228. There are many cases in which a machine for overcoming great
resistance is necessary where pulleys would be quite inapplicable.
To meet these various demands a correspondingly various number of
contrivances has been devised. Amongst these the lever in several
different forms holds an important place.
229. The lever of the first order will be understood by reference to
Fig. 38. It consists of a straight rod, to one end of which the power
is applied by means of the weight C. At another point B the load is
raised, while at A the rod is supported by what is called the fulcrum.
In the case represented in the figure the rod is of iron, 1" × 1" in
section and 6' long; it weighs 19 lbs. The power is produced by a 56
lb. weight: the fulcrum consists of a moderately sharp steel edge
firmly secured to the framework. The load in this case is replaced
by a spring balance H, and the hook of the balance is attached to the
frame. The spring is strained by the action of the lever, and the index
records the magnitude of the force produced at the short end. This is
the lever with which we shall commence our experiments.
[Illustration: FIG. 38.]
230. In examining the relation between the power and the load, the
question is a little complicated by the weight of the lever itself (19
lbs.), but we shall be able to evade the difficulty by means similar
to those employed on a former occasion (Art. 60); we can counterpoise
the weight of the iron bar. This is easily done by applying a hook to
the middle of the bar at D, thence carrying a rope over a pulley F, and
suspending a weight G of 19 lbs. from its free extremity. Thus the bar
is balanced, and we may leave its weight out of consideration.
231. We might also adopt another plan analogous to that of Art. 51,
which is however not so convenient. The weight of the bar produces a
certain strain upon the spring balance. I may first read off the strain
produced by the bar alone, and then apply the weight C and read again.
The observed strain is due both to the weight C and to the weight of
the bar. If I subtract the known effect of the bar, the remainder is
the effect of C. It is, however, less complicated to counterpoise the
bar, and then the strains indicated by the balance are entirely due to
the power.
232. The lever is 6' long; the point B is 6" from the end, and B C is
5' long. B C is divided into 5 equal portions of 1'; A is at one of
these divisions, 1' distant from B, and C is 5' distant from B in the
figure; but C is capable of being placed at any position, by simply
sliding its ring along the bar.
233. The mode of experimenting is as follows:—The weight is placed on
the bar at the position C: a strain is immediately produced upon H;
the spring stretches a little, and the bar becomes inclined. It may be
noticed that the hook of the spring balance passes through the eye of a
wire-strainer, so that by a few turns of the nut upon the strainer the
lever can be restored to the horizontal position.
234. The power of 56 lbs. being 4' from the fulcrum, while the load
is 1' from the fulcrum, it is found that the strain indicated by the
balance is 224 lbs.; that is, four times the amount of the power. If
the weight be moved, so as to be 3' from the fulcrum, the strain is
observed to be 168 lbs.; and whatever be the distance of the power
from the fulcrum, we find that the strain produced is obtained by
multiplying the magnitude of the power in pounds by the distance
expressed in feet, and fractional parts of a foot. This law may be
expressed more generally by stating that _the power is to the load as
the distance of the load from the fulcrum is to the distance of the
power from the fulcrum_.
235. We can verify this law under varied circumstances. I move the
steel edge which forms the fulcrum of the lever until the edge is 2'
from B, and secure it in that position. I place the weight C at a
distance of 3' from the fulcrum. I now find that the strain on the
balance is 84 lbs.; but 84 is to 56 as 3 is to 2, and therefore the law
is also verified in this instance.
236. There is another aspect in which we may express the relation
between the power and the load. The law in this form is thus stated:
_The power multiplied by its distance from the fulcrum is equal to the
load multiplied by its distance from the fulcrum_. Thus, in the case we
have just considered, the product of 56 and 3 is 168, and this is equal
to the product of 84 and 2. The distances from the fulcrum are commonly
called the arms of the lever, and the rule is expressed by stating that
_The power multiplied into its arm is equal to the load multiplied into
its arm_: hence the load may be found by dividing the product of the
power and the power arm by the load arm. This simple law gives a very
convenient method of calculating the load, when we know the power and
the distances of the power and the load from the fulcrum.
237. When the power arm is longer than the load arm, the load is
greater than the power; but when the power arm is shorter than the load
arm, the power is greater than the load.
We may regard the strain on the balance as a power which supports the
weight, just as we regard the weight to be a power producing the strain
on the balance. We see, then, that for the lever of the first order to
be efficient as a mechanical power it is necessary that the power arm
be longer than the load arm.
238. The lever is an extremely simple mechanical power; it has only
one moving part. Friction produces but little effect upon it, so that
the laws which we have given may be actually applied in practice,
without making any allowance for friction. In this we notice a marked
difference between the lever and the pulley-blocks already described.
239. In the lever of the first order we find an excellent machine
for augmenting power. A power of 14 lbs. can by its means overcome
a resistance of a hundredweight, if the power be eight times as far
from the fulcrum as the load is from the fulcrum. This principle it is
which gives utility to the crowbar. The end of the bar is placed under
a heavy stone, which it is required to raise; a support near that end
serves as a fulcrum, and then a comparatively small force exerted at
the power end will suffice to elevate the stone.
240. The applications of the lever are innumerable. It is used not only
for increasing power, but for modifying and transforming it in various
ways. The lever is also used in weighing machines, the principles of
which will be readily understood, for they are consequences of the
law we have explained. Into these various appliances it is not our
intention to enter at present; the great majority of them may, when met
with, be easily understood by the principle we have laid down.