Tuesday 25 August 2015

speed and velocity ... Physics can be entertainment


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,
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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. "
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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
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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
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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
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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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