160 Statics. 



40 : 38, 97 : : 8 lb : 7 lb 79. 



Adding now these 7 lb , 79 to 120 lb , 7, the quantity before found 

 for the tension of the cord 3, we shall have 1 28 lb , 5 for the force 

 of tension, both on account of friction and the stiffness of the 

 cords. 



The cord 4, on account of friction is stretched by a force 

 = 130 lb , 3 ; the whole force of tension upon the cord 3, 4, which 

 embraces the moveable block, is therefore 258 lb , 8 ; with this 

 quantity, the dimensions of the pulleys and cords remaining the 

 same, we shall find, as above, that the allowance for the stiffness 

 of the cords, would be 8 lb , 62, if this cord did not embrace the 

 moveable block ; but proceeding as we have done above, and for 

 the same reason, we must take but half of this quantity ; thus the 

 tension of the cord 4, all things considered, will be 134 lb , 6 

 nearly. 



The cord 5, on account of friction, is stretched with a force 

 = 143 lb , 5 ; the whole force by which the cord 4, 5, embracing the 

 fixed pulley, is stretched, is therefore 278 lb ,l . With this value, the 

 dimensions remaining the same, we shall find the force required 

 for the stiffness of the cords to be 9 lb , 3 ; the whole tension of the 

 eord, therefore, is 152 lb , 8. Thus friction and the stiffness of 

 the cords together require the weight 5, which would otherwise 

 be but 100 lb , to be 153 lb nearly, a quantity greater by more 

 than one half. 



We have taken only half of what the calculation furnished as 

 the quantity to be added to cords 2 and 4, on account of the 

 stiffness. The reason of this is, that the cord by which the 

 moveable pulley is made to revolve, may be considered as turn- 

 ing it on a centre placed at the point where this pulley touches 

 the other cord ; and consequently the case is similar to that of a 

 fixed pulley, having a radius equal to the diameter of the move- 

 able pulley ; and since the forces required on account of the 

 stiffness of the cords, are in the inverse ratio of the radii of the 

 pulleys, the force in this case must be diminished one half. 



