Chap. XL.] 



PARALLEL FORCES. 



493 



acting on a 

 Their 



8 



a 



v 

 c 



V 

 c 



Fig. 202. Resultant of Parallel Forces. 



influence of a force Aa at one end, and of a second 

 Bb at the other end, both being equal to one another. 

 Their resultant is cc, applied midway between A and B, 

 and equal in magnitude to both forces added together. 

 In the left-hand 

 diagram we have 

 represented two 

 unequal forces 

 and : 



rigid bar. 

 resultant is cc, 

 equal to their sum, 

 acting from the 

 point c, c being so 

 placed that the 

 distance CB is in- 

 versely propor- 

 tional to Bb, re- 

 presenting the mag- 

 nitude of the force acting at B, and the distance CA is 

 inversely proportional to Aa. Suppose AB to be 12 

 inches, the force Aa to equal 6 pounds, and Bb to 

 equal 12 pounds, then the distances CB CA being in- 

 versely proportional to 12 and 6, CB will equal 4, 

 and CA will equal 8. The distance CB is called the arm 

 of the force Bb, and CA is the arm of the force Aa. 

 Suppose c to be a fixed point, it is evident that the 

 force Bb acting on the bar will tend to pull that end 

 of the bar down. It will tend, that is to say, to turn 

 the bar on the point c. Similarly, the force Aa will 

 tend to turn the bar on the point c. The measure of 

 the power with which the force tends to turn the bar 

 on the point c is called the MOMENT OF THE FORCE, 

 and is obtained by multiplying the force into the 

 distance of the arm, that is, multiply Aa by the 

 distance CA. Let Aa 6, and Bb = 12. The 

 moment of Aa will = 6 x 8 = 48, and that of Bb 



