160 



USING MACHINES 



Force 



FIG. 261. THE PULLEY IS A LEVER 



pulley. The fulcrum is where the pulley turns up the 

 fixed rope, and the effort is applied on the other rope. 

 Since the diameter is always 

 twice the radius, it will be seen 

 that with this machine one can 

 always lift a weight which is 

 twice as great as the effort 

 force. 



Sometimes pulleys are com- 

 bined into blocks where two or 

 more pulleys make up a single 

 block. These are known as 

 block and tackle. Figure 262 

 shows how a four-strand or 

 double block and tackle is used 

 to lift a weight. 



There would probably be lit- 

 tle need for machines if through 

 their use man were not able to 

 do his work more easily or 

 more rapidly. The advantage gained over nature by 

 using a machine is called mechanical advantage. This 

 may be an advantage of either force or speed. The 

 lever is an excellent example of these two kinds of ad- 

 vantage. In the first-class lever if the resistance dis- 

 tance is less than the effort distance, the advantage is 

 one of force, while if the effort distance is shorter, the 

 advantage is one of speed. Whenever speed is gained 

 more effort force than the resistance must be applied. 

 When force is gained it is at the expense of speed. 

 In the second-class lever one can never gain speed. 

 The only advantage to be gained is power. Can you 

 explain this. What is the greatest resistance distance 

 possible in this type of lever? In the third-class lever, 

 it is impossible to gain an advantage of force. Only 

 speed can be gained by its use. Can you explain the 

 reason for this? 



Mechanical advantage can be calculated in a simple 

 lever by dividing the longer lever arm or distance by the 

 shorter one. The practical or working mechanical ad- 



FJG. 262. BLOCK AND 

 TACKLE 



vantage of any machine takes account of friction and 

 may always be found by dividing the resistance force 

 by the effort force. 



resistance 



Mechanical advantage = - - . 



effort 



To find the mechanical advantage of the wheel and 

 axle it is necessary only to divide the radius of the 

 wheel by the radius of the axle, since these are the 

 lever arms. 



Mechanical advantage of wheel and axle = 



wheel radius 



axle radius 



In the simple fixed pulley the mechanical advan- 

 tage is one, since the lever arms are equal. In the 

 single movable pulley there is always an advantage of 

 two, since the resistance arm is the radius of the pul- 

 ley and the effort arm is its diameter. To find the me- 

 chanical advantage of any pulley system, count the 

 number of strings supporting the movable pulley. 

 This is two in the single movable pulley, four in- the' 

 four-strand block and tackle, and so forth. 



Mechanical advantage of pulley system = number of. 

 cords supporting movable pulley. 



How do various types of inclined planes help us do 

 our work more easily? The inclined plane consists, 

 in its simplest form, of a board by use of which heavy 

 objects can be moved from one level to another. For 

 example, in raising a heavy barrel into a truck less 

 effort force is required to push it up an incline than 

 to lift it vertically. It is probable that the Egyptians, 

 in constructing the pyramids, built long inclines up 

 which the massive stones were drawn by slaves. As 

 the pyramid rose higher and higher, the inclines were 

 doubtless made longer and longer. Figure 252 shows 

 a simple inclined plane and Figure 263 shows how it 

 is used in modern life. 



I-IG. 263. COMMON USES OF THE INCLINED PLANE 



