178 ELEMENTS OF GENERAL SCIENCE 



system used in moving the boat, in which case 5 and not 6 

 strands of cord are used. If we suppose that a pull of 500 

 pounds was necessary to mpve the boat, and that it was 

 moved 50 feet, the work accomplished was 25,000 foot-pounds, 

 since useful work, or work accomplished, equals resistance 

 overcome (500 pounds) times distance through which resist- 

 ance was overcome (50 feet). 



We know that the applied force acted through a distance 

 5 times as great as the distance the resistance was moved, and 

 its distance was therefore 5 times 50 feet, or 250 feet. We 

 know also that the force which it was necessary to apply in 

 order to overcome this resistance was one fifth as great as the 

 resistance (neglecting friction). It was therefore 100 pounds. 

 Calculating the work done by the applied force through the 

 distance of 250 feet, we find it to be 25,000 foot-pounds. 

 This is exactly the same as the work out, as found above. We 

 conclude, therefore, that if there were no friction in the machine, 

 we should get out of the machine just what we put into it. 



It has been pointed out in a preceding section that there 

 can be no frictionless machine. We must therefore include 

 friction in our calculations. It is clear that the resistance 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 times 

 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 



