WOEK OF STEETCHING A STEING 149 



When the length of the string is x 9 its tension T, by the 

 formula of 39, is given by 



In stretching the string through a further distance dx, i.e. from 

 length x to length x + dx, the work done 



= Tdx 



= (x / ) dx. 



v 



By integration, we find that the work done in stretching a string 

 from length a to length b 



= C^(x~l)dx 



The distance stretched is I a, while (b 4- a 2 /) is the 



-^ / 



tension when half of the stretching has been completed, i.e. when 

 x = \(a 4- I). 



Thus we have found that 



The work done in stretching an elastic string from any length a, 

 greater than the natural length of the string, to a length b, is equal 

 to the tension at length ^(a + b) multiplied by (b a). 



Obviously, if the tension is measured in pounds weight and the 

 extension (b a) in feet, the product will give the amount of work 

 measured in foot pounds. If the tension is measured in poundals, 

 and (b a) in feet, the product will give the amount of work in 

 foot poundals. 



