Motion-Mountain-The-Adventure-of-Physics-1-of-6-22nd-edition.pdf

7/22/2019 Motion-Mountain-The-Adventure-of-Physics-1-of-6-22nd-edition.pdf

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Chrsph Schller

MOTION MOUNTAINthe adventure of physics

fall, flow and heat

..


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Chriph Schir

Motion Moun tain

T Avur Phyic

F, F H

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E .

P C S O .

O .I .N q, q ; .

- , , ISBN 978-300-021946-7.

C 2009 C S, 29 th O.

T f C C

A-N-N D W 3.0 GL, .//--/3.0/, , , , any , , . T f , , , f .
http://creativecommons.org/licenses/by-nc-nd/3.0/dehttp://creativecommons.org/licenses/by-nc-nd/3.0/dehttp://creativecommons.org/licenses/by-nc-nd/3.0/de


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E B


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D M , S .


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Preface

P , .*

Aq

T I 1990: , .

I simple, , . U . T .O : everyday , , , , - . N : . T . I , F 1,

.I up to date,

.I vivid, . R

. W , -, , , . W , . T - : , . N .H .

G

. T , die Menschen strken, die Sachen klren, H H , : , . E ; . C , ; . T : , .

E , 8 J 2009

Advice for learners

I , - : , , in your own words, aloud. I ,

* F , . I , ( ) motivating; L .

Mo

tionMountainTheAdventureofPhysics

availablefreeofchargeatwww.motionmountain.eu

CopyrightChristophSchillerNovember1997January2009


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preace

Galilean physics, electricity and heat

Adventures: sport, music, sailing,

cooking, using electricity and computers,

understanding the brain and people

Special relativity

Adventures:

understanding time

dilation, length

contraction

and E=mc2

Quantum theory

Adventures: death,

sexuality, biology,

enjoying art, colours

in nature, all high-tech

business, medicine,

chemistry, evolution

Quantum

theory with gravity

Adventures: bouncing

neutrons, under-

standing tree

growth

General relativity

Adventures: the

night sky, measu-

ring curved space,

exploring blackholes and the

universe, spaceand time

(Unified) theory of motion

Adventures: understandingeverything, intense fun

with thinking, catchinga glimpse of bliss

G c h, e, k

PHYSICS:

Describing motion with action.

Classical gravity

Adventures:

climbing, skiing,

space travel,

the wonders of

astronomy and

geology

Quantum field theory

Adventures: building

accelerators, under-standing quarks, stars,

bombs and the basis of

life, matter, radiation

How do

everyday,

fast and largethings move?

How do smallthings move?

What are things?

What are space,

time and quantum

particles?

F IG UR E 1 A complete map of physics: the connections are defined by the speed of light c, thegravitational constant G, the Planck constant h, the Boltzmann constant k and the elementary charge e.

. R , . Y , , . I , -

. I , . M , , .

Using this book

, , . G , ,

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preace

, URL .S challenges . C -

(), (), () (). C

, ().

A request

T . I , :

W ? W , , , ? W ?Challenge 1 s

F ../.

. Y ../. O , . F - , , . B , .

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Fall, Flow and Heat

I ,

, , , ,

.

W ,

,

,

.


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Contents

Why should we care about motion?D ? 5 H ? W ? P, D ? 5 G C S

From motion measurement to continuityW ? W ? C W -? D ? W ? A ? S , W ? 5 A E? 5 C 5 S

How to describe motion kinematicsT, E W ? W ? A O 5 L

C S

From objects and images to conservationM W ? M 5 I - ? C M R R H ? C S

From the rotation o the earth to the relativity o motionH E ? 5 D E ? I ? T I ? 5 C L ? A S G

Motion due to gravitationP D -? G T M 5 O 5 C ? 5 W ? A 5 C 5 S

Classical mechanics and the predictability o motionS ? P? F F, , - C D - ? I ? F S -

G Measuring change with action

T L W ? C L S

Motion and symmetryW ? V S- R 5 S, G


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contents

R, N C- 5 P S-

Simple motions o extended bodies oscillations and wavesW W ? H - W ? S S - C 5 S

Do extended bodies exist? Limits o continuityM C ? T G G H ? F T L T 5 C 55 C S W ? F

From heat to time-invariance T E F D ? W ? T - B E T q W ? I ? W , 5 C S -

Sel-organization and chaos the simplicity o complexityC - S - 5

From t he limitations o physics to the limits o motion

R W ? P C ? S W ? I - ?

a Notation and conventionsT L T G T H 5 D 5 T C- P N A ?

Bibliography

Challenge hints and solutions

Credits

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C h a p t e r 1

WHY SHOULD WE CARE ABOUT

MOTION?

A .

Z E*

Wham! T

. I . T

. N, , - .

M : , . I - . W , , . W , . L , . L , , . L , .

M . I everything . T .M I-E . T . B bce G, : physics.Ref. 1

M . W ? W ? W ? W ? W ? W ? W ? W ? W ? A . T .

M . T , , Ref. 2

25 : what is motion?W , , . J . T .

M . I , , , . N

* Z E (c. 40 bce), E .

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why should we care about motion 5

Physics

Motion

Mountain

Social sea

Emotion bay

Medicine

MathematicsThe humanities

Astronomy

Material sciences

Geosciences

Biology

Chemistry

Engineering

theoryof motion

quantum

field theory

quantum

theory

mechanics

electromagnetism

relativity

thermodynamics

F IG UR E 2 Experience Island, with Motion Mountain and the trail to be followed

. F ,

. T I M M ( F 2; F 1). T . T :

Does motion exist?

Das Rtsel . W F , kann .*

L W, ractatus, 6.

, F 3 F 4 . I . O Ref. 3 I K A .../~. H Ref. 4 ?Challenge 2 s

M . T . F , G PRef. 5

* Te riddle . I q , can .

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why should we care about motion

F IG UR E 3 Illusions of motion: look at the figure on the left and slightly move the page, or look at thewhite dot at the centre of the figure on the right and move your head back and forward

( c. 515 bce E, N) , . H permanence

.Ref. 6H (c. 540 c. 480 bc e ) . H

.* H , P. T conserved creation . W ; , .Challenge 3 s

P Z E ( c. 500 b ce) . I , , ,

, ; . Z infnity , , .I , .Ref. 7

Z single , . Z , . H , . Z , rest. I, , . I A E , . I , . E,

. A M M.

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F IG UR E 4 Zoom this image tolarge size or approach it closely inorder to enjoy its apparent motion( Michael Bach after the discoveryof Kitaoka Akiyoshi)

, , , , - , , , , . I

, ; , , . E :

How should we talk about motion?

J , q ,E .

C B, a Beaut.*

L , : precision curiosity. P , . B , , O : .**

I , - , M M. T F 7 . W ,

. (W?) I , . H ? W Challenge 4 ny

* C B (. 1821 P, . 1867 P) Beauty: I , , I I .Ref. 8** F , W.Ref. 9

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Thales

Plato

Sosigenes

StraboCtesibius

Archimedes

Konon

Chrysippos

PhiloofByz.

Dositheus

Biton

Asclepiades

Varro

Athenaius

DiodorusSiculus

Virgilius

Horace

Cicero

Frontinus

Mariathe Jew

Josephus

Epictetus

Marinus

Menelaos

Nicomachos Apuleiu s

Cleomedes

Artemidor

Sextus Empiricus

Athenaios

of Nauc.

Philostratus

Alexanderof Aphr.

Diogenes

Laertius

Pomponius

Mela

Dioscorides

Plutarch

Ptolemy

Eudoxus

AratosBerossos

Aristotle

Heraclides

Theophrastus

Autolycus

Euclid

Epicure

Alexander

Ptolemaios I

Ptolemaios II Ptolemaios VIII

Straton

Pytheas

Dikaiarchus Poseidonius

Socrates

Anaximander

Anthistenes

Anaximenes

Pythagoras

Almaeon

Heraclitus

Xenophanes

Parmenides

Philolaos

600 BCE 400500 300 200 100 100 2001

Zeno

Archytas

Aristoxenus

Empedocles

Herophilus

Polybios

Diophantus

Aristarchus

SeleukosArchimedes

Erasistratus

Eudoxus

of Kyz.Eratosthenes

DionysiusThrax

Diocles

Apollonius Theodosiu s

Hipparchus Lucretius

Heron

Vitruvius

Livius

Geminos

Manilius

ValeriusMaximus

Seneca

PliniusSenior

Nero Trajan

Galen

Aetius

Rufus

Dionysius

Periegetes

Theonof Smyrna

Arrian

Demonax

Lucian

Anaxagoras

Leucippus

Protagoras

OenopidesHippocrates

Herodotus

Democritus

Hippasos Speusippos

Caesar

F IG UR E 5 A time line of scientific and political personalities in antiquity (the last letter of the name isaligned with the year of death)

F IG UR E 6 An example of how precision of observation can lead to the discovery of new effects: thedeformation of a tennis ball during the c. 6 ms of a fast bounce ( International Tennis Federation)

, , . W ?

H , increases .* T M M, . T -, . T

.Ref. 10I :

, , , . L .

* D out . H . DChallenge 5 s . B this .

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F IG UR E 7 How much water is required to make a bucket hang vertically? At what angle does thepulled reel change direction of motion? ( Luca Gastaldi)

TA B L E 1 Content of books about motion found in a public library

M o t i o n t o p i c s M o t i o n t o p i c s

, , -

Ref. 11 f , Ref. 12 Ref. 13

Ref. 14 , , Ref. 15 Ref. 16 Ref. 17

What are the types of motion?

E .

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A ( 1). T ,

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F IG UR E 8 Anexample oftransport, at theEtna ( Marco

Fulle)

. A G , , . T :

1. . T transport, , , . . , .

2. . A - , , , - , , . T , , , transormations. -. , . I , , -, S .Mind change, , , , () .Ref. 18

3. G. T , growth, Ref. 19

, , , , , , . I , , biological evolution, , , cosmic evolution, . , -. I . T .

A R, . M . T

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F IG UR E 9 Transport, growthand transformation ( Philip

Plisson)

. D , , E I. E . M voli-tional, , , , -, passive. C , .* F - .

T . L , - - . H, , . A ? A - ? T 100 ** - - . (O ,

, ; , grace - .) A .Ref. 20B ,

- . T

* F , , , - , - . A - James Randi, Te Faith Healers, P B, 1989. A , . S .. .** T ; E F . I S.

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F I GU R E 10 One of the most difficultvolitional movements known, performedby Alexander Tsukanov, the first manable to do this: jumping from oneultimate wheel to another ( MoscowState Circus)

, , , , , .

I - . E , , . I , 2 000 - : .

I - ,

G: every type o change is due to the motion o particles. I , . T . (D ?)Challenge 6 s

T : . T , , . B , .

A , , . O -

. P, , . A E R : A .

, . I simplest . I , -, , . I, , . T -Ref. 21

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.* D , , , - . W .

D W W.**

L W, ractatus, 6.373

Perception, permanence and change

O ; .

B P

H . P , . T , , -. D M M

. P distinguish. W ; , . T - , memorize . M , . P, - learning. W , .

C permanence variability. T rec-ognize , .F , . R- ; , , ( ). T

generalization. W , . L .

S M M, - , - . W . S, - ; . T , : . T , , -Ref. 22 . W , : .A , .

H ? P - . A , . E -Ref. 23 . B

* T : L, subject , object , interjection ; G, symbol , problem , emblem , devil .** T .

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F I G UR E 11 How do we distinguish a deerfrom its environment? ( Tony Rodgers)

, . A , ; . N .* P . F , ; , , , .

T , , - . F, object background environment. M .** S, defne ,

. I , . T ; .D ? I ; .

W -, , , ., , () object ()body. W , . I , relative ; . T . B , . F, Challenge 7 s . (D ?) T . S, Page 309 . H, , -

* T . F , f . D .Ref. 11** T . A 6 Dona ld D. Ho ma n, Visual Intelligence How We Create What We See, W.W. N& C., 1998. H ...////. .

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why should we care about motion 5

TA B L E 2 Family tree of the basic physical concepts

motion

parts relations background

objects images states interactions phase space space-time

T :

. . . . . .

world nature universe cosmos

,

!* O Page ?? . F, , , 2.

W : .

H E

Ref. 24

Does the world need states?

D F, B G E. D G F,B; Kf W, U.**L W, ractatus, 2.027 2.0271

* C , is q . I - q f .** T f, . T f, ; f , .

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W ? I : situation confguration . T

. I variable (physical) state o motion, state.

T time. : . . B - : all (.., ) similar . , ,, ; , , . T individuality ,*

. T, . O : the state describes all aspects o a system that depend onthe observer. T : ?Challenge 9 s

D - . T observables. A , . U , motion is the change ostate o objects.**

S . I complete , . T , G ,

everyday .

Galilean physics in six interesting statements

T , G , : . F , , , surprises . N, no - . M, , predictable deterministic.

T . I , :

* A physical system . I f 2, () . I ( ). A ?Challenge 8 s** T . F , ; , . , , . P shif ; q .

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1. W , . A . W . N, , ,

, continuous.2. W ,

. T : . I , , conserved: , - . N . I , : universal.

3. W . N, . M .M relative. T .

4. W . F , . N, reversible. P (, , ).

5. M , , . N, mirror-invariant. M .

6. W : , ,, , , , , . T , - . O - : minimize change. C , . I , -, simple. S .

T , , , . T , : ,, , -, .

Curiosities and fun challenges about motion*

I , , ,

; -, poisons. E , , , ; , , . P . T, .

* *

* S .

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F I GU R E 12 A block and tackle and a differential pulley

A 9 .. 1 .. H , 9 1 . I ?Challenge 10 s

* *

E , , . C ?Challenge 11 s

* *

I ?Challenge 12 s

* *

C ? H ?Challenge 13 s

* *

D ?Challenge 14 s

* *

C ?Challenge 15 s

* *

, . H ?Challenge 16 s

* *

W ?Challenge 17 s

* *

W ? I ?Challenge 18 s

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F I G UR E 13 What happens?

v

F I GU R E 14 What is the speed of the rollers? Areother roller shapes possible?

* *

W h , F 12?Challenge 19 s

* *

A , S D, I , K S : , , , , . H ?Challenge 20 s

* *

W , . H , , ?Challenge 21 s

* *

A . A . T .W ? H ?H ?Challenge 22 d

* *

A -

, F 13. W ? I ?Challenge 23 d

* *

Y . T - . C ?Challenge 24 s

* *

W , F 14, ?Challenge 25 s

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* *

D ? I , - Ref. 18 . I , . L Challenge 26 s

; , , .1. C absolutely marvellous,

, .2. O ??

.3. T .4. R

2 3 .T , , . L ??. H ?

* *

I , N * . T . O -. T , . H ?Challenge 27 s

* *

C , F 14. T - . W -other , - curves o constant width, ? H ? A -Challenge 28 s?

Summary on motion

M . E . P : , ,, -, . S

, . W , ?Challenge 29 dW .

* N F (149917), R .

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C h a p t e r 2

FROM MOTION MEA SUREMENT TO

C O N T I N U I T Y

P S M.*

G C L

T , , - : only one thing can be at a given spot at a given time . T : impenetrable moves, instants, points. W ( ?) . T -Challenge 30 s Galilean physics, Newtonian physics.

G G (15641642), , - . B , . F -, G -. H G

R I.**T E , , , I N

(16431727) - , .***

T G , .

* P . G C L (17421799)

.** T G P R ( 244). G . B , . F , .-.. G.***N G . N , M, . A N , D.Ref. 25A , N ; L , Isaacus Neuutonus, Jeova sanctus unus. A N , C .Ref. 26

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rom motion measurement to continuity

F I G UR E 15 Galileo Galilei (15641642)

F I G UR E 16 Some speed measurement devices: an anemometer, a tachymeter for inline skates, a sportradar gun and a PitotPrandtl tube in an aeroplane ( Fachhochschule Koblenz, Silva, Tracer)

What is velocity?

T .

J R*

V . , , . T . A 3. T A ??.

E : , . W . T , 4, - ; Euclidean vector space.** M . F -Page 69 , .

W E , Galilean . V- . F , - . A ? I , ??, 2000Challenge 32 d

* J R ( 19421970), A F O , .** I E, E, G A 300 bce. E , Elements, . T . F f , E : . T , , 2000 . O , 0../

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TA B L E 3 Some measured velocity values

O b s e r va t i o n V e l o c i t y

G 80 /C f ? Challenge 31 sS 0.3 /L 7 / 10 / = 0.3/H , 4 / 30 /E 1 /S 60 160 /S S 0.1

/

K 1

/

S E Ref. 27 0.3/S 0. / 1./S Ref. 28 0./ 120/W 1 B ( ) 1. /S , 2 / 8 /F f, f (Istiophorus platypterus) 22 /S ( F M) 2.1 /F , (Acinonyx jubatus) 30 /W 12 B () 33 /S 42

/

F : q 0 /F , 0 90 /F , Falco peregrinus 60 /F 70 /A 280 /S 330 /C 70 /S 1 /S /H Voyager 14

/

S E 370

/

A ( ) 600 / (0M/)H Ref. 29 0.97 108 /S V 1 108 /S 299 792 48 /H 10 108 /S M 2 109 /H 7 1013 /H

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TA B L E 4 Properties of everyday or Galilean velocity

V e l o c i t i e sc a n

P h y s i c a lp r o p e r t y

M a t h e m a t i c a ln a m e

D e i n i t i o n

B Page ??C Page 69, Page ??P , Page 69B Page ??B Page 69H f E Page 69E f Page ??

. I , :

, .I , measurement . W - , .., . H, , . Y .

S : . D Ref. 30 .

V . P , , . C ?Challenge 33 s

H ? A : , , , , . B : - , - . S . T .

V . I , - - . A , F 17 . I ,

, . (C ?) BChallenge 34 d , allometric scaling , .

V : 4 ; none . I - G . T 4 ,

~///. .

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rom motion measurement to continuity 5

Boeing 747DC10Concorde

Boeing 727

wing load W/A [N/m2]

weightW

[N]

Boeing 737

pteranodon

cruise speed at sea level v [m/s]1 2 3 5 7 10 20 30 50 70 100 200

F-14

F-16

MIG 23

Learjet 31

Beechcraft Baron

Skysurferhuman-powered plane

whooper swan (Cygnus cygnus)

hummingbird

common wasp (Vespa vulgaris)honey bee (Apis mellifera)

fruit fly (Drosophila melanogaster)

canary (Serinus canaria)

Piper Warrior

Fokker F-28Fokker F-27

Beechcraft King Air

Beechcraft Bonanza

1041031021011

106

105

104

103

102

10-1

10-210-2

10-3

10-4

10-5

10

1

Ultralight

Quicksilver B

Schleicher ASW33B

Schleicher ASK23

wandering albatross (Diomedea exulans)

pheasant (Phasianus colchicus)wild duck (Anas platyrhynchos)

damsel fly

mosquitognat

midge

house fly (Musca domestica)

graylag goose (Anser anser)

starling (Sturnus vulgaris)blackbird (Turdus merula)

crane fly (Tipulidae)

ant lion (Myrmeleoformicarius)

small white

large white

blowfly (Calliphora vicina)

green dragonfly

yellow-striped dragonflyeyed hawk-moth

swallowtail

garden bumble bee (Bombus hortorum)

scorpion gnat

june bug (Amphimallon solstitialis)

small stag beetle (Dorcus parallelopipedus)

cockchafer (Melolontha melolontha)

sawyer beetle (Prionus coriarius)

stag betle (Lucanus cervus)

blue underwing (Catocala fraxini)privet hawkmoth (Sphinx ligustri)

goldcrest (Regulus Regulus)

winter wren (Troglodytes troglodytes)great tit (Parus major)

house martin (Delichon urbica)European Robin (Erithacus rubecula)

barn swallow (Hirundo rustica)sky lark (Alauda arvensis)

common swift (Apus Apus)house sparrow (Passer domesticus)

ortolan bunting (Emberiza hortulana)

moorhen (Gallinula chloropus)

coot (Fulica atra)

peregrine falcon (Falco peregrinus)

cormorant (Phalacrocorax carbo)

common tern (Sterna hirundo)

black headed gull (Larus ridibundus)barn owl (Tyto alba)

carrion craw (Corvus corone)

herring gull (Larus argentatus)

griffon vulture (Gyps fulvus)white-tailed eagle (Haliaeetus albicilla)

white stork (Ciconia ciconia)black-backed gull (Larus marinus)

Airbus 380

F I G UR E 17 How wing load and sea-level cruise speed scales with weight in flying objects, comparedwith the general trend line (after a graph Henk Tennekes)

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TA B L E 5 Speed measurement devices in biological and engineered systems

M e a s u r e m e n t D e v i c e R a n g e

O ,

q

0 33/O

0 10/

P

0 30 /P 0 90 /B

0 20 /S

0 3 /O f 0 30/O

0 20 /D f, ,

0 /W f

0 20 /O E () ..O E 0 60 /O E

, 0 8000

/

O

f ,

0 60/O PP 0 340/W

,

0 80/S 0 20 /B 0 20 /P 0 1000 /A E G P S,

G, G0 100/

M D 0 1000

/

M D 0 200 M/

- . B , G , G : .

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F I G UR E 18 A typical path followed by a stone thrown through the air a parabola with photographs(blurred and stroboscopic) of a table tennis ball rebounding on a table and a stroboscopic photographof a water droplet rebounding on a strongly hydrophobic surface ( Andrew Davidhazy, MaxGroenendijk)

W place, void time, . [...] I [...] , .

A* Physics, B III, 1.

What is ti me?

, , , .

L,** De rerum natura, . 1, . 460 .

I , . T L . D Ref. 21 . A .

W , sequence . O

. T , . O . A , , , . W instants time.

* A (384/3322), G .** L C (c. 9 c. bce), R .

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TA B L E 6 Selected time measurements

O b s e r va t i o n i m e

S 1044 S 1023 0.1 10 S 200 P f 108.782 77 70778 B 1 P ( ) PSR 1913+16 0.09029992712 H 20 S 0.3 A 400 79 200 A 86 400.002

1

F 1000 31.7 A 4600 U 2 105 A H 3 106 A , I B, G P C, H B

3.8 109 A E 4.6 109 A 13.7 GA 13.7 GL 180m 1015

L

209

B 1.92 1019

A , .., , event. E ; , . (B ? K Challenge 35 s .)

S , . S 6.* Duration take . W .

H , ,

? M : , ,, . A time is deduced by comparingmotions. C, , . G- Ref. 21 S local time. F M lunar calendar. I E

* A (L ).

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universal time coordinate (UC), G .*A ephemeris time ( -). A proper time;

.N . I 2000 E

86 400 , 1900, 86 400.002 .Page ??C 86 400 ?Challenge 37 s

A .I , standard , . T clock. W : time is what we read rom a clock. N

;

.** N . L . A, ; , M M. T , .I, ! B . W .E , .

A clock . O , precise , .I ? D ? W . A , , : ,

, ideal . C ?Challenge 38 s , .

E , , , . C , -. S .*** E ; . F , .Ref. 32

* O UTC , GPS . T , , . F , .. . T - . C Challenge 36 s?** T .T gnomonics. A ....***T . T , Page ??, , . F , , , .Ref. 31

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TA B L E 7 Properties of Galilean time

I n s t a n t s o t i m e P h y s i c a l M a t h e m a t i c a l D e i n i t i o np r o p e r t y n a m e

C Page ??C q Page ??Df Page ??C , Page ??A Page ??D Page 178D f Page ??A q q

necessary . I , , . I , .Y , , . D, time intervals, ; , . .

T , 7, . I Galilean time; . I,

G , . E Page??

, t, .

W G , -. H , - . C ?Challenge 39 s

W G . H, every single , . T .

Clocks

A clock . T :, - , , , , . A , 8.Ref. 33

I, : . HRef. 34 , F 20, allometric scaling law.

C . W Page 137 . W , , .Page ??

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sub-solar point

closeto Mekk a

sun's orbit

onMay15 th

mirror reflectsthe sunlight

time scale ringCEST

winter-spring

display scree n

on May 15thSuns orbit

close to Mekkasub-solar point

time read off :

11h00 CEST

light from the Sun

display screenwinter-spring

F I G UR E 19 Different types of clocks: a high-tech sundial (size c. 30 cm), a naval pocket chronometer(size c. 6 cm), and a caesium atomic clock (size c. 4 m) ( Carlo Heller at www.heliosuhren.de,anonymous, INMS)

Why do clocks go clockwise?

W N P ?

Challenge 40 s

A , , , - , . L, . M . W? M -, . T- . A ,

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TA B L E 8 Examples of biological rhythms and clocks

L i v i n g b e i n g O s c i l l a t i n g s y s t e m P e r i o d

S (alitrus saltator) S M

H (Homo sapiens) 0.023 0.03 0.08 0.13 0.3 1. 0.3 10 30 1 2 -- .4 4 14 11

(SCN), , ,.;

90

2.44M- 3.23G

C (Musca domestica) 30 F (Drosophilamelanogaster)

34

M (.. , )

() ;

A (Acetabularia) A (AP)M (.. Neurospora crassa) M ;

, 1920 G A

Arabidopsis

(Desmodiumgyrans)

200

Forsythia europaea, F. suspensa,F. viridissima, F. spectabilis

F , V G 2002

.1

. T . F -, -, , .

O , ; , , ,

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.Page ??T ,

G N, . A (384/3322 bc e ), Ref. 35

, , . N-, , , - . J .Challenge 41 eT : , , , ; , ; - , . I, Ref. 36 . P, . .

I , ( ) . A ( )

.

What is space?

T [...] [...].

H W, Philosophie der Mathematikund Naturwissenschaf.*

W , , - . W , , . P . A . P . T

, (physical) space, .C size, .S . W .

H ? D , ( ) , -, , , , ., . T . I, ? . B , -. T , , , . G, , , , - . S -.

M . B , . N , , -

* H W (18819) , . H f, q , , .

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F I G UR E 21 Two proofs of thethree-dimensionality of space: thevestibular labyrinth in the inner earof mammals (here a human) and aknot ( Northwestern University)

. , . C Challenge 42 s ?

O , - . T 9; . O continuous : .* S , length, , surace. L . S 10. T , -. I . T .

E ; . I, ()

, F 21.** S, . (W ?) A Challenge 43 s : , , - . B ? T ; .

I . T . J .Challenge 44 sF , ?

L , real numbers. I , units , - . U Galilean space : , , ,-, , , , E .I , - - Euclidean space. I , (mathematical) points,

* F f , ??.** N implies ; D - L B (. 1881 O, . 1966 B) .

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TA B L E 9 Properties of Galilean space

P o i n t s P h y s i c a lp r o p e r t y

M a t h e m at i c a ln a m e

D e i n i -t i o n

C Page ??C q Page ??C Page ??L

3- Page ??

C ,

Page ??

Df Page ??A Page ??Df E Page 69

D C f Page ??Df q Page 48

F I GU R E 22 Ren Descartes (15961650)

. T

x, y, z (1) coordinates. T . (F E , 69.)

W 2000 ,

. T - R D*, (1) Cartesian.

L , necessary . I, - . F ,

* RD C(. 196L H, . 160 S), F , , , I I . I .

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TA B L E 10 Some measured distance values

O b s e r va t i o n D i s t a n c e

G C 1085 ( )P , 1032 P 1 E C 2.426 310 2118H 30 S 0 S 0.2 W 0.4 0.8 P: 20 D ( ) 30 80 DNA 2 L , Armillaria ostoyae 3 H - , W 647 L M c. L E Eq 40 07 014.86 8 105 A S 149 97 870 69130L 9. PD 10 ES 1 ZD A 28 Z

M 12 Y

, . T .

E , . F , , natural ideal , . C ?Challenge 45 s

A , .A , . I , all . T W . I , , M M. T .

.*

C

* M (). C () L, ( c. 6200 BCE ) .

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F I G UR E 23 Three mechanical (a vernier caliper, a micrometer screw, a moustache) and three optical(the eyes, a laser meter, a light curtain) length and distance measurement devices ( www.medien-werkstatt.de, Naples zoo, Leica Geosystems and Keyence)

Are space and time absolute or relative?

I , G ; . O , ; . S , - . I absolute. O , -

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TA B L E 11 Length measurement devices in biological and engineered systems

M e a s u r e m e n t D e v i c e R a n g e

HumansM , .. f, ,

0.3 2

M 1 100 M 0.1 1000

Animals

M

100

M

3

M

f 1000

M 2 M ,,

100

M 0.1 1000

Machines

M 0.1 400 MM 0.1 0 M 0. 0 M , q

12 Y

M 1018

. I , , ; , relative. W ? T -Challenge 46 e . W , . A , Ref. 37.

Size why area exists, but volume does not

A . A , , . A , distance length . I not. S .

T L

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5 rom motion measurement to continuity

F I G UR E 24 A curvimeter or odometer(photograph Frank Mller)

n = 1 n = 2 n = 3 n =

F I G UR E 25 A fractal: a self-similar curve ofinnite length (far right), and its construction

R:* H B?F , F 24,

R l s ( 1:10000 1 : 500 000) :

l= l0 s0.25 (2)(R .) T l0 1 : 1. T , . W ? T

. C infnite ? Y, . I , ; ractals.A , F 25 .** C ?Challenge 47 e

L . T I G V 1 2. A ?Challenge 48 d

, , , . W , . T , . W

* L F R ( 1881193), E .** M sel-similar, .., -. T P B M : , - D , - -. M - e R D = 1 + e, D = 1.2 .Ref. 38

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dihedral

angle

F I GU R E 26 A polyhedron with one of its dihedral angles( Luca Gastaldi)

.I , . C-

, . Y ? Y , . , : additive, .., , ; rigid,.., , . A ? I ,

?F , :

A a b A = ab; , Challenge 49 s . S,

. T integration; Page 187 .

H, .(C ?) F , Challenge 50 s. T 1923 S B.* H , , - . , , Banach measure . M- B, .**

W three , .., ? W , V a, b,

* S B (K, 1892L, 194), P .** A, . F , , . I , f . A : , f q .

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c V = abc . B : ! T 1900 1902 MD.* H , -

, . I l , D , + = + = 0. A 0 1 . T

- . U , Challenge 51 s D .**

D D , can -

, , , , .N ,

. W Banacharski theorem (). I 1924, S B A *** Ref. 39 , . T - B . E ,

: ; fnite . I E, .S !**** V .

T B : ,

? T . S, ? I , ? B -Challenge 52 s ; , . F -, ( ). W , : , .***** I, B ; , ( ) - . S . N,

* M D ( 1878192), G , D H.

**T M. A igler & G. M. Zi egler, Proos rom the Book, SV, 1999. T P E .*** A (. 1902 W, . 1983 B), P .**** T ; I S P , New Scientist, 14 J 199, . 2831. T , . T B , Page ?? . M S W.Ref. 40***** M - ebesgue measure . T f .

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F I G UR E 27 Straight lines found in nature: cerussite (picture width approx. 3 mm, Stephan Wolfsried)and selenite (picture width approx. 15 m, Arch. Speleoresearch & Films/La Venta at www.laventa.it andwww.naica.com.mx)

.

What is str aight?

W , 99 %- -.O , , F 27.* T 18 . B , ,Ref. 42, , , , ,, , : , . H ?

A ; Page 350

. F straight - . I , . C ? C ? O-Challenge 53 s, at - .

I , . I , , , .

A hollow Earth?

S . S -

inside ; () hollow Earth theory. T M, S .T r E, E - rhe = R2Earth/r. C ? R S** Challenge 54 s* A , , - I G C. O , Page 304() q () -, .Ref. 41

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F I G UR E 28 A photograph of the Earth seen from the direction of the Sun (NASA)

. T : , ! T no way . I , - , E, F 28. M . A Challenge 55 e E equivalent .W .Page ??

Curiosities and fun challenges about everyday space and time

H , 1 3, ? H: Challenge 56 s.

* *

W : ?Challenge 57 s

* *

H ?Challenge 58 s

** R S, ( 19391986), A , - .

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F I G UR E 29 A model illustrating the hollow Earth theory, showing how day and night appear( Helmut Diehl)

F I GU R E 30 When is a conical glass half full?

* *

W , F 30, ?Challenge 59 s

* *

E : A , 10 S 10 W, , 10 N, . W ? Y . N , . T

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rubber band

F I G UR E 31 Canthe snail reachthe horse onceit startsgalloping away?

additional E; exactly ( ) ?Challenge 60 s

* *

I . O , , . B , .C ?Challenge 61 s

* *

F , 1 1000 . F !

I, , 1 0.5 1.5 , 1000 999.5 1000.5 . S . T , , 10008 1000 8 , .., 992 1008 .

* *

I . W ? T P .Challenge 62 s

* *

A () , . T

2.7. !Challenge 63 s

* *

H ?Challenge 64 e

* *

H 24 ?Challenge 65 sF , ?

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* *

H exchanged valid? W Challenge 66 s

?

* *

H E ?Challenge 67 s

* *

W ( )? W ?Challenge 68 s

* *

A E, E, . T

1 . C ?Challenge 69 s

* *

J . W , . J 10 . H . W , 600 . H ?Challenge 70 s

* *

A B . A 18 . B A B . H B?Challenge 71 e

* *

W I? ; W I? , . W?Challenge 72 s

* *

I ? A ?Challenge 73 s

* *

G , - ? A ?Challenge 74 s

* *

W ?Challenge 75 s

* *

T 400 2. C - ?Challenge 76 s

* *

H vernier ? I nonius . T -

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1 5 10

1 5 10

F I GU R E 32 A 9-to-10 vernier/nonius/claviusand a 19-to-20 version (in fact, a 38-to-40version) in a caliper

( www.medien-werkstatt.de)

w

d b

F I GU R E 33 Leaving a parking space

F * , L P ** L . I , F 32 1600 C C,*** G 1582. A // , , ? I ?Challenge 77 s

* *

F . L F 25 Page 50

. ; , . R , ( ) . W , - ?Challenge 78 s

* *

M . A : d ? (A , Challenge 79 s F 33, R, .) N : ? N Challenge 80 s : H , n, ? (T 50 - ; Challenge 81 s D H .)

* P V (1801637), F .** P N P N ( 102178), P .*** C C S (1371612), B , .

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TA B L E 12 The exponential notation: how to write small and large numbers

N u m b e r E x p o n e n t i a l N u m b e r E x p o n e n t i a l

n o t a t i o n n o t a t i o n1 100

0.1 101 10 101

0.2 2 101 20 2 1010.0324 3.24 102 32.4 3.24 1010.01 102 100 102

0.001 103 1000 103

0.000 1 104 10 000 104

0.00006 .6 105 6 000 .6 1040.000 01 105 . 100 000 105 .

* *

S , 12.

* *

I 1996 1019 , Ref. 43 F. ( , .)W ?Challenge 82 s

* *

Z, G ,

. , . Y . W ?Challenge 83 s

* *

C P , ? (T 30 .)Challenge 84 s

* *

W , , () (, ,Page 54F 28)?Challenge 85 s

* *

A . W - ?Challenge 86 s

* *

T . A F 34, (plane) angle . A /2 radian ( /2 ) 90.

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r

a

= a

r

r

= A

r2

A

F I GU R E 34 Thedefinition of planeand solid angles

horizon

sky

earth

horizon

sky

earth

F I G UR E 35 How the apparent size of the Moon and the Sun changes during a day

T solid angle . A /2 steradian /2 . (M, , .) A , dierent. C ?Challenge 87 s

* *

T . M , ,

, () . T D

D 6 s

. (3)

W? F , ../~ . B , Challenge 88 e 3, 2 3, 20. C ?Challenge 89 s

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F I G UR E 36 How the size ofthe Moon actually changesduring its orbit ( AnthonyAyiomamitis)

* *

U , sine, cosine, tangent, cotangent, secant cosecant . L . C 15 =6 2 /4, 18 = 1+5 /4, 36 = 10 25 /4, 54 = 1+5 /4 72 = 10 + 25 /4? C Challenge 90 e

x

x

=

x

2

x

4

x

8... (4)

?

* *

M . F , M ?Challenge 91 eA ; .

A , F 35, .B S M . I ,P - Moon illusion . I, M M . I , M urther away

, smaller , . C ?Challenge 92 sT M :

M E . A F 36.

* *

G . I , Dialogues, , .., y = x2. T . W ? Y Challenge 93 d

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A

BC

O F I GU R E 39 What is the area ABC, given the other three areas and three rightangles at O?

F I G UR E 40 Anticrepuscular rays - where isthe Sun in this situation? ( PeggyPeterson)

* *

OABC OAB, OBC OAC

O. I , OA, OB OC . I , OAB, OBC OAC 8, 4 1.W ABC?Challenge 99 s

* *

T S F 40 W ?Challenge 100 s

* *

A , - . C ?Challenge 101 ny

* *

. W - ? (F .)Challenge 102 s

* *

1 , . I 1.06 1 ?Challenge 103 s

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* *

C - ? A D Ref. 45 - . H , -

, , . C - ?Challenge 104 d

* *

S -. C ?Challenge 105 s

* *

O -. C ?Challenge 106 ny

Summary about everyday space and time

M , . O - E

, - E , - . M , -

. H, . F , 1025 1025 ; . W .

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C h a p t e r 3

HOW TO DESCRIBE MOTION

KINEMATICS

L ff q ( ) ... E .*

G G, Il saggiatore VI.

E G . A , , , , , , . T .

F , motion is change o position with time. T , 182. E - , , . T - , , .

C neither nor -, . I description . S, , , . A , - . T : kinematics.

T ollowed -. T ; . B , . T - path trajectory. T Ref. 46 182.

I , E , . I , - , coordinates x, y, z t. (F ??.) T x = xt = xt, yt, zt. F , G , * S (I ) ... I .

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how to describe motion kinematics

collision

F I G UR E 41 Two ways to test that the time of free fall does not depend on horizontal velocity

, z

zt = z0 + v0 t t0 12 t t02 (5) t0 , z0 , v0

=9.8

/2 ,

300, E. W

9.8 /2 ? A Ref. 47 , .

E (5) , . T v Challenge 107 s , v= 2h . A 3 27/.T . D ?Challenge 108 s

G : independent. H independent

, F 41. M : 1658 A C Ref. 48 ,

. C ? F 41 Challenge 109 s . I , , - ( ), .

I , . I . B (5)

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v

z

z

vx

mvz

x

mvx

hodograph phase space

graph

x

z

configuration

space

t

z

t

x

space-time

diagrams

F I G UR E 42 Various types of graphs describing the same path of a thrown stone

x y,

xt = x0 + vx0t t0y

t

=y0

+vy0

t

t0

, (6)

complete . A parabola; F 18, 41 42. (A Page 37 . C ?)Challenge 110 s

P . AF 42 , Ref. 49 . D , . H . S- . T confguration space . F , . I -. T . T state space diagram. I .

hrowing, jumping and shooting

T .

* *

W ? T 1997 12 / 43/ B J, 11 / 40/. H-Ref. 50, 9.5 /. H

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F I G UR E 43 Three superimposed images of a frass pellet shotaway by a caterpillar inside a rolled-up leaf ( StanleyCaveney)

? H ?I , 20, Ref. 51

. H 45? (I 45 ?)Challenge 111 s

* *

H ? T -Challenge 112 s: , . (C ?)Page ??

* *

W , ?Challenge 113 ny

* *

N : . SRef. 52C . F 43 () Calpodes ethlius .G 1.5 ( , Epargyreusclarus), ? H ?Challenge 114 s

* *

W , ?Challenge 115 s

* *

W ?Challenge 116 s

* *

I ?Challenge 117 sW ?

* *

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Data graph to be included F I G UR E 44 The heightachieved by jumpinganimals

A , , ?Challenge 118 s

* *

P 30 , 12 . W ?Challenge 119 s

* *

M , , 2 , F 44. T . C ?Challenge 120 s

T (5) . F , . A G , ; . B , .

I , .C ?Challenge 121 s

Enjoying vectors

P , , -, , vectors. L - . H .

V . N : same

, . S , . F ,

a = ax , ay, az c , , ca = ca x , cay, caz.I , , , vector space,

a b c d:

ca + b = ca + cb , c + da = ca + da , cda = cda 1a = a . (7)E positions ,

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y

tt

y

: y/t : y

/t

F I GU R E 45 The derivative in apoint as the limit of secants

. D ?Challenge 122 sA null vector negative vector

.Challenge 123 eI length (

) . T , - . T scalar product a b

aa 0 , ab = ba , a+ab = ab+ab , ab+b = ab+ab cab = acb = cab .(8)

T ; , standard -

. I C ,

ab = axbx + ayby+ azbz . (9)I orthogonal, . (S !)Challenge 124 e

T length norm : a = aa . O, , , . A Euclidean .

T . I, . C

?Challenge 125 s

What is rest? What is velocity?

I G , . I , , .., , . I , (G) rest

xt = . (10)

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F I G UR E 46 Gottfried Leibniz (16461716)

W xt xt, yt, zt. L , , . N, - . T velocityv x t. T

v= xt

. (11)

I , , /t .W derivative . T speedv v. D . T

s

t

t0

s

t, (12)

derivative at a point , F 45. T Challenge 126 e

s + rt

= st+ r

t,

cst

= c st

,

t

s

t= 2s

t2,

srt

= st

r+ s rt

, (13)

c . T . Q t s, , dierentials. T G W L.* D . L

, , .T t 0. I

, . T

* G W L (. 1646 L, . 1716 H), S , , ,, . H ; - ( N) f , De arte combinatoria, Hypothesis physica nova, Discours de mtaphysique, Nouveauxessais sur lentendement humain, Todice Monadologia.

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continuous, , connected and complete. I , infnities

. T . I, .W - . I , . T .Page ??

T Z E ( 445 bce), P.Ref. 53I - , Z , ; . N-

existence , description, . (D ?) N, Z Challenge 127 e . T : , .

L . T . F , . I ; . T Z , . T , Page ?? ; , -. F , :

.W ? A

, . T .

Acceleration

C , acceleration a v ,

a = vt= 2x

t2. (14)

A E , , . M 13. L , , bold . I , , , .

A . T . H . F , - , ,

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TA B L E 13 Some measured acceleration values

O b s e r va t i o n A c c e l e r a t i o n

W f? Challenge 128 sB- M82 10/2A 10 /2A S M W 0.2/2U P 0 .8/2C Eq E 33/2E

0/2A 1.3 /2G M 1.6

/2

G E ,

9.8

0.1

/2

S 9.806 6 /2H - 1 /2S - 20 90 /2A 32 /2G J 240/2A c. 120/2A 360 /2F - ( , Philaenusspumarius, )

4 /2 0.1 M

/2

B M/2F 0.1 G/2A 90 /2A 1031 /2H 1052 /2 . B 3 5 , 7 9 , , - , . H

.T ; .

I , , eel . (T 1 .) C - not ?Challenge 129 s

H . T , Challenge 130 s

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TA B L E 14 Some acceleration sensors

M e a s u r e m e n t S e n s o r R a n g e

D (, , , )

0 10 /2D

,

0 20/2D

0 20 /2D

0 2000 /2

F I G UR E 47 Three accelerometers: a one-axis piezoelectric airbag sensor, a three-axis capacitiveaccelerometer, and the utricule and saccule in the three semicircular canals inside the human ear( Bosch, Rieker Electronics, Northwestern University)

.

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how to describe motion kinematics 5

Objects and point particles

W G , M

V S.*L W, ractatus, 2.0123

O . W , - . I , : parts. O Challenge 131 e , , . F, matter,** ,.., . S, shape, .

I , . I , , . A particle. (T corpuscle .) P . T , negligible , single , point particle point mass. I (5), .

D - , .., , ? Y . T . A , 2 ,

. I , H E, 10 . P E , -, .

A , , , .*** B, O F 48, M C, A S, A S C M ; E. O , S, Ref. 55 , . (?)Challenge 132 s

* I I , I .** M L , Ref. 54 , .*** T .../~//. . T .../~/ .

F , K. R. Lan g & C. A. Whitn ey, Vagabondsde lespace Exploration et dcouverte dans le systme solaire, S V, 1993. T D. Ma li n, A View o the Universe, S P CU P, 1993.

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Betelgeuse

Rigel

Mintaka

Alnilam

Alnitak

Bellatrix

Saiph

F I G UR E 48 Orion in natural colours ( Matthew Spinelli) and Betelgeuse (ESA, NASA)

T -

: , , . (C !) T -Challenge 133 e . - . O , , ,* .

A point-like or the naked eye 2 = 0.6 . C - ? B , Challenge 134 s invisible - and , .., , . C - - M, ?Challenge 135 s

T - . D , ? I , ? T . I , . O . C ? D ; Challenge 136 s .

H, , , - . O , , , . T . T ,

continuum approximation, . I , . T , , , .Ref. 56

A . N-Page ??

* A satellite , M; articial satellite , S.

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F I G UR E 49 How an object can rotate continuously without tangling up the connection to a secondobject

, . T . O , , .

Legs and wheels

T . S : , . I , . T : , , , . W?

L ; , .M , connected. T ,Appendix ?? , -Ref. 57 . H, , F 49 . I , . C

? A Challenge 137 s ?Challenge 138 s

D , F 49 . C ? E Challenge 139 s : . T . O , : , ,Ref. 58 , , .

Single , , deormation : , , ,

. E F 50; Ref. 59

. W F 100 132; F ?? ??. I, , , , without , , .*

* D , , , . A -

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F I G UR E 50 Wheels and legs in living beings: the rolling shrimp Nannosquilla decemspinosa (2 cm bodylength, 1.5 rotations per second, up to 2 m, can even roll slightly uphill slopes), the rolling caterpillarPleurotya ruralis (can only roll downhill, to escape predators), the Red millipede Aphistogoniuluserythrocephalus (15 cm body length) and a Gekko on a glass pane (15 cm body length) ( Robert Full,John Brackenbury / Science Photo Library, David Parks and Marcel Berendsen)

I , - ( ) -: , ( ). H, - , . T .T . O Escherichia coli, - , Salmonella , . Flagella , . I 1970 , , . A -Page ??, 1000 ,

. (T -Ref. 60.) T , . B .

, . (S,.. .. .) T . F, . S, . I , .T ; ?Challenge 140 s

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F I G UR E 51 Are comets, such as the beautiful comet McNaught seen in 2007, images or bodies? Howcan one settle the issue? ( Robert McNaught)

Curiosities and fun challenges about kinematics

W ?Challenge 141 s

* *

A , , 30 /. C . W ?Challenge 142 s

* *

A 10 / A B, 36 . T . A , A B, 20

/. B ,

B . T A; , ,

B. I B. W ?Challenge 143 e

* *

B ( !) .H ?Challenge 144 e

* *

I A B A

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?Challenge 145 e

* *

T . F , 30 = 300/2, , . (I 80 = 800/2.) B 15 = 150/2 .

* *

T microscopic , 1035 /2. T macroscopic supernovae, . A E

, cavitation. C , F S 1934 sonoluminescence. (S F 94.)Ref. 61I 30 H . A , 1500 / , 10 11 /2.Ref. 62

* *

L . N , Illacme plenipes, 750 . T 3 4 0.5 .T .

Summary of kinematics

T xt, yt, zt , . I - . T, : .

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C h a p t e r 4

FROM OBJECTS AND IMAGES TO

CONSERVATION

W : , . S . B . R ,Ref. 63 , ,

. F , , , .

E . I , , .* I , , , .I, , . I . O . I , . IRef. 65, ,

. O , boundaries . W .

M : touch . I, , object, image.**I , . I , .Page ??A , .

* E F, , , . O - , ,

, . D ? A Challenge 146 s K. Nassau, Te Physics andChemistryo Colour the feen causes o colour, J. W& S, 1983. I , F Ma rce l G. J. Minna ert, ight and Colour in the Outdoors,S, 1993, , De natuurkunde van t vrije veld,T & C, 1937. R . O , ,Ref. 64 ./.** O q ; , q , ??, , q.

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rom objects and images to conservation

push

F I GU R E 52 In which direction does the bicycle turn?

C , , , , , , . T , inertia, (inertial) mass. I .

S , , , , . E ; . (D ?) IChallenge 147 s , , ; . F , , G ?Challenge 148 s

I matter, radiation. I- , , , , -Ref. 66 . P, , , , ( ). , ( ). H,

.

Motion and contact

D : T .

A, Opinions.

Ref. 67

W , : . I, , . A , , ,, , , , , , , , ,

. T .C ; -

. N- : , . C , . H, , - . . (S F 52.) I - , right. B

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v

v'

1

2v'

v2

1

F I G UR E 53 Collisions define mass F I GU R E 54 The standard kilogram( BIPM)

, , , . C ? B ! Challenge 149 s .

S ; , - .

What is mass?

.D , .*

A

W , , , . T , . T F 53. R , m i i.

T , ;

m2m1= v1

v2(15)

* G , I E. A ( c. 283212), G .T P. A A Ref. 68 .

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F I G UR E 55 Antoine Lavoisier (17431794) and his wife

v . T m i mass i.

I , , . T , F 54 standard kilogram S P. I - , , . T .

T . H . O, ; . (B , , L, G HRef. 54 . T .)

E , conserved:

i

m i = . (16)T A-L L. *C . I , Galilean mass is a measure or the quantity o matter.

* A-L L(17431794), F . L f ; . T , : W () F , f . H q , . L . I . I , , . I, , .Ref. 69

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rom objects and images to conservation 5

F I G UR E 56 Christiaan Huygens (16291695)

F I GU R E 57 Is this dangerous?

Momentum and mass

T . W

Motion-Mountain-The-Adventure-of-Physics-1-of-6-22nd-edition.pdf

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