Mechanics (Statics) — The resultant of coplanar forces meeting at a point

About this lesson

This unit teaches how to find the resultant of a set of coplanar forces meeting at a point, both geometrically and analytically. Geometrically, it explains the polygon of forces method, where forces are drawn head-to-tail in order and the resultant is the vector closing the polygon. Analytically, it introduces resolving forces into perpendicular components along the x and y axes, summing these components to find the resultant's magnitude and direction using the formulas R = sqrt(x^2 + y^2) and tan(theta) = y/x. The unit includes worked examples with forces given in newtons or kg.wt, often involving directions like east, north, west, south, or angles relative to these, and problems involving regular hexagons, equilateral triangles, squares, and other geometric figures. By the end, a student should be able to compute the magnitude and direction of the resultant for a set of coplanar forces meeting at a point, using both graphical and analytical methods.