7 



88 MECHANICS 



COMPOSITION OF FORCES 



If several forces act on a body, and if they are replaced by 

 a single force that has the same effect in moving the body 

 through space as the several forces combined, the single force 

 is called the resultant of the several forces; and, conversely, 

 the several forces are called the components of the single 

 force. The process of finding the resultant when the various 

 components are known is called the composition of forces. 



Parallelogram of Forces. When 

 two forces act on a body at the 

 same time and at the same point, 

 but at different angles, their final 

 effect may be obtained as follows: 

 In Fig. 2, let A be the com- 

 _ mon point of application of the 

 **'* two forces, and let AB and 



F IG; 2 AC represent the magnitude and 



direction of the forces. Let, for instance, the line AB repre- 

 sent the distance that the force AB would cause the body to 

 move in a certain length of time; similarly, let AC represent 

 the distance that the force A C woul'd cause the body to move 

 in the same length of time, when both forces are acting 

 separately. A fundamental law of mechanics states that the 

 motion is proportional to the force applied, and, therefore, 

 while AB and AC represent the magnitude of the forces to 

 some scale, they are also proportional to the distances these 

 forces would move the same body in the same length of time. 

 The force AB, acting alone, would carry the body to B. If 

 the force AC were now to act on the body, it would carry it 

 along the line BD, parallel to AC, to a point D, at a distance 

 from B equal to AC. Join C and D, then CD is parallel to 

 AB and ABDC is a parallelogram. Draw the diagonal AD. 

 The body will stop at D, whether the forces act separately 

 or together, but if they act together, the path of the body 

 will be along AD, the diagonal of the parallelogram. More- 

 over, the length of the line AD represents the magnitude of 

 a force, which, acting at A in the direction AD, would cause 

 the body to move from A to D; in other words, AD, measured 

 to the same scale as AB and AC, represents the magnitude 



