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By F. Seely, N. Ensign [non-OCR]

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Resolution of a Force into a Force and a Couple. In many problems, both in statics and kinetics, it is convenient to resolve a 18. force into a force parallel to the given force, and a couple in the plane of the force. Thus, in Fig. 22, let P represent a force acting on two a body equal, linear forces P, at at opposite, any point P 0, A. Let and col- be introduced each of the forces being parallel to the original force and of the same FIG. 22. magnitude. The three forces are equivalent to the original one, since the two equal, opposite, and collinear forces have no effect on the body.

The given system of four forces (Fig. 35) was replaced by another system of eight forces which were represented in magnitude and by the rays of the force polygon and in line of action in direction by the strings of the funicular polygon. Six of these forces occur in pairs, the two forces of each pair being collinear, equal in magniObviously, the sum of the moments tude, and opposite in sense. two forces of each pair with respect to any point in their plane equal to zero. For any moment-center in the plane, by use of Varignon's theorem, the following relations may be written, of the is moment If of AB = moment " BC= " CD= " DE= of AO+moment " BO+ CO+ DO+ " " of OB, OC, OD, OE.

This triangle was constructed by FUNDAMENTAL CONCEPTIONS AND DEFINITIONS 12 or FI parallel to ac and by drawing from A a line laying off from C another line parallel to be, the two lines to ah and parallel AC Thus, the components of ^i are represented in intersecting at B. in and and BC. direction, but not in action line, by magnitude The resolution of a force into two rectangular components is of AB special importance. The particular value of resolving into rectin the fact that these components may be angular components found from very simple algebraic expressions.

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Analytical Mechanics for Engineers by F. Seely, N. Ensign [non-OCR]

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