removed; under a lightload. individual molecules areremoved. Eventually the hills areworn down to the level ot thevalleys. and the surtace is thensmooth on a microscopic level.
7.23 The process ol polishing a
at
7.24 Adhesives are adhesivebecause ol molecular attractionbetween the suriaces oi theadhesive and ol the material towhich it is applied. Any materialcould be an adhesive. althoughmost are not uselul because ottheir other properties. Forexample. liquid water could gluethings together were it not Ior itslow shear strength Mostedhesives are liquid. at leastinitially. because cl the need tor
close contact between the glueand the materials being glued- Inorder tor two suriaces to adhere.they must be within a lewangstroms ol each other. (Anangslrom is 10 "1 m. about thesize ol small atoms andmolecules.) Most solid suriacesare too rough to allow more than atiny amount oi their surtace area tobe this close. A liquid glue can llowinto those surface irregulanties andthus provide the close conle cl.Another reason most surlaces.such as the broken edges oi mycoitee cup. do not edhere oncontact is that they are dirty. Werethey both dean and smooth. thesurlaces might spontaneouslyadhere. as was teared in the earlyspace missions. Suchspontaneous edhesion can beobserved in treshly separatedlayers oi mica- It you reioin thesurfaces a lew seconds atterseparation. the layers edhere.However. it you wait tor severalminutes. the air and its dust willcontaminate the exposed suriacesto prevent any such adhesion.
Anluretl 295
