G. P. (George Payn) Quackenbos.

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

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right out ; the wheels of a carriage would turn on the ground without moving
it forward ; and neither man nor beast could walk. It is the friction of our
feet on the ground that enables us to take steps : when the friction is lessened,
as on smooth ice, we walk with difficulty ; were there no friction, we should
find it impossible to walk at all.



192. Machines are instruments used to aid the Power
in overcoming the Resistance.

1 93. Simple machines used by the hand, are called Tools ;
as, the chisel, the saw.

194. Machines of great power are called Engines ; as,
the steam-engine, the fire-engine.

195. Machines merely aid the power in its action ; they
can not create power. This follows from the inertia of mat-
ter. The mightiest engine, therefore, remains at rest until
acted on by some motive power ; and, when thus acted on,
it can not increase the power in the smallest degree, but on



are such wheels called ? 191. Mention some of the beneficial effects of friction.
192. What are Machines? 193. What are Tools ? 194. What arc Engines? 195. What
do machines merely do? Why can not a machine increase the power? Illustrate
this principle in the case of a man who can raise 100 pounds of coal a minute from a



PERPETUAL MOTION.

the other hand diminishes it, more or less according to the
friction of its parts.

If a man standing over a pit 100 feet deep can, in the space of a minute,
just pull to the top a tub containing 100 pounds of coal, no machine can ena-
ble him to raise a single pound more in the same time. By using pulleys, he
may, to be sure, raise 600, 800, or 1,000 pounds at a time, but it will take him
6, 8, 'or 10 times as long as before ; and, therefore, in the same time he will do
no more work than with his hands alone but less, on account of the friction
of the pulleys. So, a certain amount of steam, just capable of performing
50,000 units of work in a minute, can not by any machinery be male to per-
form a single additional unit of work in the same time. Hence the great uni-
versal law which follows :

196. What a machine gains in amount of work, it loses
in time; and what it gains in time, it loses in amount of
work.

Let us apply this law. A quantity of steam capable of moving 50,000
pounds a foot in a second, may be made to move 100,000 pounds a foot, but
it will be two seconds in doing it ; or it may move the weight a foot in half a
second, but in that case it will move no more than 25,000 pounds. Under no
circumstances can there be a gain in units of work without a corresponding
loss of time, or a gain in time without a corresponding loss of units of work.

197. PERPETUAL MOTION. By Perpetual Motion is
meant the motion of a machine, which, without the aid of
any external force, on once being set in operation, would
continue to move forever, or until it wore out.

^ Such a machine many have tried to invent, but without
success. Friction and the resistance of the air are con-
stantly opposing the action of machinery ; and as matter,
on account of its inertia, can generate no power that will
compensate for this loss, every machine must in time come
to rest, unless some external force, such as wind, water, or
steam, keeps acting upon it. Hence Perpetual Motion is
impossible.

198. ADVANTAGES OF USING MACHINERY. If no addi-
tional power is generated by machinery, but there is an
actual loss from the friction of its parts, why is it employed?
Because in other respects its use is attended with impor-
tant advantages, among which are the following :

pit 100 feet deep. Give another illustration. 196. What is the great universal law
of machines? Apply this law practically. 19T. What is meant by Perpetual Mo-



90



MECHANICS.



Fig. 83.




1. Machinery enables us, with a certain amount of pow-
er, by taking a longer time, to do pieces of work that we
could not otherwise do at all.

Thus, a farmer with a crow-bar, as
shown in Fig. 83, can move a rock which
with his hands alone he could not stir.
With the aid of two other men, he could
carry it or push it where he wanted, in
one- third of the time that he could move
it there alone with the crow-bar ; but he
may not have two others at hand to help
him.

With machinery 10 men may do the
work of 1,000. Of course it will take
them 100 times as long; but this loss of time is of little consequence, com-
pared with the difficulty of getting a thousand men together and placing them
so as to work without interfering with each other. Some heavy pieces of
work are of such a nature that but few laborers can get around them at a
time ; in these cases, unless the work can be divided, which is not always
possible, it must remain undone without the aid of machinery.

2. Machinery enables us to use our power more con-
veniently.

The farmer removes a rock from his field with less difficulty and fatigue
by means of a crow-bar than if he stooped over to lift it with his hands. The
porter with his block and tackle hoists a box of goods to a loft with far greater
ease than he could push or carry it up. The apparatus he uses enables him
to hoist the load by pulling down upon a rope, and when pulling down his
weight aids his strength.

3. Machinery enables us to
use other motive powers besides
our own strength.

A horse without machinery can not lift
a weight ; but he does it readily with the
aid of the simple apparatus shown in Fig.
84. Steam, applied directly to a boat,
can not move it forward; it is only with
the help of machinery that it causes the
wheel to revolve and thus produces mo-
tion. Here, as in all other cases, the




tion ? Show that perpetual motion is impossible. 198. If no additionnl power is sren-
erated by machinery, why is it used? What is the first a.lvant;i?e of usins machine-
ry? Give an example. If, with machinery, 10 men can do the work of 1,000, how
\ong comparatively will it take them ? In some pieces of work, what difficulty pre-



STRENGTH OF MATERIALS. 91

power is not created by the machinery, but merely transmitted in a way
to make it effective.

Strength of Materials

199. There is a limit to the power of all machinery;
and this limit is the strength of the materials of which it is
made. Machines that work well in small models sometimes
utterly fail when made of full size, because, when the resist-
ance is increased and their own weight is added, no mate-
rial can be found strong enough to stand the strain.

Nature, also, recognizes this limit of size. Animals, after attaining a cer-
tain age, cease to grow. If they kept on growing, they would soon reach
such a size and weight that they could not move. If there were an animal
much larger than the elephant, it would stagger under its own weight, unless
its bones and muscles were thicker and firmer than any with which we are
now acquainted. Fish, on the contrary, being supported by the water, move
freely, no matter how heavy they may be. Whales have been found over 50
feet long and weighing 70 tons a monstrous size and weight, which no land
animal could support.

200. To determine how great a strain given materials
will bear, and how they may be put together with the
greatest advantage, becomes an important question in Prac-
tical Mechanics. The relative strength of different sub-
stances has been treated of under the head of Tenacity, on
page 23. The following general principles relating to rods,
beams, &c., should be remembered.

1. Rods and beams of the same material and uniform
size throughout, resist forces tending to break them in the
direction of their length, with different degrees of strength,
according to the areas of their ends.

Let there be two rods of equal length ; if the areas of their ends are re-
spectively 6 and 3 square inches, the one will bear twice as great a weight

sents itself? What is the second advantage of using machinery ? How is this exem-
plified in the case of the farmer ? How, in the case of the porter ? What is the third
advantage gained by using machinery ? Illustrate this in the case of a horse. In the
case of steam. In both of these cases, what does the machinery merely do ? 109. What
limit is there to the power of all machinery? Why do machines often fail, though
small models of them work well ? Show how nature recognizes a limit of size. How
is it that fish can move, though much larger and heavier than land animals ? 200. What
important question is presented in Practical Mechanics ? What is the first principle
laid down respecting rods and beams ? Give an example. When a rod is very long,



92 MECHANICS.

without breaking as the other. This law applies, no matter what the shape
of the rods may be.

2. When a very long rod is suspended vertically, its
ripper part, having to support more of the weight of the
rod than any other, is the most liable to break.

3. The strength of a horizontal beam supported at each
end diminishes as the square of its length increases.

If two beams thus placed are respectively 6 feet and 3 feet long, the
strength of the shorter will be to that of the longer as the square of 6 to the
square of 3, that is, as 36 to 9, or 4 to 1.

4. A horizontal beam supported at eacli end, is most
easily broken by pressure or a suspended weight in the
middle, and increases in strength as either end is ap-
proached. If, therefore, a beam of uniform strength is re-
quired, it should gradually taper from the middle towards
the ends.

5. A given quantity of material has more strength when
disposed in the form of a hollow cylinder than in any other
form that can be given it. Nature constantly uses hollow
cylinders in the animal creation, as in bones and the tubes
of feathers; and the artisan, imitating nature, employs it
in many cases where strength and lightness are to be com-
bined.

EXAMPLES FOE PRACTICE.

1. (See 183, 184.) "What is the horse-power of a steam-engine that can do

1, 610,000 units of work in a minute?

2. What is the horse-power of an engine that can raise 2,376 pounds 1,000

feet in a minute ?

3. What is the horse-power of an engine that can raise 1,000 pounds 2,376

feet in a minute ?

4. A fire-engine can throw 220 pounds of water to a height of 75 feet every

minute ; what is its horse-power ?

5. A cubic foot of water weighs 62 J /2 pounds. How many horse-powers are

required to raise 200 cubic feet of water every minute from a mine 132
feet deep ?

what part of it is most likely to break ? What law is given respecting the strength of
a horizontal beam supported at each end? Give an example. In what part is a hor-
izontal beam supported at each end most easily broken by pressure ? What shape.
gives a beam uniform strength ? In what form must a given quantity of material be
disposed, to have the most strength?



EXAMPLES FOB PRACTICE. 93

6. A locomotive draws a train of cars, the resistance of which (caused by

friction, &c.) is equivalent to raising 1,000 pounds, 15 miles an hour ;
what is its horse-power ?

[Find how many feet the locomotive draws the train in a minute, and then
proceed as before.}

7. How many pounds can an engine of 10 horse-powers raise in an hour from

a mine 100 feet deep ?

8. A certain man has strength equivalent to l / s of one horse-power; how

many pounds can he draw up in a minute from a pit 25 feet deep ?

9. (See 189, Fourth Law.) If the friction of a train of cars weighing 50 tons,

on a level railroad, be equivalent to a weight of 500 pounds, what will be
the friction of a train weighing 25 tons? of one weighing 100 tons? of
one weighing 60 tons ?

10. (See 1U5, 196.) C can just draw 75 pounds of coal a minute out of a
mine. With the aid of a system of pulleys, he can raise 225 pounds at a
time; the friction 'being equivalent to 75 pounds, how many minutes
will he be in raising the load ?

[In practical questions of this kind, the friction must be added to the resist-
ance.}

11. With a certain machine, one man can do as much as eight men without
the machine. Allowing the friction of the machine to be equal to one-
fourth of the resistance, how much longer will he be in doing a certain
amount of work than they ?

12. (See % 200.) [The area of a rectangular surf ace is found by multiplying
its length by its breadth ; that of a triangle, by multiplying half its base
by its perpendicular height} Which will support the greater weight
without breaking, a joist whose section is 4 inches long by 5 broad, or one
of the same kind of wood, 3 inches by 8 ?

13. Which, when suspended, will bear the greater weight without breaking,
a square rod of iron whose end is 3 inches by 3, or a rod whose cross sec-
tion is a triangle with a base of 6 inches and a perpendicular height of 2 ?

14. Two rods of copper, of equal length and uniform thickness, have ends re-
spectively 4 inches by 2, and 17 inches by half an inch. Which, when
suspended, will support the greater weight?

15. Two horizontal beams of the same material, breadth, and thickness, sup-
ported at both ends, are respectively 2 and 14 feet long. Which is the
stronger ol the two, and how many times ?



94 MECHANICS.



CHAPTER Till.

MECHANICS (CONTINUED).

THE MECHANICAL POWERS.

and varied as machines are, they are all
combinations of six Simple Mechanical Powers, known as
the Le'-ver, the Wheel and Axle, the Pulley, the Inclined
Plane, the Wedge, and the Screw. These we shall con-
sider in turn.

Tfiie ~Lcvey.

201. A Lever is an inflexible bar, capable of being moved
about a fixed point, called the Fulcrum.

The lever is the simplest of the mechanical powers. Its properties were
known as far back as the time of Aristotle, 350 years u. c. Archimedes, a
hundred years later, was the first to explain them fully.

202. KINDS OF LEVER. In the lever three things are to
be considered ; the fulcrum, or point of support, the weight,
and the power. Two of these are at the ends of the bar,
while the other is at some point between them. According
to their relative position, we have three kinds of levers :

Fig. 85. ^ A Lever of the First Kind is

one in which the fulcrum is be-
tween the power and the weight ;
as in Fig. 85, where F represents
the fulcrum, P the power, and W
the weight.

A Lever of the Second Kind is one in which the weight
is between the power and the fulcrum ; as in Fig. 83.

Of what are all machines combinations? Name the six Simple Mechanical Pow-
ers. 201. What is a Lever? How does the lever compare with the other mcchan.
ical powers? How long ago was it known ? 202. In the lever, how many things are
to be considered? According to their relative position, how many kinds of levers
are there ? What is a Lever of the First Kind ? What is a Lever of the Second Kind ?




THE LEVER.



95



Fig. 86.



Fig. 87.




A Lever of the Third Kind is one in which the power is
lutween the weight and the fulcrum ; as in Fig. 87.

203. LEVERS OF THE FIRST KIND. In levers of the first
kind, the relative position of the three important points is

POWER FULCRUM WEIGHT OU WEIGHT FULCRUM POWER.



Fig. 83.




THE CROW-BAR.



Fig. 83 shows one of the common-
est forms in which this kind of lever ap-
pears, the crow-bar. The power is
applied at the handle. The weight is at
the other end, and consists of something
to be moved. The fulcrum is a stone on
which the crow-bar rests. Using an in-
strument in this way is called prying.

204. The nearer the fulcrum is to the weight the greater
the advantage gained, and consequently the greater the
space that P will have to pass through in moving W a given
distance. This principle is stated in the following

Law. With levers of the first kind, intensity of force
is gained, and time is lost, in proportion as the distance
between the power and the fulcrum exceeds the distance be-
tween the weight and the fulcrum.

Thus, in Fig. 88, if the distance from P to F be five times as great as that
from \V to F, a pressure of 10 pounds at P will just counterbalance a weight
of 50 pounds at W, and will therefore move anything under 50 pounds ;
while, for every inch that W is moved upward, P will have to move five
inches downward.

The distance through which the power must pass, to move a weight vast-
ly greater than itself, becomes an important matter in practical applications
of the lever. When Archimedes saw the immense power that could be ex-



Whnt is a Lover of the Third Kind? 203. In levers of the first kind, what is the rel-
ative position of the three important points? Give a familiar eximple of a lever of
the first kind, and show its operation. 204. What is the law of levers of the first
kind ? Illustrate this with Fig. S3. What is sometimes aa important matter iu prac-



96



MECHANICS.



erted with this instrument, he declared that with a place to stand on he could
move the earth itself. He did not say how far he would have to travel to do
this, in consequence of the great disproportion between his strength and the
earth's bulk. Allowing that he had a place to stand on and a lever strong
enough, and could pull its long arm with a force of 30 pounds through two
miles every hour, it would have taken him, working ten hours a day, over
one hundred thousand millions of years to move the earth a single inch !

205. The Balance. When bodies of equal weight are

supported by the arms of a lever, they will balance each

Pig. so. other when placed at equal distances

^ A . from the fulcrum, as in Fig. 89. They

^ are then said to be in equilibrium.



Fig. 90.



On this principle the com-
mon Balance, represented in
Fig. 90, is constructed. A
beam is poised on the top of
a pillar, so as to be exactly
horizontal. From each end
of the beam, at equal dis-
tances from the fulcrum, a
pan is suspended by means
of cords. The object to be
weighed is placed in one of
these pans, and the weights
in the other.

When great accuracy is
required, the beam is bal-
anced on a steel knife-edge ;
the friction being thus les-
sened, it turns more easily. A balance capable of weighing ten pounds has
been made so sensitive as to turn with the thousandth part of a grain.

206. The balance weighs correctly only when the arms of the beam are
exactly equal. Hence dishonest tradesmen sometimes defraud those with
whom they deal by throwing the fulcrum a little nearer one end of the beam
than the other. When buying, they place the commodity to be weighed in
the scale attached to the short arm; and, when selling, in the other, "thus
making double gains. To prove a balance, weigh an article first in one scale
and then iu the other ; if there is any difference in the weight, the balance is
not true.




THE BALANCE.



tinal applications of the lever? Show this in the supposed case of Archimedes.
205. When arc two bodies of equal weight, supported by the arms of a lever, said to
be in equilibrium? What is constructed on this principle? Describe the Balance.
When great accuracy is required, how is the beam balanced? How sensitive has a
balance been made ? 206. When does the balance weigh correctly ? How do dishon-



THE STEELYARD. 9*7

The true weight of a body may be determined, with a false balance,
by placing it in either scale, balancing it with shot or sand, and then remov-
ing the body and replacing it with weights till equilibrium is established.
This is called double weighing. It must give the true weight; for whatever
error is made in the first weighing is corrected in the second.

207. T/ie Steelyard. When bodies of unequal weight
are supported by the arms of a lever, they will balance each
other whenever the weight of the one multiplied into its
distance from the fulcrum, is equal to the weight of the
other multiplied into its distance from the fulcrum.

In Fig. 91, let the distance WF be Fig. 91.

one inch and PF three inches. The W f p



weight of the one body, 30 pounds, mul-

tiplied into its distance from the fulcrum,

1, gives 30 ; the weight of the other, 10

pounds, multiplied into its distance from the fulcrum, 3, gives 30. These

products being equal, the bodies will balance each other.

208. On this principle the Steelyard is constructed.
The Steelyard is a kind of balance, which, though not so
sensitive as the one described above, answers very well for
heavy bodies, and is conveniently carried, as it requires but
a single weight, and may be held in the hand or suspended
anywhere.

Fig. 92 represents the steelyard. ^ Fig. 92.

It is a lever of unequal arms ; from -<rf1% r iH' 1 CT? ? '?

the shorter of which the article to
be weighed is suspended, either di-
rectly or in a scale-pan, while a con-
stant weight is moved on the longer
arm from notch to notch till equilib-
rium is established. The number THE STEELYAED.
at the notch on which the weight

then rests, shows the required weight in pounds. Thus, 15 pounds is the
weight of the sugar-loaf in the Figure. The proper distances for the notches
are found in the first place by experiments with known weights in the scale-
pan.

To enable the steelyard to weigh still heavier objects without increasing

est tradesmen sometimes defraud those with whom they deal ? How may a balance
be proved ? How may the true weight of a body be determined with a false balance ?
What is this process called? 207. When will bodies of unequal weight supported by
the arms of a lever be in equilibrium? Illustrate this with Fig. 91. 208. What is
constructed on this principle? Describe the Steelyard, and the mode of weighing
with it. How are the proper distances for the notches found in the first plce ? With
5




98 MECHANICS.

the length of its beam, it is often provided with an additional hook, hanging
in an opposite direction from the other hook and nearer the point from which
the article to be weighed is suspended. When the instrument is supported
by this hook, a new fulcrum is formed, and the weight is shown by a new
row of notches adapted to it. The greater the difference of length between
the arms of a steelyard, the greater the number of pounds that it can weigh.

209. When more than two bodies are supported on the
arms of a lever, if the weight of each be multiplied by its
distance from the fulcrum, the lever will be in equilibrium
(that is, the bodies will balance each other) when the sums
of the products on the two sides of the fulcrum are equal.

..^ Thus, in Fig. 93 equilibrium

is maintained, because the prod-
ucts of the weights on one side



iinto their distances, added to-
gether, equal the sum of the
products on the other :

weights distances weights distances

2X1=2 2X1 = 2

3X2=6 6X3= 18
4 X 3 = 12

Sum of products, 20 Sum of products, 20

210. Practical Applications. Familiar examples of
levers of the first kind are found in the scissors and pincers ;
the rivet connecting the two parts being the fulcrum, the
fingers the power, and the thing to be cut or grasped the
weight. A poker introduced between the bars of a grate
and allowed to rest on one of them, that purchase may be
obtained for stirring the fire, is a lever of the first kind. So
is the handle of a common pump.

yig. 94. When children teeter on a board



IE



$> balanced on a wooden horse, they use



a lever of the first kind. According
to the principles of the lever, if one is
heavier than the other, to preserve the
balance, he must sit nearer the fulcrum, as shown in Fig. 04.



what are some steelyards provided, and for what purpose ? What Steelyards weigh
the greatest number of pounds ? 209. If more than two bodies are supported on tho
arms of a lever, when will they balance each other? Apply this principle in Fig. 93.
210. Give some familiar examples of levers of the first kind. When children teeter
on a board, what kind of lever do they use ? If one is heavier than the other, wliex*



BENT AND COMPOUND LEVERS.



99



Fig. 95.



211. Sent Levers. Sometimes the arms of a lever are
bent, instead of straight. In that case the same principles
hold good, only that the arms of the lever are estimated,
not by their actual length, but by the perpendicular dis-
tance from the fulcrum to the line of direction in which the
power and weight respectively act.

As an illustration of bent levers of the first kind,
we may take the truck used for moving heavy arti-
cles, represented in Fig. 95. The axis on which the
wheels turn represents the fulcrum ; the weight is ap-
plied at W, and the power at P. The clawed side of
a hummer, used in drawing out nails, is also a bent
lever. The fixed point on which the head of the ham-
mer rests is the fulcrum ; the friction of the nail is
the weight ; and the power is applied at the extrem-
ity of the handle.

212. Compound Levers. Simple le-



Online LibraryG. P. (George Payn) QuackenbosA natural philosphy: embracing the most recent discoveries in the various branches of physics .. → online text (page 9 of 42)