176 ELEMENTS OF GENERAL SCIENCE 



if friction could be wholly eliminated, we should find that the 

 ratio of the force applied to the weight lifted is 1 to 6. 



We find, therefore, that in the particular pulley system which 

 we have been studying, the applied force must move six times 

 as far as the weight, but that if friction is neglected, it need 

 be only one sixth as great as the resistance of the weight. 

 With different combinations of pulleys the ratio might not 

 be represented by the number 6, but it would always be equal 

 to the number of strands supporting the weight. 



194. Mechanical advantage of pulleys. The advantage in 

 the use of pulleys lies in the fact that by their means a small 

 force may be made to overcome a great resistance. This ad- 

 vantage is measured by the number of times which the force 

 exerted against the resistance is greater than the force applied. 

 In the case considered in the preceding section, the mechanical 

 advantage was 6. The mechanical advantage of a pulley sys- 

 tem may be determined very readily, for it is always equal to 

 the number of strands of rope which are supporting the weight 

 or other resistance. 



195. Work and pulley systems. If the boy uses rope and 

 pulleys to pull the boat out of the water, he does not escape 

 the necessity of doing work in order to move the boat, for he 

 must pull on the rope. Likewise, the pulley system does work 

 upon the boat in moving it up the beach. We may call the 

 work done by the boy in pulling on the rope the work in, 

 and the work accomplished in overcoming the resistance of 

 the boat and the friction on rope and pulleys will be called 

 the work out. 



The part of the work which is performed in moving the 

 boat is the useful, work, while that wasted in overcoming fric- 

 tion in the pulley system will be known as the wasted work. 



We now arrive at a second problem in our study of pulleys. 

 We have learned that the force which the boy applies is less 

 than that which is exerted upon the boat ; but is the same true 

 of the work that he puts in and the work that he gets out ? 



