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# Two Non Para Llel Coplanar

## forces, action, resultant, sum and plane

TWO NON- PARA LLEL COPLANAR Foncr.s. The lines of action of two such forces meet in a point in their plane. Consider a case in which this point is in the rigid body on which the two forees are acting. The effect of a force upon a rigid body is evidently the same wherever its point of application is. provided it is in the line of action of the force. Therefore the action of the two forces in this ease is as if they were both ' applied at that point of the rigid body where ' their lines of action cross. Their resultant is , then found by constructing their geometrical sum at this point; for such a force has obvious ly a translational effect equivalent to the sum of the effects of the two forces, and it may he shown by simple geometry that its moment around any axis is equal to the sum of the ino ments of the two forces around that axis, and so its effect is the same as the combined effects of the two forces. The line of action of the resultant passes through the point of inter section of the two forces, but its point of appli• cation can be anywhere in this line; (muse quently, it is entirely immaterial whether the point of intersection itself is a point of the body or not.

It is evident that if the body is under the action of three forces. one of which is equal and opposite to the resultant of the other two, there is no resulting force or moment ; that is. there is neither linear nor angular acceleration. Such a condition is called 'equilibrium' (q.v./. The stability. instability. My.. of equilibrium are dis cussed in the article on Eurt Conversely, if a rigid body is in equilibrium tin der the.actimi of three non-parallel forces, their

lines of action must meet in a point. they must lie in one plane; and one must he equal and op posite to the geometrieal sum of the other two.

Two VARA 11,1-1, FORCES, Two parallel forces form a limiting case of two non-parallel coplanar forces 1.010..4. point of interseetion reeedes to an infinite distance. Their geometrieal sum then be comes their ofy, broic shun: if the two forces are in the same direction. their resultant is a form parallel to them. in the same plane, and numerie ally equal to the sum of their muuerieal rnhies; if they are in opposite directions, their resultant is a force parallel to them. in the smile plane, and numerically equal to the difference of their munerieal values. I For the time being. the ease is excluded in which the two parallel forces are equal and opposite: such a eombination is (-ailed a 'eonple,' q.v.). This resultant must have such n position relative to the two bows that its moment about any axis equals the sum of their moments about the same axis. If the forces are as shown in the figure. F, and F, being at a known distance At apart and 0 being the inter section of any axis perpendicular to their plane with the plane, OCBA, being a lino perpendieular to the forces, the resultant R must have such a position that TiBO = + Substituting for 11 its value F, + this be comes