30 NICHOLLS'S SEAMANSHIP AND NAUTICAL KNOWLEDGE
that W moves slowly upwards, the balance will still register 1 lb.,
neglecting the effect of friction, and the hand will move upwards 2 feet
to raise the weight W 1 foot, because the work or power put into the
machine at P is equal to the work accomplished by the machine against
the resistance of the weight W. This may be expressed in foot-pound
units, Px2ft. = Fxl ft or lib X2ft =21bs. X lft.=2ft.-pds.of work,
The number of pulleys may be increased. Fig. 84 shows two movable
pulleys with a 4-lb. weight at W suspended from the lower pulley.
The cord AB supports the 4-lb. weight, 2 Ibs. at A and 2 Ibs. at B
attached to the upper pulley. A second cord passed round the upper
pulley supports the 2-lb. weight at B, viz., I lb. at C and 1 lb. at the
hand P holding the spring balance which will register 1 lb., neglecting
the weight of the pulleys, thus a power of 1 lb. supports a weight of
4 Ibs.; the mechanical advantage of the machine is 4 because by its
performance a force of 1 lb equalises a load of 4 Ibs.
If the load of 4 Ibs. be now overcome by exerting more power at P
so that W moves slowly upwards, the hand at P will move 4 feet to
raise the load W 1 foot, thus
Px4ft.=PFxl ft. or, 1 lb. X4 ft. =4 Ibs. X1 ft.=4 foot-pounds of work,
again demonstrating that the work put into the machine at P is equal
to the work done by the machine against the resistance at W.
The arrangement as shown in Fig. 84 is not suitable in practice so
the sheaves are fitted into blocks as in Fig. 85. The principle is the
same, however, and the number of parts of cord at the moving block
gives the theoretical advantage or power gained by using the purchase;
that is to say, the ratio between the power and the weight which, in
this example, is one-quarter without friction.
There are four parts of rope holding the weight and it is evident that
the pull on each part will be one-fourth part of the total weight. The
load on the hook at C is equal to the weight+tackle+power exerted
on the hauling part of the rope. The weight of the load and tackle is
constant, but the power will depend upon whether W is at rest or
being raised or lowered. When at rest P=l lb , but when in motion
the value of P will be increased and diminished according to the
-speed of raising and lowering. Needless to say, power is gained at the
expense of speed. The more sheaves in the purchase the more rope
must be hauled thrdugh the frlocka to raise the weight a given distance,
and speed is thus sacrificed to gain power. It h usual in shipwork to
allow one-tenth of the weight for every sheave as an additional load
due to friction.