538 



MACHINES, WORK, AND ENERGY 



the arms. A common example of a beam balance with unequal 

 arms is the old-fashioned steelyards (Fig. 336). If, in such a 

 balance, the object whose weight is to be determined is 2 in. 

 from the point of support while the known mass is 20 in. from 

 the support, then the weight of the unknown object is exactly 

 10 times that of the known mass. 



The weight of the known mass : the weight of the unknown 

 mass:: 2: 20. 



The weights are inversely proportional to the lengths of the 

 arms. 



FIG. 336. Common steelyards. 



FIG. 337. Wagon scales. 



Generally, scales used in weighing heavy objects are con- 

 structed by using several such beams in combination. The 

 common wagon scales are a familiar example of such a combina- 

 tion of unequal armed beam balances (Fig. 337). In such 

 cases, it is common for the beams to be so combined that a 

 1-lb. mass will balance, perhaps, 1000 Ib. or more. 



632. Spring Balances. The principle of the SPRING BAL- 

 ANCE is very different. A coiled steel spring is mounted 

 within a metal case (Fig. 338). The upper end of this coiled 

 spring is secured to the upper end of the case; the lower end 

 of the spring is free but carries a small rod or wire which, in 

 turn, carries the hook upon which the mass whose weight is to 

 be determined is hung. A small pointer, or index, fastened to 



