THE INCLINED PLANE. 63 



which are often so great that two-thirds of the power 

 is lost. 



THE INCLINED PLANE. 



The inclined plane or slope possesses a power which is 

 estimated by the proportion which its lengtli bears to the 

 height. If, for example, the plane be twice as long as the 

 perpendicular height, then in rolling the body a up the 

 inclined plane (fig. 68), it will move through twice the 

 distance required to lift it directly from h to c. Therefore 

 only one-half the strength else required need be exerted for 

 this purpose. The same reasoning 

 will apply to any other proportion 

 between the height and length ; 

 that is, the more gradual or less 

 steep the slope becomes, the greater 

 will be the advantage gained. A familiar example occurs 

 in lifting a loaded barrel into a wagon : the longer the 

 plank iised in rolling it, the less is the exertion needed. 



A body, in rolling freely down an inclined plane, acquires 

 the same velocity that it would attain if dropped perpen- 

 dicularly from a height equal to the perpendicular height 

 of tiie plane. Thus, if an inclined plane on a plank road 

 be 100 yards long and 16 feet high, a freely running 

 wagon, left to descend of its own accord, will move 32 

 feet per second by the time it reaches the bottom, that 

 being the velocity of a stone falling 16 feet. Or, a rail- 

 car on an inclined plane 145 feet high will attain a speed 

 of 96 feet per second, or more than 65 miles an hour, at 

 the foot of the plane, which is equal to the velocity of a 

 stone falling three seconds, or 145 feet. 



ASCENT IN ROADS. 



All roads.not perfectly level maybe regarded as inclined 

 planes. By the application of the preceding rule, we 



