199. The next arrangement we shall employ is a pair of pulley-blocks
S T, Fig. 35, each containing three sheaves, as the small pulleys are
termed. A rope is fastened to the upper block, S; it then passes down
to the lower block T under one sheave, up again to the upper block and
over a sheave, and so on, as shown in the figure. To the end of the
rope from the last of the upper sheaves the power H is applied, and the
load G is suspended from the hook attached to the lower block. When the
rope is pulled, it gradually raises the lower block; and to raise the
load one foot, each of the six parts of the rope from the upper block
to the lower block must be shortened one foot, and therefore the power
must have pulled out six feet of rope. Hence, for every foot that the
load is raised the power must have acted through six feet; that is to
say, the _velocity ratio_ is 6.
200. If there were no friction, the power would only be one-sixth of
the load. This follows at once from the principles already explained.
Suppose the load be 60 lbs., then to raise it one foot would require
60 foot-pounds; and the power must therefore exert 60 foot-pounds; but
the power moves over six feet, therefore a power of 10 lbs. would be
sufficient. Owing, however, to friction, some energy is lost, and we
must have recourse to experiment in order to test the real efficiency
of the machine. The single moveable pulley nearly doubled our power; we
shall prove that the three-sheave pulley-block will quadruple it. In
this case we deal with larger weights, with reference to which we may
leave the weight of the lower block out of consideration.
201. Let us first attach 1 cwt. to the load hook; we find that 29 lbs.
on the power hook is the smallest weight that can produce motion: this
is only 1 lb. more than one-quarter of the load raised. If 2 cwt. be
the load, we find that 56 lbs. will just raise it: this time the power
is exactly one-quarter of the load. The experiment has been tried of
placing 4 cwt. on the hook; it is then found that 109 lbs. will raise
it, which is only 3 lbs. short of 1 cwt. These experiments demonstrate
that for a three-sheave pulley-block of this construction we may safely
apply the rule, that _the power is one-quarter of the load_.
202. We are thus enabled to see how much of our exertion in raising
weights must be expended in merely overcoming friction, and how much
may be utilized. Suppose for example that we have to raise a weight of
100 lbs. one foot by means of the pulley-block; the power we must apply
is 25 lbs., and six feet of rope must be drawn out from between the
pulleys: therefore the power exerts 150 foot-pounds of energy. Of these
only 100 foot-pounds are usefully employed, and thus 50 foot-pounds,
one-third of the whole, have been expended on friction. Here we see
that notwithstanding a small force overcomes a large one, there is an
actual loss of energy in the machine. The real advantage of course is
that by the pulley-block I can raise a greater weight than I could move
without assistance, but I do not create energy; I merely modify it, and
lose by the process.
203. The result of another series of experiments made with this pair of
pulley-blocks is given in Table X.