158 



USING MACHINES 



FIG. 253. DOING ONE FOOT 

 POUND OF WORK 



The usual conception of work is different from the 

 scientist's idea of work. When one is tired he says that 

 he has been working hard. From the scientist's point 

 of view he may not have done work at all. If, for 

 example, you were to push on a large building, trying 

 to move it, the end of a day would find you very tired. 

 You would think that you had done a hard day's work, 



but a scientist would say 

 that unless you moved 

 the building no work 

 was accomplished on it. 

 From his point of view, 

 to do work an applied 

 force must move some- 

 thing, and the amount of 

 work is measured by the 

 amount of the force ap- 

 plied and the distance the 

 object is moved. Since 

 we measure the distance moved in feet and the force 

 applied in pounds, the unit of work is called the foot 

 \pound. _ 



Work (foot pounds) = distance (feet) X force 

 (^pounds). 



~ifj for example, a one-pound weight is raised 

 through a distance of one foot, one foot pound of 

 work has been done (see Fig. 253). 



Problem: How many foot pounds of work would 

 be done by an engine raising 400 pounds of concrete 

 to the upper stories of a building 200 feet above the 

 street? 



What are the various types of levers and how do 

 they aid us? Levers have been known since early 

 times. It is difficult to say when and where the lever 

 was first known, but early man must have used it to 

 move heavy stones and logs and to provide handles 

 for his stone axes and hammers. The principle of the 

 lever was probably first explained by Archimedes, 

 a Greek scientist and mathematician who lived in the 

 city of Syracuse, in Sicily, from about 287 to 212 B.C. 

 Archimedes discovered that all levers are essen- 

 tially the same and have the same forces working on 

 them. A lever is usually a straight bar but may be 

 bent for special purposes. The see-saw which is a 

 part of every child's experience is an example of a 

 simple lever. By studying the see-saw we shall be 

 able to learn the principle which Archimedes dis- 

 covered. 



. If you can remember your "see-saw" days you will 

 recall that the board was first balanced on the saw 

 horse or log. This point of balance is found in all 

 levers and is called the fulcrum. Now if your com- 

 panion and you were of the same weight, you placed 

 yourselves at the same distance from the saw horse, 

 or fulcrum. If, however, you were heavier, it was 



necessary for you to get closer to the fulcrum and 

 your companion farther away on the other side. When 

 the see-saw was exactly in balance, how easily it 

 moved up and down and what fun you had ! Now let 

 us study the see-saw a little more closely and find out 

 some things about it which you may not know. 



Suppose you have balanced the board. Your weight 

 is 100 pounds and your companion's weight is 80 

 pounds. You already know that he must be farther 

 away from the fulcrum than you, but how much 



FIG. 254. "SEE-SAW" DAYS 



farther away is a question. The board is ten feet long, 

 and your companion sits on the very end. Where must 

 you sit to balance him? Here is where you can use 

 the discovery made by Archimedes. Archimedes found 

 that when the lever is in balance the weight on one side 

 of the fulcrum multiplied by its distance from the ful- 

 crum must exactly equal the weight on the other side 

 multiplied by its distance. Study Figure 255. Can you 

 tell how far the second boy is from the fulcrum ? What 

 is the distance from the fulcrum that you would have 

 to sit on the see-saw to balance your companion? 



so-lb. boy 



80 



= 400 



100 X. ..= HOO 



FIG. 255 



Not all levers are exactly like the see-saw. They are 

 different because the fulcrum and the two forces 

 are not placed in the same position. Levers with the 

 forces and fulcrum arranged as* in Figure 256 are 

 called the first-class levers. 



If the fulcrum is on one end of the bar, and the 

 weight anywhere between the fulcrum and the force 

 working on the other end of the bar as shown in 

 Figure 257, the lever is said to be of the second class. 

 You are no doubt familiar with many examples of this 

 type of lever, such as the wheelbarrow. 



