274 



THE PULLEY. 



force of the weight represented by A B will be equivalent to two forces repre- 

 sented by B D and B E. The number of inches in these lines respectively 

 will represent the number of ounces which are equivalent to the tensions of 

 the parts B F and B C of the cord. But as these tensions are equal, B D 

 and B E must be equal, and each will express the amount of the power P, 

 which stretches the cord at P C. 



It is evident that the four lines, A E, E B, B D, and D A, are equal. And 

 as each of them represents the power, the weight which is represented by 

 A B must be less than twice the power which is represented by A E and E B 

 taken together. It follows, therefore, that as parts of the ropes which support 

 the weight depart from parallelism, the machine becomes less and less effica- 

 cious ; and there are certain obliquities at which the equilibrating power would 

 be much greater than the weight. 



The mechanical power of pulleys admits of being almost indefinitely in- 

 creased by combination. Systems of pulleys may be divided into two classes : 

 those in which a single rope is used, and those which consist of several dis- 

 tinct ropes. Figs. 7 and 8, represent two systems of pulleys, each having a 



Fig. 7. 



Fig. 8. 



single rope. The weight is in each case attached to a moveable block B, in 

 which are fixed two or more wheels ; A is a fixed block, and the rope is suc- 

 cessively passed over the wheels above and below, and, after passing over the 

 last wheel above, is attached to the power. The tension of that part of the 

 cord to which the power is attached is produced by the power, and therefore 

 equivalent to it, and the same tension must extend throughout its whole length. 

 The "weight is sustained by all those parts of the cord which pass from the 

 lower block, and, as the force which stretches them all is the same, viz., that 

 of the power, the effect of the weight must be equally distributed among them, 

 their directions being supposed to be parallel. It will be evident, from this 

 reasoning, that the weight will be as many times greater than the power, as 

 the number of cords which support the lower block. Thus, if there be six 

 cords, each cord will support a sixth part of the weight that is, the weight 

 will be six times the tension of the cord, or six times the power. In fig. 7, 

 the cord is represented as being finally attached to a hook on the upper block. 

 But it may be carried over an additional wheel fixed in that block, and finally 

 attached to a hook in the lower block, as in fig. 8, by which one will be added 

 to the power of the machine, the number of cords at the lower block being in- 

 creased by one. In the system represented in fig. 7, the wheels are placed 

 in the blocks one above the other ; in fig. 8 they are placed. side by side. In 



