of the Electrical Current, 387 



vne 



— the vis viva of the striking body, \ the body at rest, 



- the velocity communicated to it. 



m l+x 



n 



Set. Two bodies a and a x , whose vires vivse are equal, impart to a 

 body at rest, b, the same velocity by an impact. How great is b ? 



We must have 



av a,v. 



or 

 while 



Hence 



ava. 



a-\-b a^b 

 ava x + avb = a Y v } a + a x v Y b, 



av 2 = a x v^ or v 1 = v\/ ( L. 

 V a x 



+ avb = a Y va \/—-{- a x vb \/ —, 

 V a Y V a Y 



^{a — a^ =aa 1 (a — a l ), 

 b= V ' aa v 



3/3. Two batteries of equal vires vivse, HP 2 and H^! 2 , yield 

 the same current after interposing the resistance X. How great is X? 



From the preceding, as well as by an independent solution, 

 we obtain X = ^RRi The two batteries may be obtained by 

 combining in various ways x equal elements, each of which has 

 the internal resistance /. In one case x — mn, in the other 

 ajssmjWj; hence 



V 71 W 



4a. Two bodies a and a x may strike with the velocities v and Vj 

 against a body b moving in the same direction with the velocity c, 

 and both would produce by the impact the same velocity in b. What 

 are the losses A and A x of vis viva experienced by a and b on the 

 one hand, and a x and b on the other. 

 We have 



av-\-bc __ afti + bc 

 a-\-b a x -\-b 



or 



aa x v + abv + a x bc + b 2 c = a x av { + a 1 bv 1 -f abc + b q c, 

 or 



aa x v + abv — abc = a 1 av l + a l bv l — a fie. 



