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36, RESULTANTS OF FORCE SYSTEMS 40 the proposition also holds, since the sum of the moments of and OE is equal to the moment of the resultant couple. 26. Algebraic Method. A system of coplanar AO parallel forces shown in Fig. 37, the forces being parallel to the y-axis. In the of the of such determination resultant a it was system graphical is seen that the resultant was either a force or a couple. If the resultant is a force, R, its action line is parallel to the action lines of the forces of the cated system and the algebraic by sum its magnitude and sense are indi- = 2F.

Q \' and F may placed by ant RI. \ \ \ xt forces be re- their result- Likewise and F may by At their resultant P be replaced R2 . (7, the point of intersection of the lines of action of RI and R 2 , RI be resolved into components Q and F, and R2 into components P and F. The two forces F, F at C let cancel, thereby reducing the system to two collinear forces P and Q along the line DC. The resultant of these two forces, which is also the resultant of the original two forces, is a single force of magnitude P+Q along the line DC.

The data on which many engineering computations are based are determined from experiments and hence are approximate values, the degree of approximation depending on the instruments METHODS OF SOLUTION 25 and methods used, and on the care and skill of the observer. ^The computed results which are based on these values cannot have a In greater degree of accuracy than that of the original data. general a sum, difference, product, or quotient of two approximate values will not have a greater degree of accuracy than that of the least accurate of the two numbers.

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