Friction. 147 



: g ,_/><? cos/ 



~zr~' 



= 200 X } X 0,24 = 9 lb , 6, 



which is an expression for the excess of tension of the cord 2 

 over the cord 1, on account of friction. 



Now the cord 2 and the cord 3 passing over the fixed block, 

 we shall have the excess of the tension of the cord 3, over the 

 eord 2, by the formula, 



2 p d cos/ 

 = #_-. tfcos/ 



in which p represents the tension of the cord 2, or 109 lb , 6 ; 

 since, without friction, this tension would be one fourth of the 

 weight or 100 lb . Accordingly we have 



219,2 XJXO,24 _ 1_0,522_ _ ft 

 1 0, 24 X | "0,95 



This is the quantity by which the cord 3 is more stretched thae 

 the cord 2, on account of friction. Thus the cord 3 is stretched 

 with a force equal to 1 20 lb 7. 



As the cords 3 and 4 embrace the moveable block, we deter- 

 mine how much the cord 4 is more stretched than the cord 3 by 

 the formula 



_ p $ cos/ 



~5 ' 



which would give as above z' = 9 lb , 6. Thus the cord 4 is 

 stretched with a force equal to 



100 +9, 6 + 11, 1 -f 9, 6 = 130 lb , 3. 



Finally, by supposing for greater simplicity, which will make 

 but little difference in the result, that the two cords 4, 6, which 

 embrace the fixed block, are parallel, we shall have the quantity 

 by which the cord 5 is more stretched than the cord 4 by the 

 formula 



which gives 



