Motion dozvn inclined Planes. 205 



Of the Motion of heavy Bodies down inclined Planes. 



A 



324. A heavy body left to itself upon a plane surface KLHI, Fi 156 - 

 inclined to a horizontal surface PIHN cannot yield entirely to 



its gravity. A part of the force derived from this cause, is em- 37. 

 ployed in pressing the plane, and the other serves to bear it 

 along the plane. It is necessary, therefore, to decompose Its 

 gravity into two forces, one of which produces the pressure upon 

 the plane, and the other the motion along this plane. 



325. Let G be the centre of gravity of the body in, or the 

 point in which all its action may be considered as united. Let 

 GB be the space through which it would fall in an instant, if it 

 were free. Let GC be drawn perpendicular to the plane ; and 

 suppose a plane to pass through GB, GC, this plane Avill be per- 

 pendicular to the two planes KLHI, IPNH, since it passes Georo. 

 through the straight lines perpendicular to these planes. If 

 therefore, we conceive DE, EF, to be the intersections of this 

 plane with KLHI, IPNH-, DE, EF will be perpendicular to the Geom 

 common intersection HI of these two planes. 355 - 



Draw GA parallel to DE, and construct the parallelogram 

 GABCof which GB is the diagonal, and GA, GC, the sides. 

 We may suppose that gravity, instead of urging the body accord- 

 ing to GB, urges it at the same time according to GC with the 

 velocity GC, and according to GA with the velocity GA. Now 

 it is evident that GC, being perpendicular to the plane, cannot 

 but be destroyed, if the point O where it meets the plane is at 

 the same time a point common to the plane and the body m. 



As to the force GA, since it tends neither to approach toward, 

 nor to recede from the plane, it cannot but have its full effect. 

 GA, therefore, represents the velocity with which the body tends 

 to move, and with which it would move in the first instant. 



As the force GA is in the plane of the two right lines GB, GC, 

 it is in the plane DEF. We can therefore leave out of consid- 

 eration the extent of the two planes KLHI, IPNH, and employ 

 only the plane DEF represented in figure 157, so that the body 

 may be supposed to move in the right line DE. 



