By F. Seely, N. Ensign [non-OCR]
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Additional resources for Analytical Mechanics for Engineers
Graphical Methods. The resultant of an unbalanced system of concurrent forces in a plane is a force which may be found by means of the parallelogram law. In Fig. 27 shown three forces FI, F^ and which act on a body at the point FS The forces FI and ^2 may be 0. combined into a single force Ri by are means of the parallelogram Similarly Ri and ^3 may law. be com- . Q F bined into a single force R%. R% then is the resultant of the given forces. By any number may continuing this process of concurrent forces be combined into a single forces are taken force.
A collinear the constitute resultant of which is a force along system (6) (a) FIG. 29 The the x-axis. The magnitude of this resultant is equal to 2F X ^/-components of the forces likewise constitute a collinear system the resultant of which is a force along the i/-axis of magnitude . ^F y Since the system, by this method, is reduced to two forces the resultant of the given system is the resultant of these two forces. If the magnitude of this resultant is denoted by R and the direction . which its action line makes with the in Fig.
15 lb. Therefore the resultant is not a a couple, C, the moment of which may be found by taking moments about 0. Thus, force, 24 Ib. -in. -in. will produce the same external effect on the arm (change in of 15 lb. FIG. 39. One forces, the rotational motion) as the four given is shown in the resultant couple having forces equal to 24 lb. figure. PROBLEMS 28. Fig. 40 represents a beam 12 ft. long acted upon by Find the anti-resultant of the five forces. 29. Five forces act on a body shown in Fig. 41.