TRANSLATED FROM THE RUSSIAN BY
A. SHKAROVSKY
DESIGNED BY L. L A M M
CONTENTS
From thr Authors Foreword to the 13th Edition 9
Chapter One
SPEED AND VELOCITY. COMPOSITION OF MOTIONS
HOW FAST 1)0 WE MOVE? !3
RACING AGAINST TIME 16
THE THOUSANDTH OF A SECOM) 17
THE SLOW-MOTION CAMERA 20
WHEN WE MOVE ROUND THE SUN FASTER 21
THE CART-WHEEL RIDDLE 22
THE WHEEL'S SLOWEST PART 1!4
BRAIN-TEASER 24
WHERE DID THE YACHT CAST OFF? r>
Chapter Two
GRAVITY AND WEIGHT. LEVERS. PRESSURE
TRY TO STAND UP! 28
WALKING AND RUNNING 30
HOW TO JUMP FROM A MOVING CAR . . . 3,1
CATCHING A BULLET 35
MELON AS BOMB 35
HOW TO WEIGH YOURSELF 38
WHERE ARE THINGS HEAVIER? 38
HOW MUCH DOES A FALLING BODY WEIGH? 40
FROM EARTH TO MOON 41
FLYING TO THE MOON: JULES VERNE VS. THE
TRUTH 44
FAULTY SCALES CAN GIVE RIGHT WEIGHT . 46
STRONGER THAN YOU THINK 47
WHY DO SHARP THINGS PRICK? 48
-COMFORTABLE BED ... OF ROCK 49
Chapter Three
ATMOSPHERIC RESISTANCE
BULLET AND AIR 51
BIG BERTHA 52
WHY DOES A KITE FLY? 53
LIVE GLIDERS 54
BALLOONING SEEDS 55
DELAYED PARACHUTE JUMPING 56
THE BOOMERANG 57
Chapter Four
ROTATION. "PERPETUAL MOTION" MACHINES
HOW TO TELL A BOILED AND RAW EGG APART? 60
WHIRLIGIG 61
INKY WHIRLWINDS 62
THE DELUDED PLANT 63
"PERPETUAL MOTION" MACHINES 64
"THE SNAG" 67
"IT'S THEM BALLS THAT DO IT" 68
UFIMTSEV'S ACCUMULATOR 70
"A MIRACLE, YET NOT A MIRACLE" 70
MORE "PERPETUAL MOTION "MACHINES ... 72
THE "PERPETUAL MOTION" MACHINE PETER
THE GREAT WANTED TO BUY 73
Chapter Five
PROPERTIES OF LIQUIDS AND GASES
THE TWO COFFEE-POTS 77
IGNORANCE OF ANCIENTS 77
LIQUIDS PRESS ... UPWARDS 79
WHICH IS HEAVIER? .80
A LIQUID'S NATURAL SHAPK 81
WHY IS SHOT ROUND? 81*
THE "BOTTOMLESS" WINEGLASS . . . .84
UNPLEASANT PROPERTY 85
THE UNSINKABLE COIN .87
CARRYING WATER IN A SIEVE .... 88
FOAM HELPS ENGINEERS 81)
FAKE "PERPETUAL MOTION" MACHINE . . . 90
BLOWING SOAP BUBBLES .92
THINNEST OF ALL <),>
WITHOUT WETTING A FINGKH 97
HOW WE DRINK 98
A BETTER FUNNEL 98
A TON OF WOOD AND A TON OF IRON .... 99
THE MAN WHO WEIGHED NOTHING 99
"PERPETUAL" CLOCK 10*
Chapter Six
HEAT
WHEN IS THE OKTYABRSKAYA RAILWAY LONG-
ER? 106
UNPUNISHED THEFT 107
HOW HIGH IS THE EIFFEL TOWEH? .... 108
FROM TEA GLASS TO WATER GAUGE .... 109
THE BOOT IN THE BATHHOUSE 110
HOW TO WORK MIRACLES Ill
SELF-WINDING CLOCK 113
INSTRUCTIVE CIGARETTE 115
ICE THAT DOESN'T MELT IN BOILING WATER 115
ON TOP OR BENEATH? 116
DRAUGHT FROM CLOSED WINDOW 117
MYSTERIOUS TWIRL 117
DOES A WINTER COAT WARM YOU? 118
THE SEASON UNDERFOOT 119
PAPER POT 120
WHY IS ICE SLIPPERY? 122
THE ICICLES PROBLEM 123
Chapter Seven
LIGHT
TRAPPED SHADOWS 126
THE CHICK IN THE EGG 128
PHOTOGRAPHIC CARICATURES 128
THE SUNRISE PROBLEM 130
Chapter Eight
REFLECTION AND REFRACTION
SEEING THROUGH WALLS 132
THE SPEAKING HEAD 134
IN FRONT OR BEHIND 135
IS A MIRROR VISIBLE? 135
IN THE LOOKING-GLASS 135
MIRROR DRAWING 137
SHORTEST AND FASTEST 138
AS THE CROW FLIES . 139
THE KALEIDOSCOPE 140
PALACES OF ILLUSIONS AND MIRAGES .... 141
WHY LIGHT REFRACTS AND HOW 144
LONGER WAY FASTER 145
THE NEW CRUSOES 148
ICE HELPS TO LIGHT FIRE 150
HELPING SUNLIGHT 152
MIRAGES 154
"THE GREEN RAY" 15K
Chapter Nine
VISION
BEFORE PHOTOGRAPHY WAS INVENTED . . . 1(51
WHAT MANY DON'T KNOW HOW TO DO ... 1G2
HOW TO LOOK AT PHOTOGRAPHS 163
HOW FAR TO HOLD A PHOTOGRAPH . . . 101
QUEER EFFECT OF MAGNIFYING GLASS . . . 165
ENLARGED PHOTOGRAPHS 1GH
BEST SEAT IN MOVIE-HOUSE 167
FOR READERS OF PICTORIAL MAGAZINKS . 108
HOW TO LOOK AT PAINTINGS 160
THREE DIMENSIONS IN TWO 170
STEREOSCOPE 170
BINOCULAR VISION 172
WITH ONE EYE AND TWO 176
DETECTING FORGERY 176
AS GIANTS SEE IT 177
UNIVERSE IN STEREOSCOPE 179
THREE-EYED VISION 180
STEREOSCOPIC SPARKLE 181
TRAIN WINDOW OBSERVATION 182
THROUGH TINTED EYEGLASSES 183
"SHADOW MARVELS" 184
MAGIC METAMORPHOSES 185
HOW TALL IS THIS BOOK? 186
TOWER CLOCK DIAL 187
BLACK AND WHITE 187
WHICH IS BLACKER? 189
STARING PORTRAIT 190
MORE OPTICAL ILLUSIONS 191
SHORT-SIGHTED VISION 195
Chapter Ten
SOUND AND HEARING
HUNTING THE ECHO J<)7
SOUND AS RULER 199
SOUND MIRRORS 200
SOUND IN THEATRE 202
SEA-BOTTOM ECHO 202
WHY DO BEES BUZZ? 204
AUDITORY ILLUSIONS 205
WHERE'S THE GRASSHOPPER? 205
THE TRICKS OUR EARS PLAY 207
99 QUESTIONS 208
FROM THE AUTHOR'S FOREWORD
TO THE 13th EDITION
The aim of this book is not so much to give you some fresh knowl-
edge, as to help you "learn what you already know". In other words,
my idea is to brush up and liven your basic knowledge of physics, and
to teach you how to apply it in various ways. To achieve this purpose
conundrums, brain-teasers, entertaining anecdotes and stories, amusing
experiments, paradoxes and unexpected comparisons all dealing
with physics and based on our everyday world and sci-fic are afford-
ed. Believing sci-fic most appropriate in a book of this kind, I have
quoted extensively from Jules Verne, H. G. Wells, Mark Twain and
other writers, because, besides providing entertainment, the fantastic
experiments these writers describe may well serve as instructive illus-
trations at physics classes.
I have tried my best both to arouse interest and to amuse, as I be-
lieve that the greater the interest one shows, the closer the heed one
pays and the easier it is to grasp the meaning thus making for better
knowledge.
However, I have dared to defy the customary methods employed in
writing books of this nature. Hence, you will find very little in the way
of parlour tricks or spectacular experiments. My purpose is different,
being mainly to make you think along scientific lines from the angle
of physics, and amass associations with the variety of things from every-
day life. I have tried in rewriting the original copy to follow the prin-
ciple that was formulated by Lenin thus: "The popular writer leads his
reader towards profound thoughts, towards profound study, proceeding
from simple and generally known facts; with the aid of simple argu-
merits or striking examples he shows the main conclusions to be drawn
from those facts and arouses in the mind of the thinking reader ever
newer questions. The popular writer does not presuppose a reader that
docs not think, that cannot or does not wish to think; on the con-
trary, he assumes in the undeveloped reader a serious intention to use
his head and aids him in his serious and difficult work, leads him, helps
him over his first steps, and teaches him to go forward independently.
(Collected Works, Vol. 5, p. 311, Moscow 1961.)
Since so much interest has been shown in the history of this book,
let me give you a few salient points of its "biography".
Physics for Entertainment first appeared a quarter of a century ago,
being the author's first-born in his present large family of several score
of such books. So far, this bookwhich is in two partshas been pub-
lished in Russian in a total print of 200,000 copies. Considering that
many are to be found on the shelves of public libraries, where each copy
reaches dozens of readers, I daresay that millions have read it. I have
received letters from readers in the furthermost corners of the Soviet
Union.
A Ukrainian translation was published in 1925, and German and
Yiddish translations in 1931. A condensed German translation was
published in Germany. Excerpts from the book have been printed
in French in Switzerland and Belgium and also in Hebrew in
Palestine.
Its popularity, which attests to the keen public interest displayed
in physics, has obliged me to pay particular note to its standard, which
explains the many changes and additions in reprints. In all the 25
years it has been in existence the book has undergone constant revision,
its latest edition having barely half of the maiden copy and practically
not a single illustration from the first edition.
Some have asked me to refrain from revision, not to be compelled "to
buy the new revised edition for the sake of a dozen or so new pages".
Scarcely can such considerations absolve me of my obligation constantly
to improve this book in every way. After all Physics for Enter-
tainment is not a work of fiction. It is a book on science be it even
popular science and the subject taken, physics, is enriched even in
10
its fundamentals with every day. This must necessarily be taken into
consideration.
On the other hand, I have been reproached more than once for fail-
ing to deal in this book with questions such as the latest achievements
in radio engineering, nuclear fission, modern theories and the like.
This springs from a misunderstanding. This book has a definite pur-
pose; it is the task of other books to deal \\ilh the points mentioned.
Physics for Entertainment has, besides its second part, some other
associated books of mine. One, Physics at Every Step, is intended for
the unprepared layman who has still not embarked upon a systematic
study of physics. The other two are, on the contrary, for people >\ho
have gone through a secondary school course in physics. These arc
Mechanics for Entertainment and Do You Know Your Physics?, the
Jast being the sequel, as it wore, to this book.
1936 Y. P er elm an
CHAPTER ONE
SPEED AND VELOCITY. COMPOSITION
OF MOTIONS
HOW FAST DO WE MOVE?
A good athlete can run 1.5 km in about 3 min 50 pec the 1958
world record was 3 min 36.8 sec. Any ordinary person usually does,
when walking, about 1.5 metres a second. Reducing the athlete's rate
to a common denominator, we see that he covers seven metres every
second. These speeds are not absolutely comparable though. Walking,
you can keep on for hours on end at the rate of 5 km. p.h. But the
runner will keep up his speed for only a short while. On quick march,
infantry move at a speed which is but a third of the athlete's,
doing 2 m/sec, or 7 odd km. p.h. But they can cover a much greater
distance.
I daresay you would find it of interest to compare your normal walk-
ing pace with the "speed" of the proverbially slow snail or tortoise.
The snail well lives up to its reputation, doing 1.5 mm/sec, or 5.4 metres
p.h. exactly one thousand times less than your rate. The other clas-
sically slow animal, the tortoise, is not very much faster, doing usually
70 metres p.h.
Nimble compared to the snail and the tortoise, you would find your-
self greatly outraced when comparing your own motion with other
motions even not very fast ones that we see all around us. True,
you will easily outpace the current of most rivers in the plains and be
a pretty good second to a moderate wind. But you will successfully
vie with a fly, which does 5 m/sec, only if you don skis. You won't over-
13
take a hare or a hunting dog even when riding a fast horse and you can
rival the eagle only aboard a plane.
Still the machines man has invented make him second to none for
speed. Some time ago a passenger hydrofoil ship, capable of 60-70 km.
p.h., was launched in the U.S.S.R. (Fig. 1). On land you can move faster
Fig. 1. Fast passenger hydrofoil ship
than on water by riding trains or motor cars which can do up to
200 km. p.h. and more (Fig. 2). Modern aircraft greatly exceed even
these speeds. Many Soviet air routes are serviced by the large TU-104
fig. 2. New Soviet ZIL-111 motor car
(Fig. 3) and TU-114 jet liners, which do about 800 km. p.h. It was
not so long ago that aircraft designers sought to overcome the "sound
barrier", to attain speeds faster than that of sound, which is 330 m/sec,
14
or 1,200 km. p.b. Today this has been achieved. We have some small
but very fast supersonic jet aircraft that can do as much as 2,000
km.p.h.
There are man-made vehicles that can work up still greater speeds.
The initial launching speed of the first Soviet sputnik was about
fig. 3. TU-104 jet airliner
8 km/sec. Later Soviet space rockets exceeded the so-called
velocity, which is 11.2 km/sec at ground level.
The following table gives some interesting speed data.
escape
A snail
1.5 mm/ sec or
5.4 metres p.h.
A tortoise
20 or
70
A fish
1 m/scp or
3.5 km. p.h
A pedestrian
1.4 or
f. r
D
Cavalry, pacing
1.7 or
6
M trotting
3.5 or
12.fi
A fly
5 or
18
A skier
5 or
18
Cavalry, galloping
A hydrofoil ship
8.5 or
16 or
30
58
A hare
18 or
65
An eagle
24 or
86
A hunting dog
25 or
90
A train
28 or
100
A ZIL-111 passenger car
50 or
170
A racing car (record)
A TU-104 jet airliner
174 or
220 or
633
800
Sound in air
330 or
1,200
Supersonic jet aircraft
550 or
2.000
The earth's orbital veloc-
ity
30,000 " or
108,000 '
15
RACING AGAINST TIME
Could one leave Vladivostok by air at 8 a.m. and land in Moscow
at 8 a.m. on the same day?
I'm not talking through my hat. We can really do that. The answer
lies in the 9-hour difference in Vladivostok and Moscow zonal times.
If our plane covers the distance between the two cities in these 9 hours,
it will land in Moscow at the very same time at which it took off from
Vladivostok. Considering that the distance is roughly 9,000 kilome-
tres, we must fly at a speed of 9,000:9 = 1,000 km. p.h., which is quite
possible today.
To "outrace the Sun" (or rather the earth) in Arctic latitudes,
one can go much more slowly. Above Novaya Zemlya, on the 77th par-
allel, a plane doing about 450 km. p.h. would cover as much as a definite
point on the surface of the globe would cover in an identical space of
time in the process of the earth's axial rotation. If you were flying in
such a plane you would see the sun suspended in immobility. It would
never set, provided, of course, that your plane was moving in the
proper direction.
It is still easier to "outrace the Moon" in its revolution around the
earth. It takes the moon 29 times longer to spin round the earth than
it takes the earth to complete one rotation (we are comparing, naturally,
the so-called "angular", and not linear, velocities). So any ordinary
steamer making 15-18 knots could "outrace the Moon" oven in the
moderate latitudes.
Mark Twain mentions this in his Innocents Abroad. When sailing
across the Atlantic, from New York to the Azores "... wo had balmy
summer weather, and nights that were even finer than the days. We had
the phenomenon of a full moon located just in the same spot in the
heavens at the same hour every night. The reason for this singular conduct
on the part of the mo on did not occur to us at first, but it did afterward
when we reflected that we were gaming about twenty minutes every day,
because we were going east so fast we gained just enough every day
to keep along with the moon. "
16
THE THOUSANDTH OF A SECOND
For us humans, the thousandth of a second is nothing from the angle
of time. Time intervals of this order have only started to crop up in
some of our practical work. When people used to reckon the time ac-
cording to the sun's position in the sky, or to the length of a shadow
(Fig. 4), they paid no heed to minutes, considering them even unworthy
Fig. 4. How to reckon the time "according to the
position of the sun (left), and by the length of a shadow
(right)
of measurement. The tenor of life in ancient times was so unhurried
that the timepieces of the day the sun-dials, sand-glasses and the
like had no special divisions for minutes (Fig. 5). The minute hand
first appeared only in the early 18th century, while the second sweep
came into use a mere 150 years ago.
But back to our thousandth of a second. What do you think could
happen in this space of time? Very much, indeed I True, an ordinary
train would cover only some 3 cm. But sound would already fly 33 cm
and a plane half a metre. In its orbital movement around the sun, the
earth would travel 30 metres. Light would cover the great distance of
300 km. The minute organisms around us wouldn't think the thousandth
22668
17
of a second so negligible an amount of time if they could think of
course. For insects it is quite a tangible interval. In the space of a
second a mosquito flaps its wings 500 to 600 times. Consequently in
the space of a thousandth of a second, it would manage either to raise
its wings or lower them*
We can't move our limbs as fast as insects. The fastest thing we can
do is to blink our eyelids. This takes place so quickly that we fail even
to notice the transient obscurement of our field of vision. Few know,
though, that this movement, "in the twinkling of an eye" which has
Fig. 6. An ancient water clock (loft) and an old pocket-
watch (right). Note that neither has the minute
hand
become synonymous for incredible rapidity is quite slow if measured
in thousandths of a second. A full "twinkling of an eye" averages as
exact measurement has disclosed two- fifths of a second, which gives
us 400 thousandths of a second. This process can be divided into the
following stages: firstly, the dropping of the eyelid which takes 75-90
thousandths of a second; secondly, the closed eyelid in a state of rest,
which takes up 130-170 thousandths; and, thirdly, the raising of the
eyelid, which takes about 170 thousandths.
As you see, this one "twinkling of an eye" is quite a considerable time
interval, during which the eyelid even manages to take a rest. If we
18
could photograph mentally impressions lasting the thousandth of a
second, we would catch in the u twinkling of an eye'* two smooth mo-
tions of the eyelid, separated by a period during which the eyelid would
be at rest.
Generally speaking, the ability to do such a thing would completely
transform the picture we get of the world around us and we would see
the odd and curious things that H. G. Wells described in his New Accel-
erator. This story relates of a man who drank a queer mixture which
caused him to see rapid motions as a series of separate static phenom-
ena. Here are a few extracts.
"'Have you ever seen a curtain before a window fixed in that way
before?'
"I followed his eyes, and there was the end of the curtain, frozen, as
it were, corner high, in the act of flapping briskly in the breeze.
"'No, 1 said I, 'that's odd.'
"'And here,' he said, and opened the hand that held the glass. Natu-
rally I winced, expecting the glass to smash. But so far from smashing
it did not even seem to stir; it hung in mid-air motionless. 'Roughly
speaking,' said Gibberne, 'an object in these latitudes falls 16 feet in
a second. This glass is falling 16 feet in a second now. Only you see,
it hasn't been falling yet for the hundredth part of a second. [Note also
that in the first hundredth of the first second of its downward flight a
body, the glass in this case, covers not the hundredth part of the dis-
tance, but the 10,000th part (according to the formula S=U2 gt*). This
is only 0.5 mm and in the first thousandth of the second it would be
only 0.01 mm.l
"'That gives you some idea of the pace of my Accelerator.' And he
waved his hand round and round, over and under the slowly sinking
glass.
"Finally he took it by the bottom, pulled it down and placed it
very carefully on the table. 'Eh?' he said to me, and laughed....
"I looked out of the window. An immovable cyclist, head down and
with a frozen puff of dust behind his driving-wheel, scorched to over-
take a galloping char-a-banc that did not stir....
"We went out by his gate into the road, nnd there we made a minute
examination of the statuesque passing traffic. The top of the wheels
2* 19
and some of the legs of the horses of this char-a-banc, the end of the
whip lash and the lower jaw of the conductor who was just beginning
to yawn were perceptibly in motion, but all the rest of the lumbering
conveyance seemed still. And quite noiseless except for a faint rat-
tling that came from one man's throat! And as parts of this frozen
edifice there were a driver, you know, and a conductor, and eleven
people!...
"A purple-faced little gentleman was frozen in the midst of a violent
struggle to refold his newspaper against the wind; there were many evi-
dences that all these people in their sluggish way were exposed to a
considerable breeze, a breeze that had no existence so far as our sensa-
tions went....
"All that I had said, and thought, and done since the stuff had begun
to work in my veins had happened, so far as those people, so far as the
world in general went, in the twinkling of an eye...."
Would you like to know the shortest stretch of time that scientists
can measure today? Whereas at the beginning of this century it was
only the 10,000th of a second, today the physicist can measure the
100,000 millionth of a second; this is about as many times less than a
second as a second is less than 3,000 years!
THE SLOW-MOTION CAMERA
When H. G. Wells was writing his story, scarcely could he have
ever thought he would see anything of the like. However he did live
to see the pictures he had once imagined, thanks to what has been
called the slow-motion camera. Instead of 24 shots a second as ordi-
nary motion-picture cameras do this camera makes many times more.
When a film shot in this way is projected onto the screen with the
usual speed- of 24 frames a second, you see things taking place much
more slowly than normally high jumps, for instance, seem unusually
smooth. The more complex types of slow-motion cameras will almost
Simula H. G. Wei Is 's world of fantasy.
20
WHEN WE MOVE ROUND THE SUN FASTER
Paris newspapers once carried an ad offering a cheap and pleasant
way of travelling for the price of 25 centimes. Several sim-
pletons mailed this sum. Each received a letter of the following
content:
"Sir, rest at peace in bed and remember that the earth turns. At the
49th parallel that of Paris you travel more than 25,000 km a day.
Should you want a nice view, draw your curtain aside and admire the
starry sky."
The man who sent these letters was found and tried for fraud. The
story goes that after quietly listening to the verdict and paying the
fine demanded, the culprit struck a theatrical pose and solemnly de-
clared, repeating Galileo's famous words: "It turns. 1 '
He was right, to some extent, after all, every inhabitant of the
globe "travels" not only as the earth rotates. He is transported with
still greater speed as the earth revolves around the sun. Every second this
planet of ours, with us and everything else on it, moves 30 km in space,
turning meanwhile on its axis. And thereby hangs a question not devoid
of interest: When do we move around the sun faster? In the daytime
or at night?
A bit of a puzzler, isn't it? After all, it's always day on one side of
the earth and night on the other. But don't dismiss my question as
senseless. Note that I'm asking you not when the earth itself moves
faster, but when we, who live on the earth, move faster in the heavens.
And that is another pair of shoes.
In the solar system we make two motions; we revolve around the
sun and simultaneously turn on the earth's axis. The two motions
add , but with different results, depending whether we are on the daylit
side or on the nightbound one.
Fig. 6 shows you that at midnight the speed of rotation is added to
that of the earth's translation, while at noon it is, on the contrary,
subtracted from the latter. Consequently, at midnight we move faster
in the solar system than at noon. Since any point on the equator travels
about half a kilometre a second, the difference there between midnight
and midday speeds comes to as much as a whole kilometre a second.
21
Midday
Midnighi
Fig. 6. On the dark side we move around the sun faster
than on the sunlit side
Any of you who are good at geometry will easily reckon that for
Leningrad, which is on the 60th parallel, this difference is only half as
much. At 12 p.m. Leningraders travel in the solar system half a
kilometre more a second than they would do at 12 a.m.
THE CART-WHEEL RIDDLE
Attach a strip of coloured paper to the side of the rim of a cart-wheel
or bicycle tire, and watch to see what happens when the cart, or bicycle,
moves. If you are observant enough, you will see that near the ground
the strip of paper appears rather distinctly, while on top it flashes by
so rapidly that you can hardly spot it.
Doesn't it seem that the top of the wheel is moving faster than the
bottom? And when you look at the upper and lower spokes of the moving
wheel of a carriage, wouldn't you think the same? Indeed, the upper
spokes seem to merge into one solid body, whereas the lower spokes
can be made out quite distinctly.
22
Incredibly enough, the top of the rolling-wheel does really move faster
than the bottom. And, though seemingly unbelievable, the explanation
is a pretty simple one. Every point on the rolling wheel makes two
motions simultaneously one about the axle and the other forward
together with the axle. It's the same as with the earth itself. The two
motions add, but with different results for the top and bottom of the
wheel. At the top the wheel's motion of rotation is added to its mo-
tion of translation, since both are in the same direction. At the bot
torn rotation is made in the reverse direction and, consequently, must
be subtracted from translation. That is why the stationary observer
sees the top of the wheel moving faster than the bottom.
A simple experiment which can be done at convenience proves this
point. Drive a stick into the ground next to the wheel of a stationary
vehicle opposite the axle. Then take a piece of coal or chalk and make two
marks on the rim of the wheel at the very top and at the very bottom.
Your marks should be right opposite the stick. Now push the vehicle
a bit to the right (Fig. 7), so that the axle moves some 20 to 30 cm away
from the stick. Look to see how the marks have shifted. You will find
that the upper mark A has shifted much further away than the lower
one B which is almost where it was before.
Fig. 7. A comparison between the distances away from
the stick of points A and B on a rolling wheel (right) shows
that the wheel's upper segment moves faster than its lower
part
THE WHEEL'S SLOWEST PART
As we have seen, not all parts of a rolling cart-wheel move with the
same speed. Which part is slowest? That which touches the ground.
Strictly speaking, at the moment of contact, this part is absolutely
stationary. This refers only to a rolling wheel. For the one that spins
round a fixed axis, this is not so. In the case of a flywheel, for instance,
all its parts move with the same speed.
BRAIN-TEASER
Here is another, just as ticklish, problem. Could a train going from
Leningrad to Moscow have any points which, in relation to the rail-
road track, would be moving in the opposite direction? It could, we find.
All the train wheels have such points every moment. They are at the
bottom of the protruding rim of the wheel (the bead). When the train
goes forward, these points move backward. The following experiment,
which you can easily do yourself, will show you how this happens.
Attach a match to a coin with some plasticine so that the match pro*
trades in the plane of the radius, as shown in Fig. 8. Set the coin together
with the match in a vertical position on the edge of a flat ruler and
hold it with your thumb at its point of contact C. Then roll it to and
fro. You will see that points F, E and D of the jutting part of the match
Fig. 8. When the coin is rolled
leftwards, points F t E and
D of the jutting part of the
match move backwards
Fig. 9. When the train wheel
rolls leftwards the lower part
of its rim rolls the other way
/ig. 10. Top: the curve (a cycloid) described by every
point on the rim of a rolling cart-wheel. Bottom: the curve
described by every point on the rim of a train wheel
move not forwards but backwards. The further point D the end of the
match is from the edge of the coin, the more noticeable backward
motion is (point D shifts to D').
The points on the bead of the train wheel move similarly. So when
I tell you now that there are points in a train that move not forward
but backward, this should no longer surprise you. True, this backward
motion lasts only the negligible fraction of a second. Still there is,
despite all our habitual notions, a backward motion in a moving train.
Figs. 9 and 10 provide the explanation.
WHERE DID THE YACHT CAST OFF?
A rowboat is crossing a lake. Arrow a in Fig. 11 is its velocity vector.
A yacht is cutting across its course; arrow b is its velocity vector.
Where did the yacht cast off? You would naturally point at once to
point M. But you would get a different reply from the people in the
dinghy. Why?
They don't see the yacht moving at right angles to their own course,
because they don't realise that they are moving themselves. They think
25
Fig. 11. The yacht is cutting across the rowboat's course. Arrows a and b designate
the velocities. What will the people in the dinghy see?
they're stationary, while everything around is moving with their own
speed but in the opposite direction. From their point of view the yacht
is moving not only in the direction of the arrow b but also in the di-
rection of the dotted line a opposite to their own direction (Fig. 12).
The two motions of the yacht the real one and the seeming one are
resolved according to the rule of the parallelogram. The result is that
the people in the rowboat think the yacht to be moving along the
diagonal of the parallelogram 06; that is also why they think the yacht
cast off not at point M , but at point /V, way in front of the rowboat
(Fig. 12).
Travelling together with the earth in its orbital path, we also plot
the position of the stars wrongly just as the people in the dinghy did
when asked where the yacht cast off from. We see the stars displaced
slightly forward in the direction of the earth's orbital motion. Of course,
the earth's speed is negligible compared with that of light (10,000
Fig. 12. The people in the dinghy think the yacht to be coming towards them
slantwise from point N
times less) and, consequently, this stellar displacement, known as
aberration of light, is insignificant. However, we can detect it with
the aid of astronomical instruments.
Did you like the yacht problem? Then answer another two questions
related to the same problem. Firstly, give the direction in which the
yachtsmen think the dinghy is moving. Secondly, say where the yachts*
men think the dinghy is heading. To answer, you must construct a par-
allelogram of velocities on the vector a (Fig. 12), whose diagonal will
indicate that from the yachtsmen's point of view the dinghy seems to
be moving slantwise, as if heading for the shore.
CHAPTER TWO
GRAVITY AND WEIGHT. LEVERS. PRESSURE
TRY TO STAND UP!
You'd think I was joking if I told you that you wouldn't be able
to get up from a chair provided you sat on it in a certain way, even
though you wouldn't be strapped down to it. Very well, let's have a go.
Sit down on a chair in the same way the boy in Fig. 13 is sitting. Sit
upright and don't shove your feet under the chair. Now try to get up
without moving your feet or bending forward. You can't, however
hard you try. You'll never stand up until you push your feet under
the chair or lean forwards.
Before I explain, let me tell you about the equilibrium of
bodies in general, and of the human body in particular. A thing will
not topple only when the perpendicular
from its centre of gravity goes through
its base. The leaning cylinder in Fig. 14
is bound to fall. If, on the other hand, the
perpendicular from its centre of gravity
fell through its base, it wouldn't topple
over. The famous leaning towers of Pisa
and Bologna, or the leaning campanile in
Arkhangelsk (Fig. 15), don't fall, despite
their tilt, for the same reason. The per-
pendiculars from their centres of gravity
do not lie outside their bases. Another
Fig. 13. It's impossible to ieaBon is that their foundations are sunk
get up deep in the ground.
You won't fall only when the perpendicular from your centre of
gravity lies within the area bound by the outer edge of your feet (Fig. 16).
That is why it is so hard to stand on one leg and still harder to
balance on a tight-rope. Our "base" is very small and the perpendicular
from the centre of gravity may easily come to lie outside its limits.
Have you noticed the odd gait of an "old sea dog"? He spends most of
his life aboard a pitching ship
where the perpendicular from
the centre of gravity of his body
may come to fall outside his
"base" any moment. That accus-
toms him to walk on deck so
that his feet are set wide apart
and take in as large a space as
Fig. 14. The cylinder must
topple as the perpendicular
from its centre of gravity
lies outside its base
Fig. 15. Arkhangelsk leaning
campanile. A reproduction from
an old photograph
possible, which saves him from falling. Naturally, he'll waddle in the
same habitual fashion on hard ground as well.
Another instance of an opposite nature this time. This is when the
effort to keep one's balance results in a beautiful pose. Porters who
carry loads on their heads are well-built a point, I presume, you have
noticed. You may have also seen exquisite statues of women holding
jars on their heads. It is because they carry a load on their heads that
these people have to hold their heads and bodies upright. If they
29
were to lean in any direction, this would shift the perpendicular
from the centre of gravity higher than usual, because of the head-load,
outside the base and unbalance them.
Back now to the problem I set you at the beginning of the chapter.
The sitting boy's centre of gravity is inside the body near the spine
about 20 centimetres above the level of his nave).
Drop a perpendicular from this point. It will pass
through the chair behind the feet. You already
know that for the man to stand up it should go
through the area taken up by the feet. Conse-
quently, when we get up we must either bend
forward, to shift the centre of gravity, or shove our
feet beneath the chair to place our "base" below
Fig. 16. When one the centre of gravity. That is what we usually do
stands the perpendic- wben getting up from a chair. If we are not
ular from the cen- o r
tre of gravity passes allowed to do this, we 11 never be able to stand
boumf^ thcTsoles'of u P~" as you, have already gathered from your own
one's feet experience.
WALKING AND RUNNING
The things you do thousands of times a day, and day after day all
your life, ought to be things you have a very good idea about, oughtn't
they? Yes, you will say. But that is far from so. Take walking and
running, for instance. Gould anything be more familiar? But I won-
der how many of you have a clear picture of what we really do when we
walk and run, or of the difference between the two. Let's see what a
physiologist has to say about walking and running. I'm sure most of
you will find his description startlmgly novel. (The passage is from
Prof. Paul Bert, Lectures on Zoology. The illustrations are my own.)
"Suppose a person is standing on one leg, the right leg, for instance.
Suppose further that he is lifting his heel, meanwhile bending forwards.
[When walking or running a person exerts on the ground, when pushing
his foot away from it, a pressure of some 20kg in addition to
his weight. Hence a person exerts a greater pressure on the ground
when he is moving than when standing. V. P.] In such a position the
30
perpendicular from the centre of gravity will naturally be outside the
base and the person is bound to fall forwards. Scarcely has he started
doing this than he quickly throws forward his left leg, which was
suspended thus far, to put it down on the ground in front of the per-
pendicular from the centre of gravity. The perpendicular thus comes
to drop through the area bound by the lines linking the points of
Fig. 17. How one walks. The series of positions in walking
support of both feet. Balance is thus restored; the person has taken
a step forward.
"He may remain in this rather tiring position, but should he wish
to continue forward, he will lean still further forward, shift the per-
pendicular from the centre of gravity outside the base, and again throw
his leg the right one this time forwards when about to fall. He thus
B
Fig. 18. A graph showing how one's feet move when walking. Line A
is the left foot and line B is the right foot. The straight sections show
when the foot is on the ground, and the curveswhen the foot is in the
air. In the time-interval a both feet are on the ground; in the time-
interval 6, foot A is in the air and foot B still on the ground; in the
timeinterval c both feet are again on the ground. The faster ono walks,
the shorter the time-intervals a and c get (compare with the "run-
ning" graph in Fig. 20).
takes another step forward. And so on ana so forth. Consequently,
walking is just a series of forward fallings, punctually forestalled
by throwing the leg left behind into a supporting position.
Fig. 19. How one runs. The series of positions in running, showing
moments when both feet are in the air
"Let's try to get to the root of the matter. Suppose the first step
has already been made. At this particular moment the right foot is
still on the ground and the left foot is already touching it. If the step
is not very short the right heel should be lifted, because it is this rising
heel that enables one to bend forward and change one's balance. It is the
heel of the left foot that touches the ground first. When next the entire
\
N
A
Fig. 20. A graph showing how one's feet move when running
(compare with Fig. 18). There are time-intervals (6, d and /)
when both feet are in the air. This is the difference between
running and walking
sole stands on the ground, the right foot is lifted completely and no
longer touches the ground. Meanwhile the left leg, which is slightly
bent at the knee, is straightened by a contraction of the femoral triceps
to become for an instant vertical. This enables the half-bent right
32
leg to move forward without touching the ground. Following the
body's movement the heel of the right foot comes to touch the ground in
time for the next step forwards. The left leg, which at this moment has
only the toes of the foot touching the ground and which is about to
rise, goes through a similar series of motions.
"Running differs from walking in that the foot on the ground is
energetically straightened by a sudden contraction of its muscles to
throw the body forwards so that the latter is completely off the ground
for a very short interval of time. Then the body again falls to come to
rest on the other leg, which quickly moves forward while the body
is still in the air. Thus, running consists of a series of hops from one
foot to the other. "
As for the energy a person expends in walking along a horizontal
pavement it is not at all nil as some might think. With every step made,
the centre of gravity of a walker's body is lifted by a few centimetres.
A reckoning shows that the work spent in walking along a horizontal
path is about a fifteenth of that required to raise the walker's body to a
height equivalent to the distance covered.
HOW TO JUMP FROM A MOVING CAR
Most will surely say that one must jump forward, in the direction in
which the car is going, in conformity with the law of inertia. But what
does inertia have to do with it all? Til wager that anyone you ask this
question will soon find himself in a quandary, because according to
inertia one should jump backwards, contrary to the direction of motion.
Actually inertia is of secondary importance. If we lose sight of the main
reason why one should jump forwards one that has nothing to do with
inertia we will indeed come to think that we must jump backwards
and not forwards.
Suppose you have to jump off a moving car. What happens? When
you jump, your body has, at the moment you let go, the same velocity
as the car itself by inertia and tends to move forwards. By jumping
forwards, far from diminishing this velocity, we, on the contrary, in-
crease it. Then shouldn't we jump backwards since in that case the
velocity thus imparted would be subtracted from the velocity our body
32668 33
possesses by inertia, and hence, on touching the ground, our body would
have less of a toppling impetus?
But, when one jumps from a moving carriage, one always jumps
forwards in the direction of its movement. That is indeed the best way,
a time-honoured one, and I strongly warn you against trying to test
the awkwardness of jumping backwards.
We seem to have a contradiction, don't we? Now whether we jump
forwards or backwards we risk falling, since our bodies are still moving
when our feet touch the ground and come to a halt. (See "When Is a
Horizontal Line Not Horizontal?" from the third chapter of Mechanics
for Entertainment for another explanation.) When jumping forwards,
the speed with which our bodies move is even greater than when jump-
ing backwards, as I have already noted. But it is much safer to jump
forwards than backwards, because then we mechanically throw a leg
forwards or even run a few steps, to steady ourselves. Wo do this with-
Out thinking; it's just like walking. After all, according to mechanics,
walking, as was noted before, is nothing but a series of forward fallings
of our body, guarded against by the throwing out of a leg. Since we don't
have this guarding movement of the leg when falling backwards
the danger is much greater. Then even if we do fall forwards we can
soften the impact with our hands, which we can't do if we fall on our
backs.
As you see, it is safer to jump forwards, not so much because of inertia,
but because of ourselves. This rule is plainly inapplicable to one's
belongings, for instance. A bottle thrown from a moving car forwards
Stands more chances of crashing when it hits the ground than if thrown
backwards. So if you have to jump from a moving car and have some
luggage with you, first chuck out the luggage backwards and then jump
forwards yourself. Old hands like tramcar conductors and ticket in-
spectors often jump off stepping backwards but with their backs turned to
the direction in which they jump. This gives them a double advantage:
firstly they reduce the velocity that the body acquires by inertia,
awl, secondly, guard themselves against falling on their backs, as
they jump with their faces forward, in the direction where they are
most likely to fall.
CATCHING A BULLET '
The following curious incident was reported during the First World
War. One French pilot, while flying at an altitude of two kilometres,
saw what he took to be a fly near his face. Trapping it with his hands,
he was flabbergasted to find that he had caught a German bullet! How
like the tall stories told by Baron Munchausen of legendary fame,
who claimed he had caught cannon balls with bare hands! But there
is nothing incredible in the bullet-catching story.
A bullet does not fly everlastingly with its initial velocity of 800-
900 m/scc. Air resistance causes it to slow down gradually to a mere
40 m/scc towards the end of its journey. Since aircraft fly with a sim-
ilar speed, we can easily have a situation when bullet ami plane will
be flying with the same speed, in which case the bullet, in its relation
to the piano and its pilot, will be stationary or barely moving. The
pilot can easily catch it with his hand, especially if gloved, because a
bullet heats up considerably while whizzing through the air.
MELON AS BOMB
We have seen that in certain circumstances a bullet can IOSQ its
"sting". But there are instances when a gontly thrown "peaceful"
object has a destructive impact. During the Leningrad-Tiflis motor
run in 1924, Caucasian peasants tossed melons, apples, and thfe like at
the racing cars to express their admiration. However, these innocuous
gifts made terrible dents and seriously injured the motorists. This
happened because the car's velocity added to that of the tossed melons
or apples, transforming them into dangerous projectiles. A ten-gramme
bullet possesses the same energy of motion as a 4kg melon thrown at
a car doing 120 km.p.h. Of course, the impact of a melon is not the
same as the bullet's since melons, after all, are squashy.
When we have super-fast planes doing about 3,000 km.p.h.
a bullet's approximate velocity their pilots may chance to encounter
what we have just described. Everything in the way of a super-
fast aircraft will ram into it. Machine-gun fire or just a chance handful 1 !
of bullets dropped from another plane will have the same effect; these:
bullets will strike the aircraft with the same impact as if fired from a
machine gun. Since the relative velocities in both cases are the same
the plane and bullet meet with a speed of about 800 m/sec the de-
struction done when they collide is the same as well . On the contrary,
bullets fired from behind at a plane moving with the same speed are
harmless, as we have already seen.
Fig. 21. Water-melons tossed at a fast-moving car are as dangerous as bombs
In 1935 engine driver Borshchov prevented a railway disaster by
cleverly taking advantage of the fact that objects moving in the same
direction at practically the same speed come into contact without
knocking each other to pieces. He was driving a train between Yelnikov
and Olshanka, in Southern Russia. Another train was puffing along in
front. The driver of this train couldn't work up enough steam to make
the grade. He uncoupled his engine and several waggons and set off for
the nearest station, leaving a string of 36 waggons behind. But as he
did not place brake-shoes to block their wheels, these waggons started
to roll back down the grade. They gathered up a speed of some 15 km.
p.h. and a collision seemed imminent. Luckily enough, Borshchov
had his wits about him and was able to figure out at once what to do.
He braked his own train and also started a backward manoeuvre, gradual-
36
ly working up the same speed of 15 km.p.h. This enabled him to bring
the 36 waggons to rest against his own engine, without causing any
damage.
Finally this same principle is applied in a device making it easier
for us to write in a moving train. You all know that this is hard to do
because of the jolts when the train passes over the rail joints. They do
not act simultaneously on both paper and pen. So our task is to
Fig. 22. Contraption for writing in a moving train
contrive something that would make the jolts act simultaneously on
both. In this case they would be in a state of rest with respect to each
other.
Fig. 22 shows one such device. The right wrist is strapped to the small-
er board a which slides up and down in the slots in board ft, which,
in turn, slides to and fro along the grooves of the writing board placed
on the train compartment table. This arrangement provides plenty of
"elbow-room" for writing and at the same time causes each jolt to
act simultaneously on both paper and pen, or rather the hand holding
the pen. This makes the process as simple as writing on an ordinary
table at home. The only unpleasant thing about it is that since the
jolts again do not act simultaneously on both wrist and head, you get
a jerky picture of what you're writing.
37
HOW TO WEIGH YOU RSELF
You will get your correct weight only if you stand on the scales without
moving. As soon as you bend down, the scales show less. Why? When
you bend, the muscles that do this also pull up the lower half of your
body and thus diminish the pressure it exerts on the scales. On the
contrary, when you straight en up, your muscles push the upper and
lower halves of the body away from each other; in this case the scales
will register a greater weight since the lower half of your body ex-
erts a greater pressure on the scales.
You will change your weight-readingsprovided the scales are
sensitive enough even by lifting an arm. This motion already slightly
increases your body's seeming weight. The muscles you use to lift your
arm up have the shoulder as their fulcrum and, consequently, push it
together with the body down, increasing the pressure exerted on the
scales. When you stop lifting your arm you start using another, op-
posite set of muscles; they pull the shoulder up, trying to bring it closer
to the end of the arm; this reduces the weight of your body, or rather
its pressure on the scales. On the contrary, when you lower your arm
you reduce the weight of your body, to increase it when you stop low-
ering it. In brief, by using your muscles you can increase or reduce
your weight, meaning of course the pressure your body exerts on the
scales.
WHERE ARE THINGS HEAVIER?
The earth's pull diminishes the higher up we go. If we could lift a
kilogramme 'weight 6,400 km up, to twice the earth's radius away from
its centre, the force of gravity would grow 2 2 =4 times weaker, in which
case a spring balance would register only 250 grammes instead of 1,000.
According to the law of gravity the earth attracts bodies as if its entire
mass were concentrated in the centre; the force of this attraction di-
minishes inversely to the square of the distance away. In our particu-
lar instance, we lifted the kilogramme weight twice the distance away
from th? centre of the earth; hence attraction grew 2 2 =4 times
weaker. If we set the weight at a distance of 12,800 km away from the
surface of the earth three times the earth's radius the force of attrac-
38
tion would grow 3 a =9 times weaker, in which case our kilogramme
weight would register only 111 grammes on a spring balance.
You might conclude that the deeper down in the earth \ve were to put
our one-kilogramme weight, the greater the force of attraction would
grow and the more it should weigh. However, you would bo mistaken.
The weight of a body does not increase; on the contrary, it diminishes.
Downward
attraction
Fig. 23. Gravitational pull lessens the closer we get to the
middle of the Earth
This is because now the earth's attracting forces no longer act just on
one side of the body but all around it. Fig. 23 shows you the weight in
a well; it is pulled down by the fore es below it and simultaneously up
by the forces above it. It is really only the pull of that spherical part
of the earth, the radius of which is equal to the distance from the centre
of the earth to the body, that is of importance. Consequently, the deeper
down we go, the less a body should weigh. At the centre of the earth
it should weigh nothing, as here it is attracted by equal forces on all
sides.
39
To sum up: a body weighs most at the earth's surface; its weight
diminishes whether it is lifted up from the earth's surface or interred
(this would stand, naturally, only if the earth were homogeneous in
density throughout). Actually, the closer to its centre, the greater the
earth's density; at first the force of gravity grows to some distance
down; only then does it start to diminish.
HOW MUCH DOES A FALLING BODY WEIGH?
Have you noticed that odd sensation you experience when you start
to go down in a lift? You feel abnormally light; if you were falling into
a bottomless abyss you would feel the same. This sensation is caused
by weightlessness. At the very first moment when the lift-cabin floor
has already started to go down but you yourself have still not acquired
its velocity, your body exerts scarcely any pressure at all on the floor,
and, consequently, weighs very little. An instant later this queer
sensation is gone. Now your body seeks to fall faster than the smoothly
running lift; it exerts a pressure on the cabin floor, reacquiring its
full weight.
Tie a weight to the hook of a spring balance and observe the pointer as
you quickly lower the balance together with the weight. For conveni-
ence's sake insert a small piece of cork in the slot and observe how it
moves. The pointer will fail to register the full weight; it will be much
less! If the balance were falling freely and you would be able to watch
its pointer meanwhile, you would see it register a zero weight.
The heaviest object will lose all its weight when falling. The reason
is simple. ''Weight" is the force with which a body pulls at something
holding it up or presses down on something supporting it. A jailing
body cannot pull the balance spring as it is falling together with it.
A falling body does not pull at anything or press down on anything.
Hence, to ask how much something weighs when falling is the same as
to ask how much it weighs when it does not weigh.
Galileo, the father of mechanics, wrote way back in the 17th century in
his Mathematical Proofs Concerning Two Fields of a New Science:
"We feel a load on our back when we try to prevent it from dropping.
But if we were to drop as fast as the load does, how could it press upon
40
and burden us? This would be the same as to try to transfix with a
spear [without letting go of it Y. P.] somebody running ahead of us
as fast as we are running ourselves."
The following simple experiment well illustrates this point. Place
a nutcracker on one of the scale pans, with one arm on the pan and the
Fig. 24. Falling bodies are weightless
other tied by a piece of thread to the hook of the scale arm (Fig. 24). Add
weights to the other pan to balance the nutcracker. Apply a lighted
match to the thread. The thread will burn through and the suspended
nutcracker arm will fall onto the pan. Will tho pan holding the nutcrack-
er dip? Will it rise? Or will it remain in equilibrium? Since you know
by now that a falling body weighs nothing, you should be able to give
the correct answer. The pan will rise for a moment. Indeed, though
joined to the lower arm the nutcracker's upper arm nevertheless exerts
less of a pressure on the pan when falling than when stationary. For
a moment the nutcracker's weight diminishes, and thus the pan hold-
ing it rises.
FROM EARTH TO MOON
The years between 1865 and 1870 saw the publication in France of
Jules Verne's From the Earth to the Moon, in which he set forth a fan-
tastic scheme to shoot at the Moon an enormous projectile with people
inside. His description seemed so credible that most of you who have
41
read this book have probably hazarded whether this really could
be.done. Well, let's discuss it. (Today, after Sputnik and Lunik, we know
that it is rockets, not cannon projectiles, that will be used for space
travel. However, since a rocket flies after its last engine burns out, in
accord with the same laws of ballistics, don't think Perelman is be-
fi hind the times.)
Let's see at first whether we can fire a shell
from a gun at least theoretically so that it nev-
er f a ii s j 3ac j t ear th again. Theory tells us that
it's possible. Indeed, why does a shell fired hori-
zontally eventually fall back on earth again? Be-
causo the earth attracts it, curving its trajectory.
Instead of keeping up a straight course, it curves
towards the ground and is, therefore, bound to
hit it sooner or later. The earth's surface is also
curved, but the shell's trajectory is bent still more.
^ However, if we made the shell follow a trajectory
curved in exactly the same way as the earth's
surface it would never fall back on earth again.
Instead, it would trace an orbit concentric with
the earth's circumference, becoming its satellite, a
baby moon.
But how are we to make the shell follow such
a trajectory? All we must do is to impart a suf-
ficient initial velocity. Look at Fig. 25 which
depicts a cross-section of part of the earth. A can-
non is mounted on the hilltop at point A. A shell
fired horizontally from it would reach point B a
second later if not for the earth's gravitational
pull. Instead, it reaches point C five metres lower
than B. Five metres is the distance any freely fall-
ing body travels (in a void) in the first second
due to earth's surface gravitational pull. If, after
Fig. 25. How it drops these* five metres, our shell is at exactly
to reckon a,projec- t he same distance away from the ground as it was
vlie S GSC&pB V6- i . i
lodity when fired at point A, it means that the shell is
following a trajectory curved concentrically to the earth's circum-
ference.
All that remains is to reckon the distance AB (Fig. 25), or, in other
words, the distance the shell travels horizontally in the space of a
second, which will tell us the speed we need. In the triangle AOB, the
side OA is the earth's radius (roughly 6,370,000 m); OC=OA and
fiC=5m; h nee OB is 6,370,005 m. Applying Pythagoras's theorem we get:
a (6,370,000) 2 .
We resolve this equation to find AB equal to roughly 8 km.
So, if there were no drag a shell shot horizontallyjiwitb a muzzle
velocity of 8 km/sec would never fall back to earth again] it would be
an everlasting baby moon.
Now suppose we imparted to our shell a still greater initial velocity.
Where would it fly then? Scientists dealing with celestial mechanics
have proved that velocities of 8, 9 and even 10 km/sec give a trajec-
tory shaped like an ellipse which would be the more elongated the
greater the initial .speed is. When the velocity reaches 11.2 km/sec,
the shell will describe not an ellipse but a non-locked curve, a parabola,
and fly away from the earth never to return (Fig. 26). So, theoretically it
is quite possible to fly to the Moon inside a cannon ball, provided its
muzzle speed is big enough. This, however, is a problem that may
whenvelociiy is
Fig. 26. When a projectile is fired with a starting velocity
of 8 km /sec and more
present some quite specific difficulties. Let me refer you, for greater
detail, to Book Two of Physics for Entertainment and also to Inter-
planetary Travel another book of mine. (In the foregoing we dismissed
the drag which in real life would exceedingly complicate the attain-
ment of such great velocities and perhaps render the task absolutely
impossible.)
FLYING TO THE MOON: JULES VERNE VS. THE TRUTH
Any of you who have read From the Earth to the Moon most likely re-
members the interesting passage describing the projectile's intersection
of the boundary where the Moon matches the Earth in attraction. Wondrous
things happened. All the objects inside the projectile became weight-
less; the travellers themselves began to float in the air.
There is nothing wrong in all this. What Jules Verne did lose sight
of was that this happens not only at the point the novelist gave. It
happens before and after as well in fact, as soon as free flight begins.
It seems incredible, doesn't it? I'm sure though that soon you will
be surprised not to have noticed this signal omission before. Let's
turn to Jules Verne for an example. You haven't forgotten how the
space travellers ejected the dead dog and how surprised they were to
see it continue to trail behind the projectile instead of falling back to
earth. Jules Verne described and explained this correctly. In a void
all bodies fall with the same speed, with gravity imparting an identical
acceleration to each. So, owing to gravity, both the projectile and the
dead dog should have acquired the same falling velocity (an identical
acceleration). Rather should we say that due to gravity their starting
velocities diminished in the same measure. Consequently, both should
whizz along with the same velocity; that is why after its ejection the
dead dog kept on trailing along in the projectile's wake.
Jules Verne's omission was: if the dead dog did not fall back to
earth again after the ejection, why should it fall when inside the pro-
jectile? The same forces act in both cases! The dead dog suspended in
mid-air inside the projectile should remain in that state as its speed is
absolutely the same as the projectile's; hence it is in a state of rest in
respect to the projectile.
44
What goes for the dead dog also goes for the travellers and all objects,
in general, inside the projectile, as they all fly along the trajectory
with the same speed as the projectile and should not fall, even though
having nothing to stand, sit, or lie on. One could take a chair, turn it
upside down and lift it to the ceiling; it won't fall "down", because
it will go on travelling together with the ceiling. One could sit on this
chair also upside down and not fall either. What, after all, could make
him fall? If he did fall or float down, this would mean that the projec-
tile's speed would bo greater than that of the man on the chair; other-
wise the chair wouldn't float or fall. But this is impossible since we
know that everything inside the projectile has the same acceleration
as the projectile itself. This was what Jules Verne failed to take into ac-
count. He thought everything inside the projectile would continue to
press down on its floor when it was in space. He forgot that a weight
presses down on what supports it only because this support is stationary.
But if both object and its support hurtle with the same velocity in
space they simply can't press down on each other.
So, as soon as the projectile began to fly further on by its own mo-
mentum, its travellers became completely weightless and could float
inside it, just as everything else could, too. That alone would have
immediately told the travellers whether they wore hurtling through
space or still inside the cannon. Jules Verne, however, says that in the
first half hour after the projectile was shot into space they couldn't
guess whether they were moving or not, however hard they tried.
"'Nicholl, are we moving?'
"Nicholl and Barbicane looked at each other; they had not yet trou-
bled themselves about the projectile.
"'Well, are we really moving?' repeated Michel Ardan.
"'Or quietly resting on the soil of Florida?' asked Nicholl.
"'Or at the bottom of the Gulf of Mexico?' added Michel Ardan. "
These are doubts a steamboat passenger may entertain; they are
absolutely out of the question for a space traveller, because he can't
help noticing his complete loss of weight, which the steamboat pas*
senger naturally retains.
Jules Verne's projectile must certainly be a very queer place, a tiny
world of its own, where things are weightless and float and stay where
45
they are, where objects retain their equilibrium wherever they are
placed, where even water won't pour out of an inclined bottle. A pity
Jules Verne slipped up, when this offers such a delightful opportunity
for fantasy to run riot! (If this problem interests you, we could refer
you to the appropriate chapter in A. Sternfeld's Artificial Earth Sat-
ellites.)
FAULTY SCALES CAN GIVE RIGHT WEIGHT
What is more important to get the right weight scales or weights?
Don't think both identically important. You can get the right weight
even on faulty scales as long as you have the right weights. Of the
several methods used, we shall deal with two.
One was suggested by the great Russian chemist Dmitry Mendeleyev.
You begin by placing anything handy on one of the pans. Make sure
that it is heavier than the object you want to weigh. Balance it with
weights on the other pan. Then place what you want to weigh on the
pan holding the weights and remove the necessary number of weights
to bring to balance again. Tote up the weights removed to get the weight
of what you wanted to weigh. This is called "the constant load method "
and is particularly convenient when several objects need to be weighed
in succession. The initial load is used to weigh everything you have
to weigh.
Another method, called the "Borda method" after the scientist who
proposed it, is as follows:
Place the object you want to weigh on one of the pans. Then pour
sand or shot into the other pan till the scales balance. Remove your
object from' the pan but don't touch the sand or shot in the other
pan! and place weights in the emptied pan till the scales balance
again. Tote up these weights to find how much your object weighs.
This is also called "replacement weighing".
This simple method can also be used for a one-pan spring balance,
provided of course you have correct weights. In this case you don't
need either sand or shot. Just put your object on the pan and note the
reading. Then remove the object and place in the pan as many weights
as needed to get the same reading. Their combined weight will give the
weight of the object they replace.
46
STRONGER THAN YOU THINK
How much can you lift with one arm? Let's say it's ten kilogrammes.
Does this amount qualify your arm's muscle-power? Oh, no. Your biceps
is much stronger. Fig. 27 shows how this muscle works. It is attached
close to the fulcrum of the lever that the bone of your forearm represents.
The load you are lifting acts on the other end of this live lever. The
distance between the load and the ful-
crum, that is, the joint, is almost eight
times more than that between the end
of the biceps and the fulcrum. This
means that if you are lifting a load
of 10 kg your biceps is exerting eight
times as much power, and, conse-
quently, could lift 80 kg.
It would be no exaggeration to say
that everybody is much stronger than
he is, or rather that one's muscles are
much more powerful than what we
can really do with them. Is this an
expedient arrangement? Not at all,
you might think at first glance. We
seem to have totally unrewarded loss.
Recall, however, an old "golden rule"
of mechanics: whatever you lose in
power you gain in displacement. Here
you gain in speed; your arm moves
eight times faster than its muscles do.
The muscular arrangement in animals
enables them to move extremities
quickly, which is more important
than strength in the struggle to sur-
vive. Otherwise, we would move
around at literally a snail's pace.
Fig. 27. Forearm C acts as a
lever. The force acts on point
7; the fulcrum is at point O
and the Joad ft is being lifted
from point B. BO is roughly
eight times longer thpn 10.
(This drawing is from an an-
cient book called Concerning
the Motions of Animals by the
17th-century Florentine schol-
ar Borelli who was the first to
apply the laws of mechanics
to physiology.)
47
WHY DO SHARP THINGS PRICK?
Have you ever wondered why a needle so easily pierces things? Why
is it so easy to drive a needle through a piece of cloth or cardboard and
so hard to do the same thing with a blunt nail? After all, doesn't the
same force act in both cases? The force is the same, but the pressure
isn't. In the case of the needle the entire force is concentrated on its
point; in the case of the nail the same amount of force is distributed
over the larger area of the blunt end. So, though we exert the same
force, the needle gives a much greater pressure than the blunt
nail.
You all know that a twenty-toothed harrow loosens the soil more
deeply than a sixty-toothed one of the same weight. Why? Because the
load on each tooth of the first harrow is more than on each tooth of the
second.
When we speak of pressure, we must always take into consideration,
besides force, also the area upon which this force acts. When we are
told that a worker is paid a hundred rubles, we don't know whether
this is much or little, because we don't know whether this is for a
whole year or for just one month.
Similarly does the action of a force depend on whether it is distrib-
uted over a square centimetre or concentrated on the hundredth of
a square millimetre. Skis easily take us across fresh snow; without
them we fall through. Why? On skis the weight of your body is distrib-
uted over a much greater area. Supposing the surface of our skis is 20
times more than the surface of our soles, on skis we would exert on
the snow a* pressure which is only a twentieth of the pressure we exert
when we have no skis on. As we have noticed, fresh snow will bear you
when you are on skis, but will treacherously let you down when
you're without them.
For the same reason horses used in marshlands are shod in a special
fashion giving them a wider supporting area and lessening the pressure
exerted per square centimetre. For the same reason people take the same
precautions when they want to ci;oss a bog or thin ice, often crawling
to distribute their weight over a greater area.
Finally, tanks and caterpillar tractors don't get stuck in loose ground,
48
though they are very heavy, again because their weight is distributed
over a rather great supporting area. An eight-ton tractor exerts a pres-
sure of only 600 grammes per square centimetre. There are caterpil-
lars which exert a pressure of only 160 gr/cm 2 despite a two-ton load,
which makes for the easy crossing of peatbogs and sand-beaches. Here
it is a large supporting area which gives the advantage, whereas in Ihe
case of the needle it is the other way round.
This all shows that a sharpened edge pierces things only because it
has a very minute area for the force to act upon. That is why a sharp
knife cuts better than a blunt one: the force is concentrated on a small-
er area of the knife edge. To sum up: sharp objects prick and cut well,
because much pressure is concentrated on their points and edges.
COMFORTABLE BED ... OF ROCK
Why is it pleasanter to sit on a chair than on a flat-topped stool
though both arc of wood? Why is it pleasant to lie in a hammock though
the pieces of rope that go to make it are by no means soft?
I suppose you've already guessed why. The stool-top is flat; when
you sit on it, you press down with your entire weight on a small area.
Chairs, on the other hand, usually have a concave seat; in this case you
press down on a much greater area, over which your weight is distribut-
ed. To every unit of surface you have a smaller weight, smaller pres-
sure.
The trick, as you see, is to distribute pressure more evenly. On a
soft bed we make depressions that conform to the uneven shape of our
bodies. Pressure is distributed rather evenly, with only a few grammes
per square centimetre. No wonder we find it so pleasant.
The following reckoning well illustrates the difference. An adult
person has a body surface of about 2m a , or 20,000 cm 2 . In bed roughly
a quarter of it 0.5 m a , or 5,000 cm 2 supports him. Presuming that
he weighs about 60 kg, or 60,000 gr, this would mean that we have a
pressure of only 12 gr/cm 2 . On bare boards he would have a supporting
area of only some 100 cm 2 . There are fewer points of contact. This means
a pressure per sq. cm. of half a kilogramme instead of a dozen grammes.
Quite a noticeable difference, isn't it? And one feels it at once.
42668 49
But even the hardest of beds would be as soft as eiderdown, provided
the weight of your body were distributed all over it. Suppose you left
the imprint of your body in wet clay. When it hardens drying clay
shrinks by some five to ten percent, but we shall discount this you
could lie in it again and think yourself in a featherbed. Though
you would be lying on what is practically rock, it would feel soft,
because your weight would be distributed over a much greater area of
support.
CHAPTER THREE
ATMOSPHERIC RESISTANCE
BULLET AND AIR
Every schoolboy knows that the air impedes a bullet in its flight.
Fow, however, know what a great impediment it is. Most think such
a "caressing" environment as the air which is something we usually
never feel could not really get in the way of a fast-flying rifle bullet.
Fig. 28. Flight of a bullet in the air and in a vacuum. The big arc is the
trajectory described when there is no atmosphere. The tiny, left-hand arc
is the real trajectory
However, one good glance at Fig. 28 will already make you realise
that the air places quite a serious obstacle in the bullet's way. The
large curve on the diagram designates the trajectory the bullet would de-
scribe were there no air. In this case, after flying out of a rifle tilt*
ed at 45, and with an initial velocity of 620 m/sec, the bullet would
describe a vast arc ten kilometres high and fly almost 40 km. But actu-
ally our bullet flies only 4 km, describing the tiny arc which is scarce-
ly noticeable side by side with the first one. That is what the resist*
ance of the air, the air drag, does!
4* 51
BIG BERTHA
The Germans were the first in 1918, towards the close of the First
World War, when French and British aircraft had put a stop to Ger-
man air raids to practise long-range artillery bombardment from a
distance of 100 kilometres and more.
Fig. 29. The range changes when the mouth of a long-distance gun is tilted
at different angles. In the case of angle 1, the projectile strikes P, and in the
case of angle 2, P' 9 but in the case of angle 3, it flies much farther as it goes
through the rarefied stratosphere
It was by chance that German gunners hit upon their absolutely
novel method for shelling the French capital, which was then at least
110 km away from the front lines. Firing shells from a big cannon tilt-
ed up at a wide angle, they unexpectedly discovered that they could
make them fly 40 km instead of 20. When a shell is fired steeply up-
wards with a great initial velocity, it reaches a high-altitude, rarefied
atmospheric strata, where the air drag is rather weak. Here it flies
for quite a distance, before veering steeply to fall back to earth again.
Fig. 29 illustrates the great difference in trajectory at different angles
of the gun barrel. This became the basic principle of the long-range
gun that the Germans designed to bombard Paris from 115 km away.
Such a gun was made Big Bertha and it fired more than 300 shells
at Paris throughout the summer of 1918.
52P
It was learned later that
Big Bertha consisted of a
tremendous steel tube 34 me-
tres long and 1 metre thick.
The breech walls were 40 cm
thick. The gun itself weighed
750 tons. Its 120 kg shells
were one metre long and 21 cm
thick. Each charge took 150 kg
of gunpowder which developed
a pressure of 5,000 atmos-
pheres, ejecting the shell with
an initial velocity of 2,000m/sec.
Since the angle of elevation
was 52, the shell described
a tremendous arc, reaching its
highest point way up in the
stratosphere 40 km above the
ground. It took the shell only
3.5 minutes to reach Paris,
115 km away; two minutes were
spent in the stratosphere.
Big Bertha was the first
long-range gun in history, the progenitor of modern long-range artillery.
Let me note that the greater the initial velocity of a bullet or shell,
the more resistance the air puts up, increasing, moreover, in proportion
to the square, cube, etc., of the velocity, depending on its amount.
WHY DOES A KITE FLY?
Do you know why a kite soars when pulled forward by the twine?
If you do, you will also be able to understand why airplanes fly and
maple seeds float. You'll even be able to fathom to some extent the
causes of the boomerang's very odd behaviour. Because all these things
are related. The very same air which is so great an impediment to a
bullet or a shell enables the light maple seed to float and even heavy
airliners to fly.
Fig. 30. Big Bertha
53
M
If you don't know why a kite flies,
the simple drawing in Fig. 31 will pro-
vide the explanation. Let line MN des-
ignate the kite's cross-section. When
you let the kite go and pull at the cord,
the kite, because of its heavy tail, moves
at an angle to the ground. Let the kite
move from right to left and a be the
angle at which the plane of the kite is
inclined to the horizon. We shall now
proceed to examine the forces that act
on the kite. The air, of course, should
obstruct its movement and exert some
pressure on it, designated on Fig. 31 by
the vector OC. Since the air always presses
perpendicular to the plane, OC is at
right angles to MN. The force OC may be resolved into two forces by
constructing what is called a parallelogram of forces. This gives us the two
forces OD and OP. Of these two, the force OD pushes the kite back,
thus reducing its initial velocity. The other force, OP, pulls the kite up,
reducing its weight. When this force is big enough it overcomes the
weight of the kite and lifts it. That is why the kite goes up when
you pull it forwards.
The airplane is also a kite really, with the difference that its forward
motion, which makes it go up, is imparted not by our pulling at it
but by the propeller or jet engine. This is, of course, a very crude ex-
planation. There are other factors that cause an airplane to rise. They
are explained in Book Two of Physics for Entertainment under the
heading "Waves and Whirlwinds".
Fig. 31. The forces that
make a kite fly
LIVE GLIDERS
As you see aircraft are not made like birds, as one usually thinks,
but rather like flying squirrels or. flying fish, which, by the way, em-
ploy their flying mechanism not to fly up but merely to take rather big
leapsor what a flier would call "glides". In their case, the force OP
54
(Fig. 31) is too small to offset
their weight; it merely reduces
their weight, enabling them to
make very big jumps from some
high point (Fi. 32). A flying
squirrel can jump 20-30 m from
the top of one tree to the lower
branches of another. In the East
Indies and in Ceylon a much
larger species of flying squirrel is
found. This is the kaguan, a fly-
ing lemur, which is about the size
of our house cat and which has a
wing spread of about half a me-
tre, enabling it to leap some 50 m,
despite its great weight. As for
the phalangers that inhabit the
Sunda Isles and the Philippines,
they can jump as far as 70 m.
Fig. 32. Flying squirrels jump from
20 to 30 m
BALLOONING SEEDS
Plants also often employ a gliding mechanism to propagate.
Many seeds have either a parachuting tuft or hairy appendages (the
pappus), as in dandelions, cotton balls, and "goat's beards", or "wings",
as in conifers, maples, white birches, elms, lindens, many kinds of
umbel liferae, etc.
In Kerner von Marilaum's well-known Plant Life, we find the follow-
ing relevant passage:
"On windless sunny days a host of seeds and fruits are lifted high
up by vertical air currents. However, after dusk they usually float
down a short cry away. It is important for seeds to fly, not so much
to cover a wide area as to inhabit cracks in terraces and cliffs, which
they would never reach in any other way. Meanwhile, horizontal air
currents may carry these hovering seeds and fruits rather far.
"The seeds of some plants retain their wings and parachutes only
while they fly. Thistle seeds quietly float until they encounter an
55
obstacle, when the seed discards its para-
chute and drops to the ground. That is
why we see the thistle so often near
walls and fences. But there are other
cases, when the seed is attached per-
manently to its parachute."
Fig. 33. Fruit of "goat's
beard M
Fig. 34. Winged seeds of a) maple, 6) pine-tree,
c) elm, and d) birch
Figs. S3 and 34 show some seeds and fruits that have a gliding
mechanism. As a matter of fact these pJant "gliders" beat man-made
ones on many points. They can lift a load which may be much greater
than their own weight and automatically stabilise it. Thus if the
seed of the Indian jasmine should chance to turn over, it will autom-
atically regain its initial position with its convex side bottom-most,
but when it meets an obstacle it doesn't capsize and drop like a plum-
met, but coasts down instead.
DELAYED PARACHUTE JUMPING
This, naturally, brings to mind the brave jumps parachutists some-
times make. They bail out at altitudes of some ten kilometres and pull
the ripcord only after plummeting like a stone without opening their
parachutes for quite a distance. Many think that in this delayed jump
56
the parachutist falls as if in empty space. If this were really so, the
delayed jump would be a much shorter affair, while the near-ground
velocity would be tremendous.
However, atmospheric resistance prevents acceleration. The velocity
of the falling parachutist during a delayed jump increases only in the
first ten seconds, only for the first few hundred metres. Meanwhile
atmospheric resistance increases, to finally reach a point where all
further acceleration stops and the falling becomes even.
Here is a crude idea of a delayed jump from the angle of mechanics.
Acceleration continues for only the first 12 seconds or even less, de-
pending on the parachutist's weight. In this period he drops some 400-
450 m and works up a velocity of about 50 m/sec. After that he falls
uniformly, with the same speed, until he pulls the ripcord. Raindrops
fall similarly. The only difference is that the initial period of accel-
eration for the raindrop is no more than a second. Consequently its
near-ground velocity is not so great as in a delayed parachute jump,
being between 2 and 7 metres a second, depending on its size. (Read
my Mechanics for Entertainment for more about raindrop velocity and
my Do You Know Your Physics? for more about delayed parachute
jumping.)
THE BOOMERANG
For long this ingenious weapon, the most perfect technical device
primitive man ever invented, had scientists wondcrstruck. Indeed,
the queer tangled trajectory the boomerang traces (Fig. 35} can
tease any mind. Nowadays we have an elaborate theory to explain
the boomerang; it is no longer a wonder. This theory is too intricate
to explain at length. Let me merely note that boomeranging is the
combined result of three factors: firstly, the initial throw; secondly,
the boomerang's own rotation, and thirdly, atmospheric resistance.
The Australian aborigine instinctively knows how to combine all
three, deftly changing the boomerang's tilt and direction, and he
throws it with a greater or smaller force to obtain the desired result.
You, too, can acquire some knack in boomerang-throwing. To
make one for indoors, cut it out of cardboard, in the form shown in
Fig. 36. Each arm is about 5 cm long and a little less than a centimetre
57
*ig. 35. r Australian aborigine throwing a boomerang. The dotted line shows
the trajectory of the boomerang, should it miss its target
Fig.36. A cardboard boomer-
ang and how to "throw" it
Fig. 37. Another cardboard
boomerang (real size)
58
wide. Press it under the nail of your thumb
and flick it forwards and a bit upwards.
It will fly some five metres, loop, and
return to your feet, provided it doesn't
hit anything on the way. You can make
a still better boomerang by copying the
one given in Fig. 57, and also by twisting
it to look somewhat like a propeller (as
shown at the bottom of Fig. 37). After
some experience you should be able to
make it describe intricate curves and loops
before it returns to your feet.
In conclusion let me note that the boomer-
ang is not at all exclusively an Australian
missile as is usually thought. It was em-
ployed in India and according to extant mu-
rals it was once commonly used by Assyrian
warriors (see Fig. 38). It was also familiar in ancient Egypt and Nubia.
The Australian boomerang's only distinguishing feature is the propel-
ler-like twist that we mentioned, send ing it into such a maze of whirls
and loops, returning it to the thrower, should he miss.
Fig. 38. Ancient Egyptian
warrior throwing a boomer-
ang
CHAPTER FOUR
ROTATION. "PERPETUAL MOTION" MACHINES
HOW TO TELL A BOILED AND RAW EGG APART?
How can we find out whether an egg is boiled Jor not, without break-
ing the shell?
Mechanics gives us the answer. The whole trick is that a boiled egg
spins differently than a raw one. Take the egg, place it on a flat plate
and twirl it (Fig. 39). A cooked egg, especially a hard-boiled one, will
revolve much faster and longer than a raw one; as a matter of fact,
it is hard even to make the raw egg turn. A hard-boiled egg spins so
, quickly that it takes on the hazy form of a flat white ellipsoid.
If flicked sharply enough, it may even rise up to stand on its narrow
end.
The explanation lies in the fact that while a hard-boiled egg re-
volves as one whole, a raw egg doesn't; the latter's liquid contents do not
Fig. 39. Spinning an egg
Fig. 40. Telling a boiled
from a raw one.
60
have the motion of rotation imparted at once and so act as a brake,
retarding by force of inertia the spinning of the solid shell. Then boiled
and raw eggs stop spinning differently. When you touch a twirling
boiled egg with a finger, it stops at once. But a raw egg will resume spin-
ning for a while after you take your finger away. Again the force of
inertia is responsible. The liquid contents of the raw egg still continue
moving after the solid shell is brought to a state of rest. Meanwhile
the contents of the boiled egg stop spinning together with the outer
shell.
Here is another test, similar in character. Snap rubber bands around
a raw egg and a boiled one, along their "meridian", as it were,
and hang them up by two identical pieces of string (Fig. 40). Twist the
strings, giving the same number of turns, and then let them go. You will
spot the difference between the two eggs at once. Inertia causes the boiled
egg to overshoot its starting position and give the string some more
twists in the opposite direction; then the string unwinds again with the
egg again giving several turns; this continues for some time, the number
of twists gradually diminishing until the egg comes to rest. The raw egg,
on the other hand, scarcely overshoots its initial position at all; it will
give but one or two turns and stop long before the boiled egg does. As
we already know, this is due to its liquid contents which impede its
movement.
WHIRLIGIG
Open an umbrella, stand it up with its top on the floor and twist the
handle. You can easily make it revolve rather quickly. Now throw a
little ball or a crumpled piece of paper into the umbrella. It won't stay
there; it will be shot out by what has wrongly come to be called the
"centrifugal force" but which is actually nothing but a manifestation
of the force of inertia. The ball or piece of paper will be thrown off, not
along the continuation of the radius but at a tangent to the circular mo-
tion.
At some public parks one may find an amusement (Fig. 41) based on
this principle of rotation, where you may try out the law of inertia on
yourself. This is a sort of whirligig with a round floor on which people
either stand, sit, or lie. A concealed motor starts the floor revolving,
61
Fig. 41. A whirligig. Centrifugal forces are hurling the boys off
increasing its speed till inertia makes everybody on it slither or slide
towards its edge. At first this is hardly noticeable, but the further away
one gets from the centre, the more noticeable do both speed and, conse-
quently, inertia grow. You try hard to hold on, but it is to no avail and
finally you are hurled off.
The Earth itself is, in point of fact, a huge whirligig. Though it doesn't
burl us off, it does reduce our weight. At the equator, where rotation
is fastest, one can "shed" a 300th of one's weight in this manner.
This, plus another factor, the Earth's compression, reduces weight at
the equator by about 0.5% or 1 /200th. An adult person will con-
sequently weigh 300 grammes less at the equator than at any of
the poles.
INKY WHIRLWINDS
Make a teetotum, as shown in life size in Fig. 42, out of white card-
board and a match sharpened at one end. No particular knack is needed
to twirl it it's something any child can do. But though a child's
toy, it can be very instructive. Do the following. Spill a few drops
of ink on it and set it spinning before the ink dries. When it stops, look
62
Fig. 42. Ink drop traces on a twirling teetotum
to see what has happened to the ink drops. They will have drawn
whorls a miniature whirlwind.
Incidentally, this resemblance is not accidental. The whorls on the
teetotum trace the movement of the ink drops, which undergo exactly
what you experienced on the revolving floor. As the drop shoots away
from the centre due to centrifugal forces, it reaches a place on the
teetotum having a greater speed of rotation than the speed of the drop
itself. Here the disc spins faster than the drop which seems to glide away,
lagging behind the radial "spokes", as it were. That is why the drops
curve, and we see the trace of curvilinear motion.
The same is true for air currents diverging from a centre of high at-
mospheric pressure (in "anticyclones"), or converging in a centre of
low atmospheric pressure (in "cyclones"). The ink whorls depict these
stupendous whirlwinds in miniature.
THE DELUDED PLANT
The centrifugal force produced by fast rotation may even outvie
gravity, a point that was demonstrated by the British botanist Knight
more than a hundred years ago. It is common knowledge that a young
plant always directs its stem contrary to gravity, or, in plain language,
63
Fig. 43. Seeds germinating on the rim
of a spinning wheel stem towards the
axle and send their roots outwards
grows upwards. Knight, however,
caused seeds to sprout inwards,
from the outer rim of a quickly-
spun wheel. The roots, on the
other hand, were directed outwards
(Fig. 43). He was able to fool the
plant, as it were, substituting cen-
trifugal force for gravity. The ar-
tificial gravity proved to be more
powerful than the earth's natural
pull by the by, the modern theory
of gravity does not present any
objections, in principle, to this
explanation.
"PERPETUAL MOTION" MACHINES
"Perpetual motion" is a topic that comes in for frequent mention,
but I don't think all realise what it actually means. The "perpetual
motion" machine is an imagined mechanism which continues its motion
without end and meanwhile can also do some useful work, as lifting a
load, for instance. It has never been constructed, though attempts
have been made since ancient times. The futility of this task gave
rise to the firm conviction that a "perpetual motion" machine is im-
possible, and to the law of the conservation of energy fundamental
for modern science. "Perpetual motion" as such is endless motion with-
out any work done.
Fig. 44 depicts one of the oldest projects of a "perpetual motion"
machine which certain cranks try to revive even now. Attached to the
rim of the wheel are rods with weights at their ends. In any position
of the \\hcel the weights on the right-hand side are farther from the
centre than those on the left-hand side. Consequently, the right-hand
weights should always outweigh the left side, thus compelling the wheel
to turn. Hence the wheel should spin for ever, or at least until its axis
wears through. That at any rate was what its inventor thought. Don't
try to make such a machine. It will never turn. Why?
64
Though the right-hand weights are always farther from the centre,
you are sure to have a position when they will be less in number than
those on the left-hand side. Look at Fig. 44 once again. You see only
four right-hand weights and eight left-hand ones. The entire arrange-
ment is thus balanced. The wheel will never turn; it will only swing
a bit and then come to rest in this position. (The motion of this ma-
chine is explained by the so-called theorem of momenta.)
It has been proved beyond doubt that a "perpetual motion" machine
as a source of energy is absolutely impossible. It is futile to undertake
this task, which alchemists of yore, especially of the Middle Ages, racked
their brains in vain to solve, thinking it even more tempting than
the "philosopher's stone". The famous 19th-century Russian poet Push-
kin describes such a dreamer, one Berthold, in his Chivalrous Episodes.
"'What is perpeluum mobile?' Martin inquired.
"'Perpetuum mobile,' Berthold returned, 'is perpetual motion. If 1
find perpetual motion I sec no bounds to man's creative endeavour.
For, my good Martin, while the making of gold is entrancing, a dis-
covery perhaps, both curious and profitable, the finding of per^etuum
mobile.... Ah, how grand that would be! 1 "
Hundreds of "perpetual motion" machines were invented, but none
ever moved. Every inventor invariably omitted something that "upset
the apple-cart".
Fig. 44. An "everlastingly"
moving wheel of the Middle
Ages
Fig. 45. A "perpetual motion"
machine with balls rolling in
compartments
Fig. 46. Fake pcrpcluum mobile as an advertisement
for a Los Aiigcles cafe
Fig. 45 depicts^another "supposed "perpetualf motion" machine a
wheel with heavy balls rolling in" compartments between the outer
rim and huh. The idea. was that the balls closer to the outer rim on
one side of the wheel would compel the wheeHo turn by their weight.
But this will never happenfor the same reason as the wheel in Fig.
44 doesn't turn. Still, in Los Angeles a tremendous wheel of this nature
(Fig. 46) was built to advertise a cafe. Actually it was a fake, being
66
turned by an artfully concealed mechanism though people thought
it was spun by the heavy balls rolling in the compartments. Other
such fake "perpetual motion" machines, all set in motion by electricity,
were placed in the windows of watchmaker's shops to attract the eye
of the public.
Incidentally, one ad of this nature [impressed my students so
greatly that they wouldn't believe me when I told them that perpetual
motion was impossible. Seeing is believing, they say, and when my
students saw the balls rolling and turning the wheel, it seemed far
more convincing than anything 1 could say. I told them that the fake
"wonder" machine was driven by electricity from the city mains but
that didn't help cither. Then I recalled that on Sundays tho electricity
was cut off.. So I advised my pupils to call on the shop on a Sunday.
"Did you see the 'perpetual motion' machine in action? w I asked
afterwards.
"No," they replied, their heads aLanging, "it was covered up with a
newspaper. "
The law of the conservation of energy regained their confidence and
they never lost faith in it again.
"THE SNAG"
Many ingenious home-taught Russian inventors tackled the fasci-
nating problem of a "perpetual motion" machine. One, the Siberian
peasant Alexander Shcheglov, is described under the name of Burgher
Prezentov by the well-known 19th-century Russian satirist Saltykov-
Shchedrin in his Modern Idyll. Below the writer describes a visit to the-
inventor's workshop:
"Burgher Prezentov was a man of some 35 summers, gaunt and pale
of face. He had large pensive eyes and long hair which fell in strands
onto his neck. Half of his rather roomy cottage^ was taken up by
a big flywheel and \\e barely managed to squeeze in. It was a spoked
wheel and had a rather large outer rim of boards nailed together like
a box. Inside it was empty, and held tho mechanism, the inventor's
secret. There was nothing particularly cunning about it merely bag*
of sand which were to balance one another. A stick in the spokes kept
the wheel stationary.
5* 67
' "'We've heard that you've applied the law of perpetual motion in
practice. Is that true?' I began.
"'I really don't know how to put it/ he returned in confusion. '1
think I've done it.'
"'Can we take a look?'
"Tray, do! I'll be delighted.'
"He led us up to the wheel and then took us around to the other side..
It was a wheel all right, from either side.
"'Does it turn?'
"'Well, it should. But it's a bit capricious.'
"'Can you take the stick out?'
"Prezentov removed it, but the wheel stood still.
"'It's up to its tricks again! 1 he repeated. 'It needs an impetus.'
"He gripped the rim with bolh hands, swung it back and forth sever*
al times, then pushed it with all his might. Th? wheel began to turn.
It made several turns rather quickly and smoothly. One could hear
the bags of sand inside the rim banging against the boards and sliding
away. Then the wheel began to turn more and more slowly. We heard
a rasping and a creaking and, finally, the wheel stopped altogether.
"'Must be a snag somewhere,' the inventor explained in confusion
as he strained and swung the wheel again. But the result was the same.
"'Perhaps you forgot friction?'
U 'I didn't.... Friction you ay? It's not because of that. Friction's
nothing. Sometimes it make? you happy and then, bang, it's up to
its tricks, gets ornery, and that's that. If the wheel were made of real
stuff, not scraps!'"
It was of course not the "snag" or the "real stuff" that was at fault, but
. the wrong principle at the root. The wheel turned for a time owing to
the impetus that the inventor gave it, but was bound to stop when
friction exhausted the imparted outside energy.
"IT'S THEM BALLS THAT DO IT"
, The writer Karonin (the pen-name of N. Y. Petropavlovsky) describes
.another Russian "perpetual motion" machine inventor in his story
"Perpetuum Mobile". This was Lavrenti Goldyrev, a peasant from
,68
Perm Gubernia who died in 1884. Karon in, who changed the name in'
the story to Pykhtin, describes the machine in great detail.
"Before us was a large queer machine resembling at first glance
the sort of thing a blacksmith uses to shoe horses on. We could see some
badly planed wooden pillars and beams and a whole system of flywheels
and gear wheels. It was all a very clumsy-looking affair, rough and'
ugly. Several iron balls lay on the floor underneath the machine and
there was a whole pile of them a bit to the side.
"'Is that it?' the major-domo asked.
44 'That's it.'
"'Well, does it turn?'
44 'How else?'
"'Have you got a horse to turn it?'
"'A horse? What for? It turns by itself,' Pykhtin returned and began
to demonstrate the monster's workings.
"The main role was played by iron balls heaped up nearby.
"'It's them balls that do it. Look. First it goes whack into this
scoop. Then it flies like lightning along that groove, is scooped
up by that scoop, flies like mad back Co that wheel and again gives
it a good push so hard thai it even begins to whine. Meanwhile another
ball is on its way. Again it flies along and goes whack here. From here
it dashes plong the groove and strikes that scoop, skips to the wheel,
and again uhack! That's how it goes. Wait, I'll start it off.'
"Pykhtin darted to and fro, hastily collecting the scattered balls.
Finally, after heaping them up into a pile by his feet, he picked one
up and threw it with all his mi^l.t at the nearest scoop on the wheel.
Then he quickly picked up a second, then a third. The noise was some-
thing unimaginable. The balls clanked against the iron scoops, the
wheel creaked, the pillars groaned. An infernal whine and racket filled
this gloomy place."
Karonin claims that Goldyrev's machine moved. But this was pat-
ently a misunderstanding. The wheel could have turned only \ihile
the balls were dropping down at the expense of the potential energy
accumulated when lifted, much in the manner of the weights of a pen-
dulum clock. However, it couldn't have turned long because when all
the lifted balls had "whacked" against the scoops and had slipped
69.
down, it would stop provided it hadn Vstopped before by the counter-
effect of all the balls it was supposed to lift.
Later on, Goldyrev became disappointed in his invention when at
an exhibition in Yekaterinburg, where he showed it, he saw real in-
dustrial machines. When asked about his "perpetual motion" contrap-
tion, he dejectedly replied: "The L devil take it! Tell 'em to chop it up
for firewood."
UFIMTSEV'S ACCUMULATOR
Ufimtsev's so-called accumulator of kinetic energy well illustrated
the pitfalls that may trap a cursory observer of a "perpetual motion"
machine. Ufimtsev, an inventor from Kursk, devised a new kind of
windmill power station with a cheap flywheel type of "inertia accumu-
lator". In 1920 ho built a model of it, shaped as a disc that spun round
a vertical axis set on ball bearings inside an air-free jacket. When revved
to 20,000 r.p.m., the disc was able to turn for 15 days on end. The
unthinking observer could well believe that ho had before him a real
"perpetual motion" machine*
"A MIRACLE, YET NOT A MIRACLE"
The futile search for a "perpetual motion" machine clouded many
lives. I once knew a factory worker who sank into absolute destitution,
spending all his earnings and savings in the delusion that he could
make a "perpetual motion" machine. Poorly clad and always hungry,
he^would beg everyone he met to give him some money to make the
"finished model", which would "certainly move". It was a great pity
to sec this man suffering so much only because of his ignorance of the
rudiments of physics.
It is curious to note that whereas the search for a "perpetual motion"
machine was always abortive, the profound realisation of its impossi-
bility, on the contrary, often led to discoveries of great value.
A wonderful illustration in point is the method which the remark-
able Dutch scientist Stevin, who lived at the turn of the 16th cen-
tury, evolved to establish the law of the equilibrium of forces on an
TO
inclined plane. He deserves far greater fame than befell him for his
many major discoveries that we now constantly address ourselves to.
These are decimal fractions, the introduction of denominators in al-
gebra, and the establishment of the hydrostatic law that Pascal redis-
covered later.
Stevin evolved the law of the equilibrium of forces on an inclined
plane without invoking the rule of the parallelogram of forces. He
proved it with the aid of a drawing,
which is reproduced in Fig. 47. A
chain of fourteen identical spheroids
is slipped round a three-sided prism.
What happens to it? The bottom,
which droops garland-like, is in a
state of balance, as you see. But do
the other two [parts balance each
other? In other words, do the two
spheroids on the right offset the four
on the left? The answer is yes. Other-
wise the chain would keep on rolling
of its own accord from right to left
for ever. Otherwise other spheroids
take the place of those that slide "'off and "equilibrium would
never be restored. But we know that a chain disposed in Ibis fashion
does not move of its own accord at all It is quite obvious that the two
spheroids on the right really offset the four on the loft.
It seems a minor miracle, doesn't it? Two spheroids pull with the
same force as four! This enabled Stevin to deduce an important law
of mechanics. This is how he reasoned. The two parts the long one
and the short one possess a different weight, ono being as many times
heavier than the other as the longer side of the prism is longer than the
short side. Consequently, any two linked lofds in general balance on
tilted planes, provided their weight is directly proportional to the
length of these planes.
When the short plane is vertical we get a well-known law of mechan-
ics, which is: to hold a body in place on a tilted plane we must act
in the direction of this plane with a force as many times loss the weight
Fig. 47. "A miracle, yet
not a miracle"
of -the body as the length of the plane is greater than its height. So*
did the idea that a "perpetual motion" machine is impossible led to
an important discovery in the realm of mechanics.
MORE "PERPETUAL MOTION" MACHINES
Fig. 48 shows a heavy chain fitted around wheels in such a way
that the right-hand part is always longer than the left-hand part,
whatever its position. The inventor thought that since the right-hand
part would always weigh more than the left-
hand part, it would always outweigh the
left-hand part and thus cause the entire ar-
rangement to keep going. But does this really
happen? Of course not. You already know
that the [heavier part of a chain may be
offset by the lighter part, provided they are
pulled by forces acting at different angles. In
this particular system, the left-hand part of
the chain 'droops vertically down, while the
right-hand part is inclined. So, though it is
heavier, still it cannot pull over the left-hand
part and we do not achieve the "perpetual
motion" expected.
I think the cleverest "perpetual motion"
machine ever invented was one displayed at
the Paris Exposition in the 1860's. It consisted
of a large wheel with balls rolling about in
its compartments. The inventor claimed that
nobody would ever be able to stop the wheel.
r
fig. 48. Is this a "perpot- Many visitors tried to stop it but it went on
ual motion" machine? turning as soon as they took their hands off
it. Not a single person realised that the wheel
turned precisely because of the effort he made to stop it. The backward
push he gave to stop it wound up the spring of an artfully concealed
mechanism.
72
THE "PERPETUAL MOTION" MACHINE PETER
THE GREAT WANTED TO BUY
Preserved in archives is a bulky correspondence which Peter the
Great of Russia carried on between 1715 and 1722, when he wanted
to buy a "perpetual motion" machine that had been devised in
Germany by one Councillor Orffyreus. This man whose "self-moving
wheel" won him nation-wide fame consented to sell it to the tsar
only fora princely sum. Peter the Great's librarian Schumacher, whom
the tsar had sent to Western Europe to collect rare oddities, reported
the following, when asked to negotiate the purchase:
"The inventor's last words were: One hundred thousand thalers and
you get the machine. "
As for the machine itself, according to Schumacher, the inventor
claimed that it was no fake and that it could not be defamed "except
out of malice, and the whole world is full of spiteful people whom
one cannot believe".
In January 1725 Peter the Great decided to go to Germany to see
this notorious "perpetual motion" machine himself, but he died
before he could accomplish his purpose.
Who was this mysterious Councillor Orffyreus and what was his
"famous machine" really like? I was able to learn something both
about the Councillor himself and his machine.
Orffyreus 's real name was Bessler. He was born in Germany in 1680.
He studied theology, medicine and painting before he essayed the "per-
petual motion" machine. Among the many thousands who tried to
invent such a machine he is probably the most famous and, at any rate,
the luckiest. Till the end of his days he died in 1745 he lived in
comfort on the income he netted by demonstrating his contraption.
Fig. 49 is a reproduction of a drawing from an old book depicting
Orffyreus's machine as seen in 1714. It shows a large wheel which ap-
parently not only turned by itself, but even lifted a heavy load to quite
a height.
The fame of this "miracle" machine, which the learned councillor
first exhibited at various market fairs, quickly spread throughout
Germany. Soon Orffyreus acquired powerful patrons. The Polish
73
Fig. 49. Orffyreus's self-moving wheel which Peter the Great wanted to buy. (From
an old drawing.)
king displayed interest and then the Landgrave of Hesse-Cassel patron-
ised the inventor, placing his castle at the latter's disposal and sub-
jecting the machine to every kind of trial.
On November 12, 1717, the machine was placed in a room all apart
and set into motion. The room was then locked and sealed, and two
grenad iers" were posted outside. For a whole fortnight, until the seal
was broken on November 26, no one dared to come near. Thon the room
was unlocked and the Landgrave and his retinue entered. The wheel
was still spinning "with undiminishing speed". It was stopped, in-
spected carefully, and again set going. Now the room was locked and
sealed for 40 days on end with grenadiers again stationed at the
door. The seal was broken on January 4, 1718. A commission of experts
entered and found that the wheel was still going. But this did not sat-
isfy the Landgrave and he staged a third trial, locking up the machine
for two whole months at a stretch. When he found the wheel still going
74
oven after that, he was delighted. He granted the inventor a parchment
to certify that his "perpetual motion" machine did 50 revolutions
per minute, could lift 16 kg to the height of 1.5 m and could also work
a grinder and bellows. With this document in his pouch, Orffyreus
travelled the length and breadth of Europe. He apparently netted a
princely income, considering that he consented to sell his machine
to Peter the Great for not less than 100,000 rubles.
The fame of the councillor's marvel quickly spread, finally reaching
the ears of Peter the Great, who had a very weak spot in his heart for
all sorts of curious and cunning artifices, and, naturally, it intrigued
him greatly. His attention had been called to it back in <715 when
travelling abroad, and it was then that he charged the celebrated dip-
lomat A. 1. Ostermann to inspect it. The latter soon forwarded an
oxtenshe report about the machine though he had not been able to see
it with his own eyes. The tsar even thought of inviting Orffyreus as
an eminent inventor to his court to take up service and asked the then
well-known philosopher Christian Wolf to give his opinion.
Orffyreus was showered with offers, one better than the other. Kings
and princes bestowed munificent awards. Poets composed odes in honour
of his wonder-wheel. But there were some who thought him a charlatan.
The more daring openly accused him, even offering 1,000 marks to
anyone who would come forth and expose the councillor. One lampoon
against him gave a drawing which is reproduced in Fig. 50 and which
provides a rather simple explanation for the mystery a cunningly
hidden person who pulled at a rope wound round that part of the axle
which was concealed in the pillars supporting the wheel.
The trick was bared by chance only because the councillor had had
a tiff with his wife and maid who had both been initiated into the
secret. Otherwise we would probably still be guessing. It seemed that
the notorious machine was indeed turned by a hidden person Orffyre-
us's brother, or maid pulling at a slender cord. But the councillor
did not lose face, persistently assuring all and sundry even on his death-
bed that his wife and maid had maligned him out of spite. However,
trust in him was shattered. No wonder he tried to drum into the head
of the tsar's envoy, Schumacher, the point that human beings were full
of malice.
75
Fig. 50. The secret of Orffyreus's machine.
(From an old drawing.)
Around the same time there also lived in Germany another renowned
"perpetual motion" machine inventor, one Hertner. Schumacher wrote
of his contraption the following: "Herr Hertner's perpetuum mobile,
which I saw in Dresden, consists of tarpaulin filled with sand and a
grinder-like machine which turns forwards and backwards by itself.
However the inventor says it cannot be made larger." Undoubtedly
this machine, too, gave no "perpetual motion", being at best an artfully
contrived device with a just as artfully concealed livingbut by
no means "perpetual motion" machine. Schumacher was right when
he wrote to Peter the Great that French and English scholars "mock
these perpetuum mobiles as objectionable to principles of mathematics".
CHAPTER FIVE
PROPERTIES OF LIQUIDS AND GASES
THE TWO COFFEE-POTS
Fig. 51 shows two coffee-pots of the same width. One, however, is
taller than the other. Which of the two will hold more? An unthinking
person would probably point to the taller one. However, we would
be able to fill it up only to the level of its spout, and if we poured more
in, it would all spill out Now since the spouts of both coffee-pots are
on the same level, the lower one takes
just as much liquid as the taller
one does. You will easily realise why.
The coffee-pot and its spout are two
communicating vessels and hence
inside both the liquid should be
at an identical level, even though
the liquid in the spout weighs much
less than that in the coffee-pot
proper. Unless the spout is high
enough, you will never be able to fill the coffee-pot up to the top; the
water will simply keep on spilling out. Usually the spout is even a
bit higher than the top of the coffee-pot to enable one to incline it
without spilling out its contents.
IGNORANCE OF ANCIENTS
Romans today still use what is left of the aqueducts t
forefathers built. Though the Roman slaves of old did
we can't say that of the Roman engineers in charge.
Fig. 51. Which coffee-pot takes
more?
of elementary physics was plainly inadequate. Fig. 52 reproduces a
picture preserved at the German Museum in Munich. As you see,
the Romans did not sink their water systems in the ground but placed
Fig. 52. The aqueducts of ancient Rome
them on high supports of masonry. Why? Aren't underground pipes
of the type we use today simpler? Roman engineers of old had a very
hazy notion, however, of the laws of communicating vessels. They
feared that in two reservoirs connected by a very long pipe, the
water would not rise to the same level. Furthermore, if the pipes were
laid in the ground and followed the natural relief, in some places the
water would have to flow upwards, and this was something the
Romans were afraid it would not do. That is why their aqueducts
usually slope all along the way. They often had either to take the pipes
on a roundabout route or erect tall arches. One Roman aqueduct,
known as the Aqua Marcia, is 100 km long, though it is half the distance
between its two points as the crow flies. As yon see, the ancient Romans'
ignorance of an elementary law of physics caused 50 km of extra
masonry to be built.
78
LIQUIDS PRESS ... UPWARDS
Even people who have never studied physics know that liquids press
down on the bottom of the vessels holding them and sideways at the
walls. Many, however, have never suspected that liquids also press
upwards. An ordinary lamp-glass will easily reveal this. Cut out of
a piece of thick cardboard a disc large enough to cover the top of the
lamp-glass. Cover the top of the glass
with it and then dip the glass into a
jar of water as shown in Fig. 53. To
prevent the disc from slipping off when
the lamp is immersed, tie a piece of
thread to it and hold it as shown, or
simply press it down with your finger.
After you have dipped the glass far
enough, you" can let the thread, or your
finger, go. The disc will remain where it
is, being kept in place by the water
pressing up on it.
If you want to, you can even gauge the
value of this upward pressure. Carefully
pour some water into the glass. As soon as
the level of the water in the glass reaches
that of the water in the jar, the disc slips
off, because the pressure exerted by the water on the disc from below
is offset by the pressure v exerted on it from above by the column of
water in the glass, the height of which is equal to the depth to which
the glass has been dipped. Such is the law concerning the pressure that
a liquid exerts on any immersed body. This incidentally results
in that "loss" of weight Jn liquids of which Archimedes's famous prin-
ciple speaks.
With the help of several lamp-glasses of different shapes but with
tops of one and the same size you may test another law dealing with
liquids: that the pressure a liquid exerts on the bottom of the contain-
ing vessel depends only on the size of the bottom and the height of
Fig.53. A simple way to demon-
strate_tbat liquids [press up-
waids
79
the "column" of liquid; it does not
depend at all on the vessel's shape.
This is bow you test this law. Take
different glasses and dip them to
one and the same depth. To see
that no mistakes occur, first glue
strips of paper to the glasses at equal
heights from the bottom. The card-
board disc you used in the first
experiment will slip off every time
you pour in water to the same level
(Fig. 54). Consequently the pressure
exerted by columns of water of
different shapes is the same as
long as the bottom and height are
the same. Note that it is the height,
and not the length, that is impor-
tant, because .a long but inclined
column exerts exactly the same
Fig. 54. The pressure liquid exerts
on the bottom of the vessel depends
only on the area of the base and the
liquid's height. The drawing shows
you how to check this
pressure on the bottom as is exerted by a shorter but perpendicular col-
umn as high as tht inclined one provided, of course, the bottom of
each is the same.
WHICH IS HEAVIER?
Place a pail of water, full up to
the rim, on one pan of a pair of
scales. Then put on the other
pan another pail of water, also
full up to the rim, but with a piece
of wood floating in it (Fig. 55).
Which of the two is heavier? I
asked this of different people and
got contradictory answers. Some
said the pail with the piece of
wood in it would be heavier be-
cause it held a piece of wood in
Fig. 55. Both pails are full to the
rim. One has a piece of wood in it.
Which is heavier?
addition to the water. Others said the pail of water without the piece of
wood would be heavier, since water generally weighs more than wood.
Neither were right. Both pails weigh the same. The second pail, true,
contains less water than the first one, because the wood displaces some
of the water. But, according to the related law, every floating body
displaces with its immersed part exactly as much liquid (in weight) as
the whole of this body weighs. That is why the scales balance.
Now try to solve another problem. Take a glass of water, put it on
one of the pans, and put a weight next to it. Balance the scales. Then
drop the weight next to the glass into it. What happens to the scales?
According to Archimedes's principle, in the water the weight should
weigh less than when on the pan.
Consequently, oughtn't this pan rise? However, the pans main-
tain their equilibrium. Why? When dropped into the glass the weight
displaced some of the water which then rose to a level higher than
before. This added to the pressure exerted on the bottom of the
vessel, which thus sustained an additional force equivalent to the
weight lost by the weight.
A LIQUID'S NATURAL SHAPE
We are used to thinking that liquids have no shape of their own. That
is not true.
The natural shape of any liquid is that of a sphere. As a rule,
gravity prevents liquids from assuming this shape. A liquid either
spreads in a thin layer if spilled out of a vessel, or takes the vessel's
shape. But when inclosed in another liquid of the same specific
weight, it, according to Archimedes's principle, "loses" its weight,
seeming to weigh nothing; now gravity has no effect on it and it as-
sumes its natural spherical shape.
Since olive oil floats in water but sinks in alcohol we can mix the
two in such proportions that the oil will neither sink nor float in this
mixture. An odd thing happens when we drip in a little oil with the
help of an eyedropper. The oil collects into a large round drop which
neither floats nor sinks, but hangs suspended (Fig. 56). To get a true
image of the sphere, you should do the experiment in a flat- walled
62668 31
vessel or in one of any shape but placed inside a flat-walled vessel
full of water.
You must do this experiment patiently and carefully, because other-
wise you will get several smaller drops instead of a large one. Don't
feel disheartened if it doesn't work out; even then it's sufficiently
illuminating.
Fie. 56. Oil inside diluted alcohol
collects into a drop which neither
sinks nor floats. (Plateau's experi-
ment.)
Fig. 57. A ring is given off when
the oil drop in the alcohol is spun
by means of a rod
Let's carry this experiment further. Take a long stick or a piece of
wire and transfix the oil drop. Start turning. The drop also participates
in this revolution. You get still bettor results by attaching to the stick
or wire a small cardboard disc soaked in oil and inserting it fully in
the drop you are twirling. The spin compels the drop to compress and
then give off a ring a few seconds later (Fig. 57). As it breaks up the
ring creates new drops which continue to revolve round the central one.
The Belgian physicist Plateau was the first to conduct this instruc-
tive experiment, of which I have given you the classical description.
It would be much easier and just as instructive to do this experi-
ment in another way. Take a small tumbler, rinse it with water, and
fill it with olive oil. Place it on the bottom of a larger glass. Then
carefully pour into the glass enough alcohol to cover the tumbler.
Gradually add a little water with the help of a spoon. Do this very
carefully, so that the water drips down the walls of the glass. The top
of the oil in the tumbler starts to bulge, and when enough water has
been pou
