MACHINES IN EVERYDAY LIFE 



161 



There are four important parts in the simple in- 

 clined plane: the length, the height, the weight, and 

 the effort. Experiment shows that the mechanical ad- 

 vantage of an inclined plane may be found by dividing 

 the length by the height. 



length 

 Mechanical advantage of an inclined plane = 



height 



The wedge and the screw are inclined planes. Just 

 as the wheel and axle and pulley make up two special 

 kinds of levers, so the wedge and the screw make up 

 two special kinds of inclined planes. The wedge forms 

 a double inclined plane and is used in splitting logs 

 and in many other everyday situations. The screw is 

 a spiral inclined plane and finds many uses in every- 

 day life, such as" the wood screw, the bolt and nut, the 

 food chopper, and the builder's lifting jack. You can 

 see how the screw may be formed from the simple 

 inclined plane by cutting a piece of paper in the form 

 of a right triangle about four inches high and twelve 

 inches long as shown in Figure 264. Beginning away 

 from the point, roll this on a round stick and see how 

 the length of the plane spirals to make the threads. 

 Keep the bottom edge even. 



L. 



FIG. 264. THE SCREW IS AN INCLINED PLANE 



Figure 263 shows the uses of the wedge in every- 

 day life. Can you explain why a plow, a knife, an axe, 

 and a saw are inclined planes? 



How may machines be made more efficient? Simple 

 and complex machines are used by man to give him 

 an advantage in applying forces, but they do not make 

 the work done any less. More work is always put into 

 a machine than is obtained from it. In the block and 

 tackle, if there are four cords supporting the load, one 

 applies an effort force which is only one fourth the 

 load being raised, but the effort force must move four 

 times farther than the load force so that the work put 

 in (effort force X effort distance) just equals the work 

 put out by the machine (resistance force X resistance 

 distance) if friction be neglected. Suppose, for ex- 

 ample, that a twenty-pound weight is to be raised 

 with a four-strand block ^nd tackle. Experiment will 



n 



show that if the load is raised one foot the effort force 

 will move four feet but will be only one fourth of the 

 load, or five pounds. The work put in and got out 

 would then be found to be 



Effort X effort distance = work in. 



5 X 4 =20 foot pounds. 



Resistance X resistance distance = work out. 



20 1 =20 foot pounds. 



In the inclined plane the work put into the machine is 

 found by multiplying the effort by the length of the 

 plane. The work got out of the machine is obtained by 

 multiplying the resistance by the height of the plane. 



Work in = effort X length. 



Work out = resistance X height. 

 The work obtained from any machine is always less 

 than that put in because some of the effort force is 

 required to overcome the friction in the machine. Man 

 is constantly trying to overcome friction. The next 

 topic will tell you n\ore about this. 



Reducing friction increases the efficiency of ma- 

 chines. A machine which has a large amount of fric- 

 tional resistance must use much of the work put into 

 it in overcoming this friction. A machine which has 

 little frictional resistance can produce more useful 

 work. Machines are rated on their ability to turn the 

 work put into them into useful work or output, and 

 the rating is called the efficiency of the machine. It is 

 obtained as a percentage by dividing the output in 

 work units by the input in work units and multiplying 

 by 100. 



Output (foot pounds) 



Efficiency = 



Input (foot pounds) 



Suppose an inclined plane ten feet long were used in 

 rolling a 200-pound barrel of flour into a truck three 

 feet high. Assume the force required to push the barrel 

 up the incline as seventy pounds; then 



Input = length X effort = 70 X 10 or 700 foot 

 pounds. 



Output = weight X height = 200 X 3 or 600 foot 

 pounds. 



Efficiency = output/input = 600/700 == 6/7 

 85.7%. 



Machines can never be 100 per cent efficient because 

 of friction. That is, we must always put more work 

 into a machine than we can get out of it. This makes 

 perpetual motion in a mechanical device impossible. 



REFERENCES FOR FURTHER STUDY 

 Texts 



Caldwell and Curtis, Science for Today. Chap. 9 

 Clement Collister, and Thurston, Our Surroundings, Chaps. 

 2, 6, 18 



