SIMPLE MACHINES 187 



one-half the length AB, the force F is one-half the 

 weight W. If the height BC is one-fourth the length 

 AB, then the force F is one-fourth the weight W. 

 Now let BC be 4 feet, the length AB be 8 feet, and 

 the weight be 400 pounds; then the force will be 200 

 pounds, because the force multiplied by the force dis- 

 tance equals the weight multiplied by the weight dis- 

 tance: (200 X 8 = 400 X 4). If BC is 2 feet, AB is 8 

 feet, the weight is 400 pounds, and the force is 100 

 pounds: 100 X 8 = 400 X 2. From this experiment it 

 is again evident that the work done by the force moving 

 the length of the plane is equal to the work resulting 

 from lifting the weight up the vertical height of the 



W i 



plane, that is, F X i = W X h, and ; = , i. e. the 



mechanical advantage of the inclined plane is the ratio 

 of the length of the plane to the height of the plane, or 

 the ratio of the weight lifted to the force acting parallel 

 to the plane. 



The use of the inclined plane is for loading barrels or 

 logs on a wagon and for unloading them; to roll or slide 

 objects down into a cellar or for taking them out. By 

 using a very long plane heavy objects can be loaded on 

 a wagon with but little force. If the wagon is 3 feet 

 high and the plane 18 feet long, a force of 100 pounds 

 will roll a 6oo-pound barrel up on the wagon. 



The grade of a highway or railroad is the number of feet 

 that the road rises vertically per hundred feet. A railroad 

 running straight up a hill a mile long (5280 feet) has a 

 grade of 2 per cent, if the top of the hill is 105.6 feet above 

 the level of the road at the bottom. The mechanical ad- 

 vantage of this grade or inclined plane is 5280 feet -r- 105.6 

 feet ; or 50; hence, in order to pull a train to the summit 



