MACHINES 647 



Efficiency of a machine = 



Work or energy delivered, or output 



Work or energy put in, or input 



It is generally expressed in percentage. It is usually less 

 than 100 per cent, but it may be greater than 100 per cent. 

 Illustrations: 



1. If a block and tackle, i.e., a set of pulleys, be used to raise 

 a piano from the ground to the top floor of a building, we 

 find that we are obliged to put considerably more work into 

 the machine than we get out of it. If the piano weighs 1000 

 Ib. and it is raised 50 ft., how much work is accomplished? 

 In this case we are obliged, not only to do this amount of work, 

 but we must also do work in overcoming friction. The 

 efficiency of the machine in this case is not likely to be more 

 than 50 to 75 per cent. 



2. Supposing now that we wish to lower the same piano from 

 the top floor of the building to the ground again. If we use 

 the same block and tackle we shall find that we are not now 

 obliged to put as much work into the machine as we get out 

 of it. Exactly the same amount of work will be accomplished 

 in lowering the piano as was accomplished in raising it but 

 the friction of the machine tends to keep the piano from falling. 

 Friction is now aiding us it is working with us. The effi- 

 ciency of the machine will now probably be from 133 to 

 200 per cent. 



648. Friction is Often Useful. We generally find it an ad- 

 vantage to reduce friction in a machine as much as possible; 

 sometimes, however, we find friction of great service to us. 

 When we wish to haul a heavy load up a hill we make every 

 effort to reduce friction. When we start down hill, how- 

 ever, we set the brakes, or possibly chain one rear wheel, in 

 order to increase friction. A locomotive owes its power to 

 pull a train to the friction between its drive wheels and the 

 rails. The largest locomotive ever built weighs 336 tons and 

 can exert a pulling force of about 60 tons and can easily pull 

 a train of 200 cars each weighing 50 tons (Fig. 340). If this 



