vi PARALLEL FORCES AND CENTRE OF GRAVITY 77 



The first part of a record of this kind will show that the 

 magnitude of the resultant force is equal to the sum of the 

 components, while the second part will prove that in each case 

 when the rod is in equilibrium one weight multiplied by its 

 distance from the point of action of the resultant is equal to 

 the other weight multiplied by the other's distance from the 

 resultant. Or, expressing the result as an equation, and sub- 

 stituting the word force for weight, we have : 



Force on _ Distance from Force on _ Distance from 



one side 



Resultant 



other side 



Resultant. 



If the component forces are equal, their distances from the 

 resultant will also be equal ; and if they are unequal the re- 

 sultant will always be nearer to the greater force. In other 

 words, a small force is at a large distance from the resultant, 

 and a large force is at a small distance. 



This follows from what has been already said (p. 49) con- 

 cerning the moments of forces tending to turn a body in 

 opposite directions. It will be remembered that the moment 

 of a force is obtained by multiplying the force (measured in 

 units) by the perpendicular distance between the point at which 

 it acts, and the fulcrum or hinge about which the body turns. 

 If a rigid object such as a lever or balance, capable of turning 

 about a fixed point in one plane is at rest, then the sum of the 

 moments of the forces tending to turn it in one direction is 

 equal to the sum of those tending to turn it in the opposite 

 direction. Expressed as an equation, we have : 



Sum of moments 

 on one side of fulcrum 



Sum of moments 

 on other side of fulcrum. 



Still another way of regarding this important truth is to say 

 that the algebraic sum of the moments is always equal to 0. 



Conditions for the Equilibrium of Three Parallel Forces. 

 The student should now be in a position to understand clearly 

 the conditions which must prevail for three parallel forces to be 

 in equilibrium. 



