WORK AND MACHINES 167 



restricted to any more or less complicated and lifeless mechanism 

 devised and made by man. 



By means of machines man can employ not only the strength of 

 himself and of other animals to advantage, but he harnesses the differ- 

 ent forms of energy of inanimate nature to do his bidding. The force 

 of gravitation in the energy of winds and of running waters, the heat 

 energy in steam, and electrical energy from the dynamo and from 

 batteries, are familiar sources. 



There is always waste of energy (not destruction of it) in the run- 

 ning of any machine. The larger this waste the less efficient is the 

 machine. The efficiency of a machine is expressed by stating what 

 per cent the useful work done by the machine is of the energy 

 expended in doing it. 



A study of the so-called simple machines such as levers, pulleys, 

 and the inclined plane, aids in an understanding of the mechanism of 

 those that are more complicated and whose parts may be modified 

 almost beyond recognition. The screw and wedge may be considered 

 forms of the inclined plane, and the wheel and axle a form of pulley. 



A lever is free to move only about a fixed point as a fulcrum, and 

 does not travel from place to place. In the use of a set of pulleys, those 

 that are known as the movable pulleys are attached to the body that 

 is being moved, and travel with it. 



Disregarding all waste of energy in any machine, the product of the 

 effort put forth as a power into the distance through which it acts 

 equals the product of the resistance overcome into the distance through 

 which the resistance is offered. As commonly stated, power times 

 power distance equals weight times weight distance. This is a "law" 

 or general statement concerning machines. 



Since the time involved in the motion of both the power and the 

 weight is the same, this law of machines may likewise be stated as 

 power times power velocity equals weight times weight velocity. 



Whatever effort is required to overcome resistance beyond this cal- 

 culated value may be considered as used in overcoming the resistance of 

 the machine. So far as useful work is concerned it is energy wasted. 



The term momentum is applied to the product of the mass (or 

 weight) of a body into its velocity. This makes the term applicable 

 only in cases when bodies are moved from place to place. 



The moment of. a force has no reference to velocity. It is appli- 

 cable in cases of levers where the motion is about a fixed point as a 

 fulcrum. A body is in equilibrium when the moment of the effort ex- 



