15. If an effort of 50 lbs. acting on a machine moves 10 ft., how far can it lift a weight of 1000 lbs.? 16. A bar 10 ft. long is to be used as a lever. The weight is kept 2 ft. from the fulcrum. What different levers can it represent? 17. The effort arm of a lever is 6 ft., the weight arm 6 in. How long will the lever be? Give all possible answers. 18. Two boys carry a weight of 100 lbs. on a pole 5 ft. long between them. Where should the weight be placed in order that one boy may carry one and one-fourth times as much as the other? (4) THE WHEEL AND AXLE AND THE PULLEY =124. The Wheel and Axle.=--1. One of the simple machines most commonly applied in compound machines is the _wheel_ and _axle_. It consists of a wheel _H_ mounted on a cylinder _Y_ so fastened together that both turn on the same axis. In Fig. 90, ropes are shown attached to the circumferences of the wheel and axle. Sometimes a hand wheel is used as on the brake of a freight or street car, or simply a crank and handle is used, as in Fig. 91. The _capstan_ is used in moving buildings. Sometimes two or three wheels and axles are geared together as on a derrick or crane as in Fig. 92. [Illustration: FIG. 90.--The wheel and axle.] [Illustration: FIG. 91.--Windlass used in drawing water from a well.] [Illustration: FIG. 92.--A portable crane.] [Illustration: FIG. 93.--The wheel and axle considered as a lever.] [Illustration: FIG. 94.--View of transmission gears in an automobile. 1, Drive gear; 2, High and intermediate gear; 3, Low and reverse gear; 4, 8, Reverse idler gears; 5, 6, 7, Countershaft gears. (_Courtesy of the Automobile Journal_.)] [Illustration: FIG. 95.--Reducing gear of a steam turbine.] Fig. 93 is a diagram showing that the wheel and axle acts like a lever. The axis _D_ is the fulcrum, the effort is applied at _F_, at the extremity of a radius of the wheel and the resisting weight _W_ at the extremity of a radius of the axle. Hence, if _D_{f}_, the effort distance, is three times _D_{w}_, the weight distance, the weight that can be supported is three times the effort. Here as in the lever, _f × D_{f} = w × D_{w}_, or _w:f = D_{f}:D_{w}_, or _the ratio of the weight to the effort equals the ratio of the radius of the wheel to the radius of the axle_. This is therefore the mechanical advantage of the wheel and axle. Since the diameters or circumferences are in the same ratio as the radii these can be used instead of the radii. Sometimes, when _increased speed_ instead of increased force is desired, the radius of the wheel or part to which power is applied is less than that of the axle. This is seen in the bicycle, buzzsaw, and blower. Sometimes geared wheels using the principle of the wheel and axle are used to reduce speed, as in the _transmission_ of an automobile (see Fig. 94), or the reducing gear of a steam turbine. (See Figs. 95 and 293.) A _bevel gear_ is frequently used to change the direction of the force. (See Fig. 94.)