# Polygon of Forces

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## Polygon of Forces

a broken line that is constructed to determine the resultant vector (geometric sum) of a given system of forces. In order to construct a force polygon for the system of forees F_{1}, F_{2}, … , F_{n}; (Figure 1, a), we successivel plot the following vectors in the chosen scale. The vector which represents the force F_{1}, is plotted from an arbitrary point *a;* the vector which represents the force F2, is plotted from the head of the first vector. Continuing in this manner, we finally reach the vector this last vector, which represents the force F_{n}, (Figure 1,b), is plotted from the head *m* of the penulti-mate force.

The figure *abc* … *mn* in Figure 1, b is called the polygon of forces, or force polygon. The vector which joins the tail of the first force with the head of the last force in the force polygon, represents the geometric sum R of the given system of forces. When the point *n* coincides with the point *a,* the force polygon is said to be closed. In this case, R = 0. The polygon law of forces can be derived by successive application of the parallelogram law of forces.

The construction of a force polygon is used in the graphical solution of problems in statics for systems offerees located in the same plane.