CHAPTER VI 



CENTER OF GRAVITY 



85. As we have seen, the action of gravity on a system of 

 masses may be represented by a system of parallel forces, these 

 forces consisting of a force acting on each particle equal to the 

 weight of the particle, its direction being vertically downwards. 

 By the rules explained in the last chapter, these forces may be 

 compounded into a single force. The magnitude of this force is 

 the sum of all the component 



forces, and is therefore the total 

 weight of the body, while the 

 direction of the force, being par- 

 allel to the component forces, 

 is itself vertically downwards. 

 The problem discussed in the 

 present chapter is that of de- 

 termining the position of the 

 line of action of this force. 



86. Let the particles be of 



masses m l} m 2 , -. Let rectangular axes be taken, the axis of z 

 being vertical, and let the coordinates of the first particle be 

 x i> 2/i' z i> the coordinates of the second be # 2 , y z , z 2 , and so on. 



The weight of the first particle is m^g, and its line of action 

 cuts the plane Oxy in a point of which the coordinates are 

 x lt y 13 0. Hence the moment of the force about the axis Oy is 

 m l gx r Let the line of action of the resultant cut the plane Oxy 

 in the point x, y, 0. Then the moment of the resultant about the 

 axis Oy is C^m^\gx, where Vm x is the sum of the masses of all 

 the particles. 



117 



FIG. 64 



