WHEEL AND AXLE 



169 



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 win- 

 dow 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. 



When the large wheel makes 

 one revolution, P falls a dis- 

 tance equal to the circumfer- 

 ence 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 Wean be sustained by a force of 25 at P. The in- 

 crease 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. 



FIG. 112. The wheel and axle. 



