G. P. (George Payn) Quackenbos.

A natural philosphy: embracing the most recent discoveries in the various branches of physics .. online

. (page 5 of 42)
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fall. If it met with no resistance, it would
rise to about the same height on the oppo-
site side. But, encountering B, it imparts
B to it a portion of its motion, and both move
on together, as shown in Fig. 37, though only
half as far as A would have gone alone. The
reaction of B is clearly equal to the action of
A ; for the latter loses just as much motion as
the former gains.

If the two balls be of ivory, or any other
highly elastic substance, A will impart the whole of its mo-
tion to B, and remain stationary after striking ; while B, as

of reaction ? What humorous instance is given of the nullifying effect of reaction ?
State the case of the man with the sail-boat. 92. In what two classes of bodies are
action and reaction differently exhibited ? How is this difference shown? What
does Fig. 36 represent? Show the effect of action and reaction in these non-elastio



Fig. 36.




Mg. 37.




ACTION AND REACTION.



45



Fig. 38.



shown in Fig. 38, will swing to the same
height that A would have reached if unre-
sisted. Here again the reaction of B, which
brings A to rest, is evidently equal to the
action of A, which sets B in motion.



AO



93. Fig. 39 affords a further illustration of action and reaction in elastic
bodies. Five ivory balls are suspended by strings of equal length, so as to




Fig. 89.




fall in front of a graduated arc, with the aid of
which the distance they move can be observed.
Let the first, A, be drawn out and allowed to
fall. It will impart all its motion to the second,
and by the reaction of the latter will be brought
to rest. In like manner, the second imparts its
motion to the third, and is kept at rest by reac-
tion ; and so with the third and the fourth. The
fifth, B, finally receives the motion ; and, there
being in this case no reaction to stop it, it flies
off to the same height from which A started.

94. REFLECTED MOTION. Reflected Motion is the mo-
tion of a body turned from, its course by the reaction of
another body against which it strikes. A ball rebounding
from a wall against which it has been thrown, affords an
example of Reflected Motion.

If a body possessing little or no elasticity be thrown against a wall, it will
rebound but a short distance, if at all. We find the most striking instances
of reflected motion in the most elastic bodies. Every boy knows that an
india rubber ball will bound higher than one made of yarn, and that a yarn
ball will bound higher than one stuffed with cotton.

95. When a ball is thrown perpendicularly Fig. 40.

against another body, it rebounds in the same
line towards the hand from which it was thrown.
Thus, in Fig. 40, if a ball be thrown from F against
the surface B C so as to strike it perpendicularly
at A, it will return in the line A F. If thrown
from D, however, it will glance off on the other _
side of the perpendicular, at the same angle, to E.

If D were nearer the perpendicular, the line A E would also be nearer to it ;
if it were farther from the perpendicular, AE would be farther in proportion.

balls. What does Fig. 38 represent? 93. Describe the apparatus represented in Fig.
3D, and tell how it operates. 94. What is Reflected Motion ? Give an example.
What bodies exhibit reflected motion most strikingly ? 95. When a ball is thrown
perpendicularly against another body, how does it rebound? When thrown so as to
make an angle with, the perpendicular, how will it rebound ? Illustrate this with




46 MECHANICS.

96. The angle D AF in Fig. 40, made by the body in
its forward course with the perpendicular at the point of
contact, is called the Angle of Incidence.

The angle EAF, made by the body in its backward
course with the same perpendicular, is called the Angle of
Reflection.

The great law of reflected motion is as follows : The
Angle of Reflection is always equal to the Angle of Inci-
dence.



CHAPTER V.
MECHANICS (CONTINUED).

GRAVITY.

97. TERRESTRIAL GRAVITY. When a stone is let go, we
all know that it does not fly up in the air or move sideways,
but falls to the ground. This is owing, as already men-
tioned, to a universal property of matter. The stone and
the earth mutually attract each other ; but the earth, being
vastly superior in size, draws the stone to itself, or in other
words, causes it to fall.

The tendency of bodies, when unsupported, to approach
the earth's surface, is called Terrestrial Gravity, or simply
Gravity.

98. GRAVITATION. Attraction is universal. It is not
confined to things on and about the earth's surface, but
extends throughout space, millions of miles, and is in fact
the great agent by which the heavenly bodies are kept
moving in their respective spheres. The earth as certain-
ly attracts the planet Uranus, at the vast distance of
1,828,000,000 miles, as it does the filling stone.

Figure 40. 96. What is the Angle of Incidence ? "What is the Angle of Reflection ?
What is the great law of reflected motion ?

97. "When a stone is let go, what does it do ? To -what is this owing ? What is
meant by Terrestrial Gravity ? 98. What is Gravitation ? How far does gravitation



GRAVITATION. 47

The attraction subsisting between the heavenly bodies
is called Gravitation.

To Sir Isaac Newton the world owes the great discovery of the law of
Universal Gravitation. Galileo had investigated the subject of terrestrial
gravity (A. D. 15'Ju), but he did not imagine that any similar force existed
beyond the neighborhood of the earth. Kepler advanced a step nearer the
truth, and spoke of gravitation as acting from planet to planet; still he did
not conceive of its having any effect on the planetary motions. This discov-
ery, one of the most important that modern science has achieved, was re-
served for the mighty genius of Newton. Sitting in his orchard one day
(A. D. 1G66), he observed an apple fall from a bough. This simple circum-
stance awakened a train of thought. Gravity, he knew, was not confined to
the immediate surface of the earth. It extended to the greatest heights with
which man was acquainted; why might it not reach out into space? Why
not affect the moon ? Why not actually cause her to revolve around the
earth? To test these speculations, Newton at once undertook a series of la-
borious calculations, which proved that the attraction of gravitation is uni-
versal ; that it determines the orbits and velocities of the planets, causes the
inequalities observed in their motions, produces tides, and has given its
present shape to the earth.

99. Three facts have been established respecting gravi-
tation :

1. Gravitation acts instantaneously. Were a new body
created in space 1,000 miles from the earth, its attraction
would be felt at the sun just as soon as at the earth, though
the one would be 95,000,000 miles off, and the other only
1,000.

2. Gravitation is not lessened by the interposition of
any substance. The densest bodies offer no obstacle to its
free action. Were a body placed on the other side of the
moon, it would be attracted by the earth just as much as
if the moon were not between them.

3. Gravitation is entirely independent of the nature of
matter. All substances that contain equal amounts of mat-
ter attract and are attracted by any given body with equal



extend? Give an example. By whom was the law of Universal Gravitation discov-
ered ? What advance had been made towards it by Galileo ? What, by Kepler ?
Give an account of the circumstances and reasoning that led Newton to this discov-
ery. What was proved by his calculations? 99. What is the first fact that has been
established respecting gravitation? Give an example. What is the second fact?
Give an example. What is the third fact? What evidence is thereof this? 100. What




48 MECHANICS.

force. The action of the sun is found to be the same on
all the heavenly bodies.

100. DIRECTION OF GRAVITY. If a piece of lead sus-
pended by a string be left free to move, it will point to-
wards the earth. This is the case in all parts of the globe.
Now, as the earth is round, it follows that at two opposite
points of its surface, the plummet, or plumb-line (as this
rig. 41. suspended lead is called), will

point in opposite directions.
This will be seen from the
relative positions of A and
B, C and D, in Fig. 41. The
lead, therefore, has no ten-
dency to fall in any particu-
lar direction as such, but
takes all directions accordinc:

O

to the part of the earth's
surface which it is near. The

universal law is, that it must point towards the centre of

the earth.

It is not because any peculiar attractive power resides in the centre that
a falling body tends towards that point ; but because, in a sphere, this is the
result of the attraction of all the particles. The particles on one side attract
the falling body as much as those on the other ; and consequently it seeks a
point between them.

No two plummets suspended in different places have exactly the same di-
rection, for the lines in which they hang would meet at the centre of the
earth. At short distances, however, the difference of direction is so slight as
to be imperceptible, and the plummets seem to point the same way.

101. It follows that up and down are relative and not absolute terms.
What is up to a person in New York, is down to a ship a few miles south-west
of Australia. If a person in a standing position at New York were to be
carried in a straight line through the earth to its centre, and on in the same
direction to the opposite side of the earth, he would come out in the Indian
Ocean south-west of Australia, but would find himself on his head instead of
his feet. His head, which at New York pointed up, would now point down.

is a piece of lead suspended by a string called ? How docs the plummet ahvays
point? On what does the absolute position of the plummet depend? Why does a
falling body tend towards the centre of the earth? What is said of the difference of
direction in plummets suspended in different places ? 101. What is said of the terms
up and doicn ? Exemplify this. What is the real meaning of up and down ? Why



LAWS OF GEAVITY. 49

Down, therefore, simply means towards the centre of the earth, and up away
from the centre.

This explains what the unreflecting are sometimes puzzled to account for,

why persons and things on the side of the earth opposite to them do not

fall off. Regarding themselves as on the upper side, they can not see what
keeps those on the under side from being precipitated into space. But really
there is no under side. All things are alike drawn towards the centre ; all
are kept on the earth's surface by the same force of gravity.

102. LAWS FOE THE FOKCE OF GEAVITY. The force of
gravity (and the term is here used in its widest sense, in-
cluding gravitation) depends on two things, 1. Amount
of matter ; 2. Distance, according to the following laws :

1. The force of gravity increases as the amount of mat-

ter increases.

2. The force of gravity decreases as the square of the

distance increases.

103. According to the first law, if the sun contained
twice as much matter as it now does, it would attract the
earth with twice its present force ; if it contained three
times as much matter, with three times its present force ;
&c. Observe, we say if it contained twice as much matter,
not if it were twice as large / for it might be twice its
present size, and yet so rare as to contain less matter and
attract less strongly than it now does. If there were two
heavenly bodies, the one of iron and the other of cork, the
Latter, though twice as large as the former, would have less
attraction because it would contain less matter.

As already remarked, the earth is so much larger than the bodies near
its surface that it is not perceptibly affected by their attraction. Even if a
ball .100 feet in diameter were placed in the atmosphere 500 feet from the
earth's surface, the earth, being 530 million million times greater than the
ball, would draw the latter to itself, while it would advance to meet it, less
than one ninety-six-thousand-millionth of an inch a distance so small that it
can not be appreciated.

The sun is 800 times greater than all the planets put together. It is on
account of this enormous amount of matter that its attraction is felt by the
most remote bodies of the solar system at a distance of many millions of miles.

do not objects on the under side of the earth fall off? 102. On what does the force of
gravity depend? Eepeatthc two laws of gravity. 103. Explain the first law. Why
is not the earth perceptibly affected by the attraction of bodies near its surface ? Givo
an example. Why is the attraction of the sun so great? What would be its effect

3



50 MECHANICS.

A man carried to the surface of the sun would be so strongly attracted by its
immense mass that he would be literally crushed by his own weight.

104. According to the second law, if the sun were twice
as far from the earth as it now is, it would attract the latter
with but i of its present force ; if three times as far, with
i ; if four times as far, with r V, & c . g o? if two equal masses
were situated respectively 5,000 miles and 10,000 miles from
the earth's centre, the nearer would be attracted not twice,
but 4 times, as strongly as the more distant.

105. All bodies on the earth's surface, however small,
attract each other with greater or less force according to
their masses and distance. This attraction, in most cases,
is absorbed in the far greater attraction of the earth, and
consequently can not be perceived. In the case of moun*
tains, however, it is so strong as to have a sensible effect on
plummets suspended at their base. Instead of pointing di-
rectly towards the centre of the earth, a plumb-line in such
a position is found to incline slightly towards the mountain.

106. WEIGHT. When a body is supported or prevented
from following the impulse of gravity, it presses on that
which supports it, more or less strongly according to the
force with which it is attracted. This downward pressure
is called its Weight.

Weight is simply the measure of a body's gravity, and is proportioned to
the amount of matter contained. A ball of iron is heavier than a ball of cork
of equal size, because it contains more matter.

Weight being nothing more than the measure of the force with which
bodies are drawn towards the earth, it follows that, if the earth contaiiieJ
twice as much matter as it now does, they would have twice their present
weight ; if it contained three times as much matter, three times their present
weight, &c.

107. Weight above and below the Eartli's Surface.
Since the weight of a body is the measure of its gravity,
and since gravity decreases as the square of the distance
from the earth's centre increases, it follows that bodies be-
on a man carried to its surface? 104. Illustrate the secon.l law with an example.
1.5. Why is not attraction exhibited between small bodies on the earth's surface?
How is a plummtt suspended near the base of a mountain affected? 106. What is
Weight? To what is weight proportioned? If the earth contained twice as much
matter as it now does, how would the weight of objects on its surface compare with



WEIGHT ABOVE THE EARTH'S SURFACE.



51



come lighter in the same proportion as they are taken up
from the earth's surface. A mass of iron which at the
earth's surface weighs a thousand pounds, taken up to a
height of 4,000 miles, would weigh only 250 of such pounds,
or one-fourth as much as before.



Fig. 42.

20,000 miles y 40 pounc 1 *



6 times surface distance



16,000 miles | ea'/Q pounds
4 times surface distance 1[ IQ surface weight



12,000 miles
S times surface distance



?,000 miles
1 Twice surface distance



Srfac distance



111 1 /, Pounds
l/ 9 surface weight



250 pounds

I/, surface weight



The reason of this is clear. The earth
being about 8,000 miles through, from its
centre to its surface is 4,000 miles; and
from its centre to a point 4,000 miles
above its surface, is 8,000 miles. 4,000 is
to 8,000 as 1 to 2 ; but the weight at the
surface would not be to the weight 4,000
miles above the surface as 2 to 1, but as
the squares of these numbers, 4 to 1.
Hence, if it would weigh 1,000 pounds at
the surface, it would weigh only */ 4 as
much, 4,000 miles above the surface. For
the same reason, it would weigh 1 / g of
1,000 pounds at a distance of 8,000 miles
from the surface ; l / ia , at a distance of
12,000 miles; VSB, at a distance of 16,000
miles, &c. These results are exhibited
in Fig. 42.

At small elevations, the weight which
an object loses amounts to but little. Four
miles above the earth's surface, a body
weighing 1,000 pounds would become only
two pounds lighter. Raised to a height
of 240,000 miles, the distance of the moon
from the earth, its weight would be re-
duced to less than five ounces.

108. If we could go from the
surface of the earth to the cen-
tre, we should find a given object weigh less and less as we
advanced. The moment we descended beneath the surface,
we would leave particles of matter behind us, and the at-
traction of these would act in a direction exactly opposite
to gravity.

their present weight ? 107. What is said of the weight of bodies taken up from the
earth's surface ? What would 1,030 pounds of iron weigh, 4,000 miles above the
earth's surface ? Show the reason of this. What is said of the loss of weight at small
elevations? Four miles above the surface, how much would a body weighing 1,000
pounds lose ? What would be its weight, 240,000 miles from tho earth ? 108. If we




52



MECHANICS.



Thus, in Fig. 43, let C represent the centre of the earth, and any object
beneath the surface. All the particles below the line A B attract down-
Fig. 43. Fig. 44.





ward, but all above that line attract it upward, and thus diminish its
weight.

At the centre of the earth (see Fig. 44) no object would weigh any thing.
There would be as many particles above the line D E as below it ; and 0, be-
ing equally attracted on all sides, would have no weight.

109. All bodies carried below the earth's surface would, therefore, become
lighter as they approached the centre. Their weight at any given number
of miles below the surface may be found as follows :

For 1 mile below, take f|- of the surface weight.

For 2 miles, take f||| of the surface weight.

For 100 miles, take | of the surface weight.

For 1,000 miles, take { of the surface weight, &c.

no. Law of Weight. From the
above principles the following law of
we *o nt i g Deduced: All objects weigh
the most at the surface of the earth:
ascending from the surface, their
weight diminishes as the square of
their distance from the centre in-
creases descending towards the cen-
tre, tJieir weight diminishes as their
distance from the surface increases.

Fig. 45 shows the operation of
this law in the case of an object weigh-
ing 1,000 pounds at the earth's surface.

could go from the surface of the earth to the centre, what would we find respecting
the weight of a given body? What is the reason of this decrease? Illustrate this
with Fig. 43. What would all objects vreigh at the centre ? Show the reason of this
with Fig. 44. 109. How may we find the weight of a given body one mile below the




WEIGHT IN DIFFERENT LATITUDES,



53



111. Weight at different Parts of the Earth's Surface.
The weight of a body differs at different parts of the
earth's surface. A mass of lead, for instance, that weighs
1,000 pounds at the poles, will weigh only 995 such pounds
at the equator.

112. This is owing to two causes :

1. The equatorial diameter is about 26^ miles longer
than the polar diameter ; and therefore an object at the
equator is farther from the centre and less strongly at-
tracted than at any other point.

2. The centrifugal force, as shown in 79, is greatest
at the equator, and therefore counterbalances more of the
downward attraction there than at any other part of the
surface, making the weight less. It has been computed,
that, if the earth revolved 1 7 times as fast as it now does,
the centrifugal force at the equator would counterbalance
gravity entirely, and thus deprive all bodies of weight. If
the earth's velocity were further increased, all things at the
equator would be thrown off into space.

113. The general effect of gravity is
to draw bodies towards the earth ; but
sometimes it causes them to rise. A
balloon, for instance, mounts to the
clouds. This is because it contains less
matter than a mass of air of the same
bulk, or, as we say briefly, it is lighter
than air. Hence the air, acted on more
strongly by gravity than the balloon, is
drawn towards the earth under the lat-
ter, which is thus caused to rise.

For the same reason, smoke ascends.
So, if a flask of oil be uncorked at the



Fiar. 46.




A BALLOON.



earth's surface ? Two miles ? A hundred miles ? A thousand miles ? 110. Eepeat
the law of weight. 111. What is said of the weight of a body at different parts of the
earth's surface ? Give an example. 112. To what causes is this owing ? What would
be the result, if the earth revolved on its axis with seventeen times its present velo-
city ? 113. Show how gravity sometimes causes a body to rise. Give some illustra-



54 MECHANICS.

bottom of a pail of water, the water will be drawn down
below the oil, and force the latter to the top.

Falling Bodies.

114. VELOCITY OF FALLING BODIES. If a feather and
a cent be dropped from a height at the same time, the cent
will reach the ground some seconds before the feather.
This fact Aristotle and his successors explained by teaching
that the velocity of falling bodies is proportioned to their
weight ; that a body of two pounds, for instance, would
reach the ground in just half the time required by a body
weighing one pound. Galileo was the first to correct this
error (about A. D. 1590). He held that the velocity of fall-
ing bodies is independent of their weight, and that, if no
other force than gravity acted on them, all objects dropped
at the same time from the same -height would reach the
ground at the same instant.

So startling a proposition was at once condemned by the learned men of
the day ; but Galileo, convinced of the truth of his position, challenged his
opponents to a trial.

The leaning tower of Pisa [pe'-zah], Italy, was chosen as the scene of the
experiment, and multitudes flocked to witness it. Two balls were produced,
one of which weighed exactly twice as much as the other, and after being
examined, to prevent the possibility of deception, at a given signal they were
dropped. In breathless anxiety the crowd awaited the result, doubting not
that it would confound the bold youth of six-and-twenty years, who had dared
to oppose not only the sages of his own time, but also the established opin-
ion of centuries and the great master Aristotle himself. To their amazement,
the bold youth was right ; the balls reached the earth at the same instant.
Unable to credit their own senses, again and again they repeated the experi-
ment, but each time with the same result. This triumph, though it awakened
the jealousy of his defeated rivals, and cost Galileo his place as professor of
mathematics in the university of Pisa, established the fact that gravity causes
all bodies to descend with equal rapidity, without reference to their weight, and
that all apparent differences are caused by some other agency.

115. RESISTANCE OF THE AIR. The cause of the differ-



tions. 114. If a feather and a cent be dropped at the same time, which will reach the
ground first? How did Aristotle explain this fact ? What was Galiico's opinion on
the subject ? How was his theory received by the learned men of the day ? Give an
account of the trial that was made at Pisa. What fact was established by the experi-



RESISTANCE OF TIIE 'AIR.



55



Fig. 47.



ence of velocity in a falling feather and a falling cent is the
Resistance of the Air.

This resistance is proportioned to the extent of surface
which the falling body presents to the air. The surface,
indeed, may be so extended that gravity can
hardly overcome the air's resistance; thus, gold
may be beaten into a leaf so thin that it will be
exceedingly slow in its descent, floating for a time
in the air.

116. That the resistance of the air causes the difference of ve-
locity exhibited by falling bodies, may be proved in two ways :

1. A piece of paper, a sheet of gold-leaf, or a feather, with its
surface extended, floats slowly downward ; roll it into a compact



Online LibraryG. P. (George Payn) QuackenbosA natural philosphy: embracing the most recent discoveries in the various branches of physics .. → online text (page 5 of 42)