8 



FORCES IN THE SAME STRAIGHT I IM . 



When several forces act in -1 motions, but in the 



same straight line, on a partiel- . tin- resultant of the i 

 ^ in one <lii equal to the sum of these f. 



and act* in the same direction; and so of the forces m Minir in 

 the opposite direction. r i ,tant, then-Inn-, of all the 



forces is equal to the (Inference of these sums, and acts in the 

 the greater sum. 



: ie forces acting in 01. ion are rrcknm-d 



and tlmsc in the opposite direction negative, then thrir r- - 

 .-ultant is equal to th< roibaJ sum; its .si^u determines 



the direction in which it acts. 



In order tlint the forces may be in equilibrium. their 

 resultant, and therefore their algebraical sum. miM vanish. 



There is another case in which wo can easily <1 

 mine the magnitude and direction of the resultant. 



Let AB y AC, AD be the directions of three, equal forces 

 - on the particle A', suppose these forces all in the 

 same plane and the three angles ]!A<\ ('Ah, l>Mi 

 equal to 120; the particle will remain at rest, for then is 

 no reason why it should move in one direction rather than 

 another. Each of the forces is therefore equal and op] 

 to the resultant of the other two. 

 But if we take on the directions 

 of two of them, AB, A C, two equal 

 straight lines AG, All to re; 

 sent the forces, and complete the 

 parallelogram GAllE, the diago- 

 nal AE will lie in the same straight 

 ''. Also the triangle 

 A QE will be equilateral, and t h r 

 fore AE*= A<< , the diago- 



nal AE of the parallelogram con- 

 structed on AG, AH represents 

 the resultant of the two forces which AG and AH respec- 

 y represent. 



;* proposition is a particular case of one to which we 



n.w proceed. 



