G. P. (George Payn) Quackenbos.

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

. (page 4 of 42)
Online LibraryG. P. (George Payn) QuackenbosA natural philosphy: embracing the most recent discoveries in the various branches of physics .. → online text (page 4 of 42)
Font size
QR-code for this ebook


bank, how far will the other penetrate?

22. A stone weighing 15 ounces is thrown from the hand with a velocity of
1,320 feet in a minute. A rifle-ball weighing 3 ounces is discharged at
the rate of 15 miles a minute. How do their velocities compare ?

How do they compare in momentum ?

How many times greater is the striking force of the rifle-ball than thai
of the stone ?

2*



MECHANICS.



CHAPTER IY.

MECHANICS (CONTINUED).

LAWS OF MOTION.

Mathematical definitions.

70. BEFORE treating of the laws of motion, it is neces-
sary to define the mathematical terms used in connection
with them.



Fi?. 13.



Fig. 14.



Fig. 15.



1. A Right or Straight Line is one that has the same
direction throughout its whole extent; as, AB.

2. Parallel Lines are those which have the same direc-
tion ; as, C D, E F.

3. A Curve Line, or Curve, is one that changes its di-
rection at every point ; as, G H.

4. A Circle is a figure bounded by a curve, every point
of which is equally distant from a point within, called the
Centre. Fig. 16 represents a circle, and E its centre.

5. The Circumference of a circle is the curve that
bounds it; as, AC FED.

6. Any part of the circumference is called an
Arc ; as, A C, C F.

7. A Diameter of a circle is a straight line drawn
through the centre, terminating at both ends in the
circumference ; as, A B. Every circle has an infinite
number of diameters, all equal to each other.

8. A Radius (plural, radii) of a circle is a straight line drawn from the
centre to the circumference; as, ED, EC, EF, EA, EB. Every circle has
an infinite number of radii, all equal to each other. The radius of a circle is
just half its diameter.

9. A Tangent of a circle is a straight line that touches the circumference




70. What is a Eight Line ? What are Parallel Lines? What is a Curve Line?
What is a Circle ? What is the Circumference of a circle ? What is an Arc ? What
is a Diameter of a circle ? How many diameters has every circle ? What is a Radius?
How mauy radii has every circle ? How does the radius of a circle compare with its




MATHEMATICAL DEFINITIONS. 35

in a single point, without cutting it at either end when pro- Fig. It.

duced ; as, A 13, C D.

10. The circumference of every circle is divided into 3GO
equal parts, called Degrees. One fourth of the circumfer-
ence contains 90 degrees, and is called a Quadrant.

11. An Angle is the difference in direction of two straight c-
lines that'meet or cross each other.

12. The Vertex (plural, vertices) of an angle is the point at which its sides
meet ; -us, D in Fig. 18.

An angle is named from the letter at its vertex, if but Fig. 18.
one angle is formed there. Otherwise, it is named from
the letters on each side and at the vertex, that at the vertex
being placed in the middle. Thus the angle in Fig. 18 is
called D ; if more than one angle were formed there, it
would be distinguished as C D B or B D C.

The size of an angle does not depend on the length of its sides, but sim-
ply on their difference of direction. "We may extend the lines DC, D B, as
far as we choose, without making the angle D any larger.

13. When a straight line meets another straight line in such a way as to
make the two adjacent angles equal, that is, so as to incline no more to one
side than the other, it is said to be Perpendicular

to the latter; and the angle which it makes on either
side is called a Right Angle. Thus, F E B and F E A
(being equal) are Right Angles, and the line F E is
Perpendicular to the line A B.

A right angle, it will be seen, is measured by
one fourth of the circumference of a circle, or 90 de-
grees.

14. An Obtuse Angle is one that is greater than a
right angle; as, FED in Fig. 19.

1"). An Acute Angle is one that is less than a right angle;
as, FECin Fig. 19.

16. A Triangle is a figure bounded by three straight
lines ; as, ABC, Fig. 20.

17. A Quadrilateral is a figure bounded by four straight
lines ; as, A B C D, Fig. 21.

18. A Diagonal of a quadrilateral is a straight line -p, v
which joins the vertices of two opposite angles ; as,

AC, DB, in Fig. 21.

19. A Parallelogram is a quadrilateral whose oppo-
site sides are parallel ; as, A B C D, Fig. 21. A B

diameter? "What is a Tangent of a circle? How is the circumference of every circle
divided ? What is a Quadrant ? "What is an Angle ? What is the Vertex of an an-
gle ? How is an angle named? On what alone does the size of an angle depend?
When is one line said to be Perpendicular to another ? What is a Eight Angle" ? By
what is a right angle measured ? What is an Obtuse Angle ? What is an Acute An-




36 MECHANICS.

Fig. 22. 20. A Rectangle is a quadrilateral whose angles are

all right angles ; as, E F G H, Fig. 22. Fi<y

21. A Square is a rectangle whose sides are equal ; j a ~j'
as, UK L, Fig. 23.




22. A Sphere is a solid bounded by a curved surface,



J




all the points of which are equally distant from a point within called
the centre ; as, AB CD, Fig. 24.

23. The Axis of a sphere is a straight line
passing through its centre and terminating in its
surface, round which it revolves ; as, the straight
line connecting A and B, in Fig. 24.

24. The Poles of a sphere are the extremities
of its axis ; as, the points A, B, in Fig. 24.

25. The Equator of a sphere is a great circle
which we imagine to be drawn round it on its
surface, midway between the poles ; as, the cir-
cle C D, in Fig. 24.

26. An Oblate Spheroid is a figure which dif-
fers from a sphere only in being flattened at its
poles, like an orange.

27. A Prolate Spheroid is a figure which differs from a sphere only in be-
ing lengthened out at its poles, like a lemon.

28. A Cylinder is a circular body of uniform diameter, the ends of which
form equal and parallel circles. A lead-pencil, before it is sharpened, is a
cylinder ; a stove-pipe is a hollow cylinder.

71. By investigating the principles of motion, Newton
arrived at three great laws, which have ever since been
received.

First Law of Motion.

72. A. body at rest remains at rest, a body in motion
moves in a straight line with uniform velocity, unless acted
on by some external force.

This law follows from inertia. No body has power of itself to move, to
cease moving, or to change its direction or velocity.

73. The air is a powerful agent in stopping motion. This is shown by
causing a wheel to revolve on a pivot, first in the air, and then under a glass

gle ? What is a Triangle ? What js a Quadrilateral ? What is a Diagonal of a quad-
rilateral? What is a Parallelogram? What is a Eectangle? What is a Square?
What is a Sphere ? What is the Axis of a sphere ? What are the Poles of a sphere ?
What is the Equator of a sphere ? What is an Oblate Spheroid ? What is a Prolate
Spheroid? What is a Cylinder ? 71. TTow many laws of motion did Newton arrive
at? 72. What is the First Law of Motion? From what does this law follow?
73. How may it be shown that the air is a powerful agent in stopping motion ?



FIRST LAW OF MOTION. 37

receiver from which the air has been removed with an air-pump. In the for-
mer case, the wheel soon ceases to move ; in the latter, it retains its motion
for a long time. A pendulum (see 138) will vibrate nearly a day in an ex-
hausted receiver.

74. Friction is the resistance with which a body meets from the surface
on which it moves. The rougher the surfaces brought in contact, the great-
er the friction, and the sooner the moving body will come to rest. A ball
rolled over a stony road is soon stopped by the obstacles it encounters ; on a
level pavement it goes much farther, and farther still on a smooth sheet of
ice. This is because the friction becomes less in proportion as the surface
on which the ball rolls becomes smoother.

75. According to this law, every body left free to obey
the force that set it in motion will move in a straight line.
We observe few such motions in nature. The planets in
their orbits, rivers in their channels, rolling waves, and as-
cending smoke, all move in curves, in consequence of their
being acted on by other forces, besides those that set them
in motion. The tendency of the moving body, however,
is always to continue in a straight line, even when from
overruling causes it moves in a circle.

Attach a ball, for instance, to a cord ; and, Fig. 25.

fastening the end of the cord at a point, 0, give E _B y

a quick impulse to the ball. It will be found to
move in a circle, AB C D, because the cord keeps
it within a certain distance of the centre. Were
it not for this, it would move in a straight ime.
Thus, let the cord be cut when the ball is at A,
and it will be found to move to E in a tangent to
the circle AB C D. In like manner, at B it will
fly oil' in a tangent to F, and so at C, D, or any
other point. ^

76. THE CENTRIFUGAL FORCE. The force which tends
to make a body fly from the centre round which it revolves,
is called the Cen-trif-u-gal Force.

The opposite force, which draws a body towards the
centre round which it revolves, is called the Cen-trip'-e-tal
Force.

Magnificent examples of these two forces are exhibited

74. What is Friction ? On what kind of surfaces does a moving body encounter th
most friction ? Exemplify this. 75. What is said of the motions that we find in na-
ture ? Give F ome instances. What is the tendency of the moving body ? Illustrate
this with a ball and cord. 76. What is tho Centrifugal Force ? What is the Centri>



38



MECHANICS.



Fig. 26.



by the planets revolving round the sun in space. At each
successive point of their orbits, in obedience to the Cen-
trifugal Force, they tend to fly off in tangents, disturbing
the harmony of the universe and carrying desolation in
their path. They are constantly restrained, however, by a
Centripetal Force equally powerful, the sun's attraction ;
and the result is that they revolve in curves.

77. Familiar Examples. "Whirl a wet mop rapidly round,
and drops of water, propelled by this force, will fly off from
it in straight lines.

Suspend a glass vessel containing some colored water, by
a cord passed round the rim, as shown in Fig. 2G. Turn the
vessel round till the cords become tightly twisted, and then
suddenly let it go. It will rapidly revolve, and the centrifu-
gal force will give the water an impulse away from the centre.
As it can not escape, it will spread up the sides. Should there
be water enough, it will rise above the top of the vessel, and
fly off in straight lines.

We take advantage of the centrifugal force in discharging
a stone from a sling. The stone is whirled quickly round the
hand as a centre, which it is prevented from leaving by two
strings connected with the strap on which it rests. The in.
stant one of the strings is let go, the centrifugal force carries
off the stone in a tangent to the circle it was describing. Its
direction varies according to the point at which the string is let go, as will
appear from Fig. 27. Great velocity may be communicated to the stone with
this simple apparatus. In the hands of the Per-
sians, the Rhodians, and other ancient nations,
the sling was a formidable weapon.

When a wagon turns a corner rapidly, it is
liable to be upset in consequence of the'centrif-
ugal force. A person sitting in it feels his body
sway outward, and one who is on his feet has
to grasp the wagon to avoid being thrown from

\V I his place. To counteract the effects of the cen-

\^w / trifugal force in curves on railroads, the outer

rail is laid higher than the inner one, as repre-
sented in Fig. 28. Were it not for this precau-





fctal Force ? What examples of these two forces does nature furnish us ? 77. IIow
3nay a mop be made to illustrate the centrifugal force ? IIow does the apparatus rep-
resented in Fig. 26 illustrate the Centrifugal Force ? Describe the mode in which a
etone is discharged from a sling, and explain the principle. What is the effect of tho
centrifugal force, when a wagon turns a corner rapidly ? IIow is this effect counter-



THE CENTRIFUGAL FOKCE.



39




tion, trains moving swiftly round a curve Fig. 28.

would often be thrown from the track.

Instinct teaches a horse running rapidly
round a small circle, to incline his body in-
ward, that he may counteract the centrifugal
force. For the same reason, a circus-rider,
going swiftly round the ring, has to lean to-
wards the centre.

Jugglers take advantage of the centrifu-
gal force to astonish their audiences with a
striking experiment, represented in Fig. 29.
A 13 is a wheel with a broad rim, or felly. A
wine-glass partly filled with water is placed
on the inner surface of the felly, and the wheel
is then made to revolve rapidly round the
axle 0. If the proper amount of motion be communicated
to the wheel, not only will the wine-glass keep its place
on the felly, but the water also will remain in it, not a
drop being spilled, even when the glass is at VV. Grav-
ity, which, if the wheel were stationary, would at once
cause both glass and water to fall, is completely nullified
by the centrifugal force.

78. Law oftlie Centrifugal Force. The
centrifugal force of a revolving body in-
creases according to the square of its velocity. If, there-
fore, the earth revolved round the sun twice as fast as it
now does, its centrifugal force would be 4 times as great ;
if 3 times as fast, 9 times as great; if 4 times as fast, 16
times as great, &c.

This explains why a cord with which a stone is whirled round, as in a
sling, is more apt to break under a rapid motion than a slow one. Every
time the velocity is doubled, the strain on the cord is increased fourfold.

79. Effect of the Centrifugal Force on Revolving Bod-
ies. The centrifugal force acts, not only on bodies moving
in curves, but also on fixed bodies revolving on their own
axes.

When large wheels are turned rapidly by machinery,
the centrifugal force at the circumference becomes an agent




acted in railroads ? How does instinct teach a horse to counteract the centrifugal
force ? Describe the juggler's trick performed with the aid of the centrifnffal force.
T8. "What is the law of the centrifugal force ? When is the cord of a sling most apt to
break, and why ? 79. On what, besides bodies moving in curves, does the centrifugal



40



MECHANICS.



Fig. 30.




of tremendous power. Unless such wheels are made of
very strong materials, their cohesion will be overcome by
the centrifugal force, and they will fly into fragments. Pon-
derous grindstones sometimes burst, with the most disas-
trous effects, when too great a velocity is imparted to them.

Fig. 30 represents a sphere
revolving on its axis. All parts
of the surface have to complete
their revolution in exactly the same
time ; therefore, as the parts lying
on the equator CD are further from
the axis, and have a greater distance
to go, they must travel faster than
the rest. Now we have seen that
the centrifugal force increases with

the square of the velocity ; and, therefore, at the equator
CD it will be stronger than at any other part of the sur-
face.

Hence the general law: On a revolving sphere, the
centrifugal force is greatest at the equator, and diminishes
from that point till at the poles it wholly disappears.

Fig. 31. 80. This difference of intensity in the cen-

trifugal force at different points is shown when
a sphere of moist clay is made to revolve rapid-
ly, as on a potter's wheel. The tendency of par-
ticles on and near the equator to fly off is so great
that in those parts the sphere bulges out, becom-
ing proportionately flattened at the poles.

A similar result is produced in the apparatus
represented in Fig. 31. Two thin and flexible
metal hoops are fixed, at right angles to each
other, on the axis E F, fastened at the end F,
but loose at E, so as to admit of their moving
freely up and down the rod E F. A rapid rotary
motion being communicated to the hoops, they will assume an oval form,
bulging out more and more as their velocity is increased. When allowed
to come to rest, they will rise to their original position at E.

force act? What is sometimes its effect on large wheels moved by machinery ? What
is the law of the centrifugal force in the case of revolving spheres ? Explain the rea-
son of this. 80. What is the effect of the centrifugal force on a sphere of moist clay
made to revolve rapidly? Describe the experiment with the apparatus represented




SECOND LAW OP MOTION.



41



81. The centrifugal force, acting as just described, is supposed to have
given the earth its present form. The matter of which our planet is com-
posed seems at one time to have been soft, and under a rapid rotary motion,
before becoming solid, it swelled out at the equator and became depressed at
the poles. The earth thus became an oblate spheroid, the distance from pole
to pole being about 26 miles less than the equatorial diameter.

Second ILaw of Motion.

82. A given force always produces the same effect,
whether the body on which it acts is in motion or at rest
whether it is acted on by that force alone or by others at
the same time.

The earth, as it turns on its axis, carries all things on
its surface with great velocity from west to east ; yet a
force acting on any object OR the surface causes it to move
in the same direction, and with the same rapidity, as if the
earth were at rest.

Let a stone be dropped from the mast-head of a vessel, and it will fall at
the bottom of the mast, whether the vessel moves or is at rest.

A person sitting in a wagon throws up an orange and catches it in his
hand, whether the wagon is moving or not.

83. SIMPLE MOTION. Mo-
tion produced by a single force
is called Simple Motion.

84. RESULTANT MOTION.
Motion produced by the joint
action of more than one force
is called Resultant Motion.

Resultant motion is illustrated with
the apparatus represented in Fig. 32.
The ball C is placed on a square frame
between- two upright wires, on each of
which a ball slides so as to strike C when it descends. Let the ball A drop,
and it will drive C to D ; this is an example of simple motion. Let the ball
B drop, and it will drive C to E ; this, also, is simple motion. Let A and B

in Fie:. 31. 81. "What is supposed to have been the effect of the centrifugal force on
the form of the earth? How does the equatorial diameter of the earth compare with
the distance from pole to pole ?. 82. What is the Second Law of Motion ? Give somo
familiar illustrations of this law. 83. What is Simple Motion ? 84 What is Result-
ant Motion? Describe the apparatus with which resultant motion is illustrated.



Fig. 32.




42



MECHANICS.




drop at the same instant, and they will drive C to F; this is resultant

motion.

Fig. 33. 85. We have an example of resultant motion in

a boat (see Fig. 33) which a person attempts to
row north across a river, while the tide carries it
to the east. Each force produces the same effect
as if it acted alone ; and the boatman, when he
has crossed the river, will find himself neither due
north nor due east of the point from which he

A O started, but north-east of it.

If, in addition to the boatman's efforts and the tide, the wind should blow,

this also will produce its full effect ; and the boat will exhibit a resultant

motion produced by the joint action of the three forces.

80. THE PARALLELOGRAM OF MOTION. If Figures 32
and 33 be examined, it will be seen that a body acted on
by two forces moves in a diagonal direction, between the
lines in which they would separately propel it.

In Fig. 33, the boatman, starting at A, would row his boat to B ; the tide
in the same time would carry it to D. "When both act, to get the direction
of the boat and the point it would reach, we must draw the other sides cf the
parallelogram, B C, D C ; the diagonal A C will then show the course of the
boat, and its extremity C the point it would reach.

87. If the two forces are equal, the body will move in
the diagonal of a square, that is, directly between the lines
in which they would carry it. If one is greater than the
other, the parallelogram, must be constructed
accordingly.

Let, for instance, the force used by the boatman be twice
as great as that of the tide. Then by the time he would reach
B, the tide would have carried his boat one-half of that dis-
tance, to D. Completing the parallelogram, as in Fig. 34, and
drawing the diagonal A C, we find that under the joint action
of these forces the boat would reach C.




Tliird &aw of Motion.

88. Action is the force which one body exerts on an-
other subjected to its operation.

85. How may resultant motion be illustrated in the case of a boat? 86. How does a
body acted on by two forces move? Illustrate this with Figure 33. 87. If the two
forces are equal, how will the body move ? If the forces are unequal, how will it
move? Apply this principle in Fig. 34 88. What is Action? What is Reaction?



THIRD LAW OF MOTION. 43

Reaction is the counter-force which the body acted
upon exerts on the body acting.

The third Law of Motion is as follows : Reaction
is always equal to Action, and opposite to it in direc-
tion.

89. Examples of Action and Reaction. We strike an egg against a table ;
the table reacts on the egg with the same force and in the contrary direction,
breaking its shell. We push a wagon forward, and feel the reaction in the
resistance it offers. A bird, when flying, strikes the air downward blows with
its wings ; the air reacts upward and supports the bird. A rower pulls his
oar against the water ; the water reacts and drives the boat in the opposite
direction. A boy lires a gun ; the exploding powder carries forward the
ball, but the air thus struck reacts on the gun and causes it to recoil against
the boy's shoulder. Two boats of equal weight, A and B, are connected with
a rope : a man in A pulls the rope ; action and reaction being equal, not only
will the boat B move towards him, but the boat A, which he is in, will move
with the same velocity towards B.

90. It is reaction that kills a person who fulls from a height on a hard
pavement. Another, falling the same distance, lights on a feather bed, and
receives little or no injury ; not because there is less reaction, but because the
reaction is more gradual, and therefore his body does not receive so great a
shock. On the same principle, if a steamboat in making her landing is likely
to strike violently against the dock, the force of the collision is deadened and
the boat saved from damage by interposing a coil of rope, or some other sub-
stance softer than wood.

Hence also a bullet, which would penetrate a board, will not go through
a soft cushion, its motion being gradually and not instantaneously opposed
by the reaction of the cushion. A person may catch a very heavy stone
without being hurt, if he allows his hand, the instant he catches it, to be car-
ried in the direction in which the stone was moving, and thus makes the re-
action gradual.

91. Reaction often nullifies action. This was the case
with the man who tried to raise himself over a fence by
pulling at the straps of his boots. Tug as he might, he
found that all the upward impulse he could give himself
was counterbalanced by an equally strong downward im-
pulse, and that his utmost efforts could not reverse the law

"What is the Third Law of Motion ? 89. Give some familiar illustrations of the third
law of motion. 90. What is the effect of reaction on a person falling from a height on
a hard pavement? What is the effect, if the person falling lights on a feather bed?
What causes the difference ? Give another instance of gradual reaction. How may a
person catch a very heavy stono without being hurt? 91. What is often the effect



44



MECHANICS.




85 - of nature that action

and reaction are equal in
force and opposite in di-
rection.

We read of another man no
less ingenious, who rigged a huge
bellows in the stern of his sail-
boat, that he might always be
able to make a fair wind. On
trying the experiment, he found
that with all his blowing he could
not move the boat an inch ; for
the reaction of the air on the bel-
Jows kept her back as much as its action on the sail tended to move her for-
ward.

92. ACTION AND REACTION IN NON-ELASTIC AND ELASTIC
BODIES. Action and reaction are always equal, but they
are exhibited differently in non-elastic and elastic bodies.
This difference is shown with suspended balls of soft clay
and ivory, the latter of which are elastic, while the former
are the reverse.

Fig. 36 represents two clay or non-
elastic balls. A is raised and allowed to



Online LibraryG. P. (George Payn) QuackenbosA natural philosphy: embracing the most recent discoveries in the various branches of physics .. → online text (page 4 of 42)