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 walking
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 classically
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 yourself
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-
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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
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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
kilometres,
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 parallel,
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 moon 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 according
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 pocketwatch
(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
motions
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 Accelerator.
This story
relates of a man
who drank a queer mixture
which
caused him to see
rapid motions as a series
of separate static phenomena.
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. Naturally
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 distance,
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 overtake
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
rattling
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 evidences
that all these people
in their sluggish way were exposed to a
considerable breeze,
a breeze that had no existence so far as our sensations
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 ordinary
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. WeiIs 's world of fantasy.
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