By F. Seely, N. Ensign [non-OCR]
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Extra info for Analytical Mechanics for Engineers
PROBLEMS 3. Given the three concurrent forces as shown in Fig. 7. Find the magnitude and the sense of the component of the system (sum of the components FUNDAMENTAL CONCEPTIONS AND DEFINITIONS 14 of the forces) along the line A B. Solve algebraically and check the result by the graphical method. Ans. 2 Sense, Ib. Downward to the left. so ib 2011) 30 ' ,200 Ib. ,801b FIG. FIG. 7. 8. 4. Resolve the weight of 200 Ib. (Fig. 8) into (a) two rectangular components perpendicular and parallel respectively to AC, (6) into two components parallel to 5.
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. 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.
13 is in accordance with the principle of moments. It is often convenient to obtain the moment of a force about a point in its plane (or about an axis through the point It will about a line as perpendicular to the plane) by finding the sum of the moments of rectangular components. In accordance with the principle of transmissibility a force may be resolved into components at any its point along its line of action. Thus, in Fig. 15, Fx and Fv are one FUNDAMENTAL CONCEPTIONS AND DEFINITIONS 18 pair of rectangular components and F' x and F' y are another pair The moment of the force F about of components of the force F.