315. In the wheel and axle upon which we have been experimenting,
we have found that about 30 per cent. of the power is consumed by
friction. We shall be able to ascertain to what this loss is due,
and then in some degree to remove its cause. From the experiments of
Art. 165 we learned that the friction of a small pulley was very much
greater than that of a large pulley—in fact, the friction is inversely
proportional to the diameter of the pulley. We infer from this that by
winding the rope upon a barrel instead of upon the axle, the friction
may be diminished.
[Illustration: FIG. 47.]
316. We can examine experimentally the effect of friction on the axle
by the apparatus of Fig. 47. B is a shaft 0"·75 diameter, about which a
rope is coiled several times; the ends of this rope hang down freely,
and to each of them hooks E, F are attached. This shaft revolves in
brass bearings, which are oiled. In order to investigate the amount
of power lost by winding the rope upon an axle of this size, I shall
place a certain weight—suppose 56 lbs.—upon one hook F, and then I
shall ascertain what amount of power hung upon the other hook E will be
sufficient to raise F. There is here no mechanical advantage, so that
the excess of load which E must receive in order to raise F is the true
measure of the friction.
317. I add on weights at E until the power reaches 85 lbs., when E
descends. We thus see that to raise 56 lbs. an excess of 29 lbs. was
necessary to overcome the friction. We may roughly enunciate the result
by stating that to raise a load in this way, half as much again is
required for the power. This law is verified by suspending 28 lbs. at
F, when it is found that a power of 43 lbs. at E is required to lift
it. Had the power been 42 lbs., it would have been exactly half as much
again as the load.
318. Hence in raising F upon this axle, about one-third of the power
which must be applied at the circumference of the axle is wasted. This
experiment teaches us where the loss lies in the wheel and axle of
Art. 304, and explains how it is that about a third of its efficiency
is lost. 85 lbs. was only able to raise two-thirds of its own weight,
owing to the friction; and hence we should expect to find, as we
actually have found, that the power applied at the circumference of
the wheel has an effect which is only two-thirds of its theoretical
efficiency.
319. From this experiment we should infer that the proper mode of
avoiding the loss by friction is to wind the rope upon a barrel of
considerable diameter rather than upon the axle itself. I place upon
a similar axle to that on which we have been already experimenting a
barrel of about 15" circumference. I coil the rope two or three times
about the barrel, and let the ends hang down as before. I then attach
to each end 56 lbs. weight, and I find that 10 lbs. added to either of
the weights is sufficient to overcome friction, to make it descend,
and raise the other weight. The apparatus is shown in Fig. 47. A is
the barrel, C and D are the weights. In this arrangement 10 lbs. is
sufficient to overcome the friction which required 29 lbs. when the
rope was simply coiled around the axle. In other words, by the barrel
the loss by friction is reduced to one-third of its amount.