155. Every one is familiar with the ordinary form of the pulley; it
consists of a wheel capable of turning freely on its axle, and it has
a groove in its circumference in which the rope lies. But why is it
necessary to give the pulley this form? Why could not the direction of
the rope be changed by simply passing it over a bar, as well as by the
more complicated pulley? We shall best answer this question by actually
trying the experiment, which we can do by means of the apparatus of
Fig. 34 (see page 90). In this are shown two iron studs, G, H, 0"·6
diameter, and about 8" apart; over these passes a rope, which has a
hook at each end. If I suspend a weight of 14 lbs. from one hook A, and
pull the hook B, I can by exerting sufficient force raise the weight on
A, but with this arrangement I am conscious of having to exert a very
much larger force than would have been necessary to raise 14 lbs. by
merely lifting it.
156. In order to study the question exactly, we shall ascertain what
weight suspended from the hook B will suffice to raise A. I find that
in order to raise 14 lbs. on A no less than 47 lbs. is necessary on B,
consequently there is an enormous loss of force: more than two-thirds
of the force which is exerted is expended uselessly. If instead of the
14 lbs. weight I substitute any other weight, I find the same result,
viz. that more than three times its amount is necessary to raise it by
means of the rope passing over the studs. If a labourer, in raising a
sack, were to pass a rope over two bars such as these, then for every
stone the sack weighed he would have to exert a force of more than
three stones, and there would be a very extravagant loss of power.
157. Whence arises this loss? The rope in moving slides over the
surface of the iron studs. Although these are quite smooth and
polished, yet when there is a strain on the rope it presses closely
upon them, and there is a certain amount of force necessary to make the
rope slide along the iron. In other words, when I am trying to raise up
14 lbs. with this contrivance, I not only have its weight opposed to
me, but also another force due to the sliding of the rope on the iron:
this force is due to friction. Were it not for friction, a force of 14
lbs. on one hook would exactly balance 14 lbs. on the other, and the
slightest addition to either weight would make it descend and raise the
other. If, then, we are obliged to change the direction of a force, we
must devise some means of doing so which does not require so great a
sacrifice as the arrangement we have just used.