Chapter 5 : Equilibrium of Forces 71
5.7. CONVERSE OF THE LAW* OF TRIANGLE OF FORCES
If three forces acting at a point be represented in magnitude and direction by the three sides a
triangle, taken in order, the forces shall be in equilibrium.
5.8. CONVERSE OF THE LAW† OF POLYGON OF FORCES
If any number of forces acting at a point be represented in magnitude and direction by the sides
of a closed polygon, taken in order, the forces shall be in equilibrium.
Example 5.11. An electric light fixture weighing 15 N hangs from a point C, by two strings AC
and BC. The string AC is inclined at 60° to the horizontal and BC at 45° to the horizontal as shown
in Fig. 5.27.
Fig. 5.27.
Using Lami’s theorem, or otherwise, determine the forces in the strings AC and BC.
††Solution. Given. Weight at C = 15 N
Let TAC = Force in the string AC, and
TBC= Force in the string BC.
First of all, draw the space diagram for the joint C and name the forces according to Bow’s
notations as shown in Fig. 5.28 (a). The force TAC is named as RQ and the force TBC as PR.
Fig. 5.28.
Now draw the vector diagram for the given system of forces as shown in Fig. 5.28 (b) and as
discussed below :
* Triangle Law of Forces states, “If two forces acting simultaneously on a particle be repressented in
magnitude and direction by the two sides of a triangle taken in order, their resultant may be represented
in magnitude and direction by the third side of the triangle, taken in the opposite order.”
† Polygon Law of Forces states, “If a number of forces acting simultaneously on a particle be represented in
magnitude and direction by the side of the a polygon taken in order, then the resultant of all these forces
may be represented in magnitude and direction by the closing side of the polygon, taken in the opposite
order”.
†† We have already solved this example analytically as 5.1.