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

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

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FUNDAMENTAL CONCEPTIONS AND DEFINITIONS 26 (L 3 the dimensional equation ), is L4 +L3 = L3 and is hence the given incorrect. equation Consider also the equation P+kv = as in which P represents a force, k a weight (force) per unic volume, v a volume, a an area, and s a force per unit area. The dimensional equation then may be written, L3 That -L3 = L 2 ' L2 ' F+F = F, is, and hence the equation is dimensionally correct. Further, consider the equation E = PI , in which ae P represents a force in pounds, I a length in inches, a an area in square inches, and e a length in inches.

A equals zero and hence R = ^P2 +Q 2 +2PQ = P+Q. Similarly, the resultant of two forces P and Q having opposite senses (P being the larger of the two forces) is a force the magnitude of the sense of R being the which is given by the equation R = same as the sense of the larger force P. Hence, the resultant of any two collinear forces is a single force having the same line of action as the given forces, the magnitude and sense being indicated by the algebraic sum of the forces. The extension of this method Thus the to any number of collinear forces may easily be made.

In of the forces, that is, order to locate the line of R action of the resultant force moments will the principle of For convenience be applied. F, the origin, 0, will be taken as the center of moments. The moment -x respect to ments R to the y-axis with respect to the origin of the the origin may be if moments R then with equal to the of the moforces with respect to the same point. If the distance from the FIG. 37. sum is algebraic sum of the F2 action line of of denoted by is x, the moment of R equal to Rx.

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