PULLEYS, INCLINED PLANES, AND WEDGES 51 



always exceeds the useful work by the amount that is trans- 

 formed into heat. The ratio of the useful work to the total 

 work done by the acting force is called the efficiency of the 

 machine. 



Useful work accomplished 

 Efficiency = - 



Total work expended 



The efficiency of simple levers is very nearly 100% because 

 the friction is so small as to be disregarded. In the inclined 

 plane the friction is greater than in the lever because the 

 two bodies come in contact with a larger surface. The 

 efficiency of a lever is somewhere between 90 and 100%. 

 The efficiency of the commercial block and tackle with several 

 movable pulleys varies from 40 to 60%. In the case of the 

 jack screw there is necessarily a large amount of friction 

 so that its efficiency is often as low as 25%. Gear wheels 

 or chain gears, such as are used in bicycles, are machines of 

 high efficiency, often running as high as 90% or more. 



Questions 



1. A crane consists of what simple machines? 



2. Name a number of "twisting tools and appliances" such as 

 are used in placing a nut in position. Notice the manner in which 

 they are used. Are two distinct circumferences made in their 

 operation? Name the mechanical principles involved. 



3. Name a number of "screw tools and appliances," that is, 

 tools and appliances that are based on a spiral groove. Divide 

 them into two parts: those that communicate motion and those 

 that are used as fastening agents. 



4. Explain the manner in which a screw communicates motion. 



5. Name a number of "hoisting tools and devices." How do 

 they work? What is the mechanical principle involved? 



6. Name a number of "cutting tools." What is the shape of 

 the cutting edge? Does the part that "cuts" come to a point 



