PULLEYS, INCLINED PLANES, AND WEDGES 39 



The principle of the wheel and axle is very important, 

 since a great many machines, such as derricks, cranes, eleva- 

 tors, steam shovels, etc., are con- 

 structed on this plan. 



Figure 23 shows the simplest form 

 of wheel and axle, in which A is the 

 wheel and B the axle or drum. If 

 a weight P is hung from a cord 

 wound on A it will wind up a certain 

 weight W on drum B. 



Fit;. 23. Wheel and Axle. 



40. Comparison with the Pulley. In theory the wheel 

 and axle is nothing more than a single movable pulley, which 

 instead of being a lever of the second class, and always lift- 

 ing the weight exactly at its center, is a lever of the first 

 class and lifts the weight some distance off the center. A 

 single movable pulley moves the weight in the same direc- 

 tion in which the rope is pulled, but the wheel and axle 

 moves the weight in the opposite direction from which the 

 rope is pulled. The lengths of rope wound or unwound 

 from the wheel and axle are always inversely proportional 

 to the weights raised or lowered. 



Problems on Wheel and Axle 



Note carefully in all problems on the wheel and axle that more 

 force is required the faster the weight is lifted. Moreover, if the 

 axle is made smaller, the weight will be lifted more slowly and less 

 force will be required. 



These same principles are true in the case of pulleys and tackles. 

 In fact, it will be found that in all machinery it takes more force 

 to do work quickly than to do it slowly. 



1. Figure 24 shows a common winch or hoist which is a good 

 illustration of the wheel and axle; the crank is the wheel and the 



