Chap. XLL] 



PULLEYS, 



499 



xS\'.\y '. \ 



in the least the result of the movable one. The 

 latter has a hook attached from which a weight 

 is suspended. Now when the rope is pulled with a 

 force of 1 pound, let us say, that force is communi- 

 cated to the hook in the beam. It is a law of 

 dynamics that action and reaction are equal. If the 

 hook is pulled on with a force of 1 pound, it reacts 

 with a force of 1 pound. Now the force of 1 pound 

 acts in a direction to raise the movable pulley, and 

 the force of reaction acts for the same end. The 

 pulley with its attached weight is thus pulled up- 

 wards with a force of 2 pounds. But 

 the movable pulley does not rise in the 

 same degree that the free end of the 

 rope descends ; owing to the doubling 

 of the rope, it is raised by only half the 

 distance. It is also plain that if several 

 movable pulleys were used, connected 

 together, the rope passing from one to 

 the other, and the weight hanging to 

 the sj^stem, the power necessary to 

 raise the weight would be diminished 

 in proportion to the number of pulleys. 

 Such a system of pulleys is shown in 

 Fig. 211. It is to be noted that the 

 height to which the weight is raised 

 with a certain length of rope pulled, 

 smaller and smaller as the 

 of pulleys is increased. A 

 force is capable of raising 



becomes 



number 



smaller 



w 



through 



the weight, but it must act 

 distance. In short, the work done is 

 whether the pulleys be many or few. 

 done is estimated bv the weight raised 



distance through which it is 

 of 10 pounds raised 1 foot is 

 of 1 pound raised 10 feet. 



Fig. 211. A 

 Sys t e m of 

 Movable Pul- 

 leys. 



a longer 

 the same 

 The work 

 into the 



weight 



same as a weight 

 weight 



raised. Thus a 

 the 

 So that if 



