78 



ELEMENTARY GENERAL SCIENCE 



CHAP. 



FIG. 29. Equilibrium of Three Parallel Forces. 



EXPT. 64. Suspend a light rod horizontally from two spring 

 balances (Fig. 29), and hang a weight from any point between 

 the balances. 



Observe (a) the readings of the balances. 



(b) The length of the rod between the balances. 



(c) The length of rod between the weight and the balance 

 on each side. 



Vary the distance of the weight, and again make observa- 

 tions. Also repeat 

 the experiment with 

 a different weight. 



Neglecting the 

 weight of the rod, this 

 experiment is a de- 

 monstration of the con- 

 ditions for the equi- 

 librium of three paral- 

 lel forces. The weight 

 will be found to be 

 equal to the sum of the 



readings of the spring balances. In other words, the resultant 

 force will be found equal to the sum of the components. More- 

 over, the readings of the spring balances will be found to be in 

 inverse ratio to the distances of the balances from the weight ; 

 while the weight itself will be proportional to the length of the 

 rod between the balances. The relation is shown graphically 

 by Fig. 30, in which the three forces are represented 



8 



w 



FIG. 30. Equilibrium of Parallel Forces. 



by the lines, CW, AD, BE. The forces bear exactly the same 

 proportion to one another as the distances AB, BC, CA. We 

 have, therefore, as the conditions of equilibrium of three parallel 

 forces the following expression : 





