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

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Extra info for Analytical Mechanics for Engineers

Example text

2000 lb. 1500 lb. and carrying four RESULTANTS OF FORCE SYSTEMS 42 An arm mounted on an axle at 27. (Fig. 39) is acted Determine the resultant of the shown. on by the four forces forces. Solution. 20 Ib. R = ZF = 15 + 15 -20 -10=0. 24 lb. 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.

In the two preceding arti- was assumed that a certain body was acted on by two other bodies, and the action of a third body was found cles it which FIG. 3. allowed to replace the two would have the same external effect on the body in question. The reverse of this process, namely, the resolution of a force, if importance in mechanics. The action of one body be may replaced by that of two bodies. The resolution of a force is accomplished by means of the parallelogram and triangle laws and the components (resolved parts) may be found graphically or For example, in Fig.

The origin) and the distance d moment is is called moment-center the moment-arm. , etc. , respect to a point may 15 of a force also be regarded as the moment with of the with respect to the line which passes through the point perpendicular to the plane determined by the point and the action line of the force. Thus, in Fig. 10, Fd also represents the moment of F about the axis YY. The physical significance of the moment of a force as defined above is built up intuitively from our experiences in which we have exerted moments on other bodies.