CHAPTER IV 
THE POLYGON OF FORCES | 
52. Composition and Resolution of Forces.—The single force 
which would produce the same effect as a number of forces acting 
together is called the resultant of these forces, and the forces are called 
components of their resultant. : 
The single force which will balance a. number of forces acting together 
is called the equilibrant of these forces. The equilibrant has the same 
magnitude as the resultant, and acts along the same line, but in the 
opposite direction. 
The process of finding the resultant of a number of forces is called 
the composition of forces, and the converse process of replacing a forces 
by two or more components is called the resolution of a force. 
The resultant of a number of forces acting in the same straight line 
is equal to the algebraical sum of the forces. If forces acting in one 
direction along a straight line are positive (+), those acting in the 
opposite direction are negative (— ). 
53. Parallelogram of Forces and Triangle of Forces.—If OP 
and OQ (Fig. 28) represent in magni- 
tude and direction two forces acting 0 piesa ge g 2:8 
at the point O, then the diagonal / 
OR of the parallelogram OPRQ will / 
represent the magnitude and the Q ~~~ c 
direction of their resultant, Con- Fria. 28 
versely, if a parallelogram OPRQ be Mare 
described on OR as diagonal, OP and OQ will represent components of 
the force represented by OR. 
In applying the parallelogram of forces OPRQ it should be noticed 
that the forces OP and OQ must both act either from O towards P and 
Q respectively, or towards O from P and Q respectively. Since the only 
difference between the resultant and the equilibrant of two forces is that 
the sense of the one is opposite to the sense of the other, the parallelo- 
gram of forces may be applied to find the equilibrant of two forces. 
If AB and BC be drawn parallel and equal to OP and OQ respec- 
tively, and CA be joined, then it is obvious that the triangle ABC is equal 
in all respects to the triangle OPR, and therefore AC is equal and 
parallel to OR. Hence the resultant or the equilibrant of two forces 
OP and OQ may be. determined by drawing the triangle of forces ABC. 
If arrow-heads be placed on the sides of the triangle of forces to show 
the sense of the forces, then, when two forces and their resultant are 
represented, the arrow-head for the resultant will point in the opposite 
direction round the triangle to that of the other two arrow-heads. But 
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