546 MACHINES, WORK, AND ENERGY 



common sliding bearing. Every boy or girl who rides a 

 bicycle or uses roller skates knows that a ball-bearing wheel 

 runs easier than one without ball bearings. 



Exercise 104. A Study of Ball Bearings 



Examine the ball bearings in a bicycle or a roller skate to see ex- 

 actly how they are constructed and how they work. 



645. The Law of Machines. The work (or energy, see 

 Art. 85) put into a machine and also the work (or energy) 

 taken out of a machine must, of course, be measured in 

 work units, i.e., in such units as foot-pounds, or gram-centi- 

 meters, or kilogram-meters. The work put into a machine 

 is equal to the product of the applied force and the distance 

 through which that force acts; the work delivered by a 

 machine equals the product of the force delivered and the 

 distance through which it acts. If there were no friction, the 

 work delivered by a machine would exactly equal the work 

 put into it. 



LAW OF MACHINES. The work or energy put into a machine 

 would equal the work or energy delivered by the machine 

 if all friction were eliminated. 



646. Friction Generally Hinders but Sometimes Helps. 

 In fact, however, the work delivered by a machine is never 

 exactly equal to that put into it. In most cases the work 

 delivered by a machine is less than that put into it because of 

 friction in the machine. Occasionally, however, a machine 

 is used in such a manner as to yield an output greater than 

 the input. For example, if a set of pulleys, an inclined 

 plane, or an elevator is used to lower a heavy object from the 

 top floor of a building to the basement, the work put into the 

 machine is less than that taken out of it. Friction, in this 

 case, tends to keep the body from falling; it is working with 

 the operator. 



647. Efficiency of a Machine. The EFFICIENCY OF A MA- 

 CHINE is measured by the ratio of the work (or energy) delivered 

 by a machine to the work (or energy) put into it. 



