182 ELEMENTS OF GENERAL SCIENCE 



due to friction would be added to the resistance offered by 

 the boat. The pull on the end of the rope would need to 

 be greater than 100 pounds in order to overcome both types 

 of resistance. The work in would be correspondingly greater. 

 If it were necessary to pull with sufficient additional force 

 to make the total applied force amount to 125 pounds, 

 the total amount of work done upon the machine would be 

 125 x 250 foot-pounds, or 31,250 foot-pounds. These relations 

 may be tabulated as follows : 



FOOT-POUNDS 



Total work in 31,250 



Useful work out 25,000 



Wasted work 6,250 



Total work out 31,250 



The total work out is in this case and in all cases the 

 same as the total work in. Useful work out is less than 

 total work in. 



196. Efficiency. The proportion of wasted work will not 

 always be the same as in the problem above. If the machine 

 is very carefully constructed the friction may be so reduced 

 chat there is very little waste. Such a machine is said to be 

 very efficient, since it does its work with but little waste. 



The efficiency of a machine is measured by the fraction 

 of the total work done upon it which appears in the useful 

 work accomplished by it. 



^,,v. . useful work out 



Efficiency = 



total work in 



In the particular case which we have been considering, the 

 efficiency is calculated as follows: 



Efficiency = ' , therefore 



O I , I-- )^ ' 



Efficiency = -|, or 80 per cent. 



