MECHANICS 89 



and direction of the combined effect of the two forces AB 

 and AC. 



The force represented by the line AD is the resultant of 

 the forces AB and AC. Suppose that the scale used was 

 50 Ib. to the inch; then, if AB = 50 Ib. and AC=62$ lb., the 

 length of AB would be 50-5-50 = 1 in., and the length of AC 

 would be 62.5-5-50 = 11 in. If the line AD measures If in., 

 the magnitude of the resultant, which it represents, would be 

 UX50 = 87} lb. 



Therefore, a force of 87i lb., acting on a body at A, in the 

 direction AD, will produce the same result as the combined 

 effects of a force of 50 lb. acting in the direction AB and a 

 force of 62J lb. acting in the direction AC. 



Triangle of Forces. Let Fig. 3 represent a parallelogram 

 of forces. AB and AC are the two component forces and 

 AD is the resultant. Now, to find this resultant AD without 

 drawing the entire parallelogram, first lay off AB, and then 

 from the point B lay off BD 

 equal to AC and parallel to its 

 line of action; then, draw AD, 

 which completes the triangle 

 ABD and makes it unnecessary 

 to draw AC and CD. Or, 

 the force AC could be drawn * 

 first, and then from C, the line F IG - 3 



CD, thus completing the triangle ACD and not drawing AB 

 and BD. In either case, it is seen that, if desired, the result- 

 ant of two forces can be found by drawing a triangle instead 

 of a parallelogram. 



Resultant of Several Forces. When three or more forces 

 act on a body at a given point, their resultant may be found 

 as follows: Find the resultant of any two forces; treat this 

 resultant as a single force, and combine it with a third force 

 to find a second resultant. Combine this second resultant 

 with a fourth force, to find a third resultant, etc. After all 

 the forces have been thus combined, the last resultant will 

 be the resultant of all the forces, both in magnitude and 

 direction. The order in which the forces are taken is 

 immaterial. 



