162.  Combination of Pulleys.  A combination of pulleys called block and tackle is used where very heavy loads are to be moved.  In Figure 111 the upper block of pulleys is fixed, the lower block is movable, and one continuous rope passes around the various pulleys.  The load is supported by 6 strands, and each strand bears one sixth of the load.  If the hand pulls with a force of 1 pound at P, it can raise a load of 6 pounds at W, but the hand will have to pull downward 6 feet at P in order to raise the load at W 1 foot.  If 8 pulleys were used, a force equivalent to one eighth of the load would suffice to move W, but this force would have to be exerted over a distance 8 times as great as that through which W was raised.

[Illustration:  FIG. 111.—­An effective arrangement of pulleys known as block and tackle.]

163.  Practical Application.  In our childhood many of us saw with wonder the appearance and disappearance of flags flying at the tops of high masts, but observation soon taught us that the flags were raised by pulleys.  In tenements, where there is no yard for the family washing, clothes often appear flapping in mid-air.  This seems most marvelous until we learn that the lines are pulled back and forth by pulleys at the window and at a distant support.  By means of pulleys, awnings are raised and lowered, and the use of pulleys by furniture movers, etc., is familiar to every wide-awake observer on the streets.

164.  Wheel and Axle.  The wheel and axle consists of a large wheel and a small axle so fastened that they rotate together.

[Illustration:  FIG. 112.—­The wheel and axle.]

When the large wheel makes one revolution, P falls a distance equal to the circumference of the wheel.  While P moves downward, W likewise moves, but its motion is upward, and the distance it moves is small, being equal only to the circumference of the small axle.  But a small force at P will sustain a larger force at W; if the circumference of the large wheel is 40 inches, and that of the small wheel 10 inches, a load of 100 at W can be sustained by a force of 25 at P.  The increase in force of the wheel and axle depends upon the relative size of the two parts, that is, upon the circumference of wheel as compared with circumference of axle, and since the ratio between circumference and radius is constant, the ratio of the wheel and axle combination is the ratio of the long radius to the short radius.

For example, in a wheel and axle of radii 20 and 4, respectively, a given weight at P would balance 5 times as great a load at W.

165.  Application. Windlass, Cogwheels. In the old-fashioned windlass used in farming districts, the large wheel is replaced by a handle which, when turned, describes a circle.  Such an arrangement is equivalent to wheel and axle (Fig. 112); the capstan used on shipboard for raising the anchor has the same principle.  The kitchen coffee grinder and the meat chopper are other familiar illustrations.