Mechanics

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

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

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Tute a couple having a moment-arm, AB, equal to p. Through 0, the midpoint of the arm, draw any line CD making an angle 6 with AB and scale off OD and OC each equal to %p. At C introduce two opposite forces, PS and P4, which are perpendicular to CD, each of which is equal in magnitude to the PI and PZ of the given forces couple. Similarly at D intro- duce two forces, PS and PQ, perpendicular to CD, each being equal in magnitude to the forces of the given couple. Prolong the action line of PI it intersects the action until FIG.

Closes, that is, if the end of the last vector coincides with the begin- ning of the first vector, the resultant of the given system is equal to zero. Method. In Fig. 29 (a) is represented a coplanar which is concurrent. Each of the four forces of the be resolved into two components, one lying along the 23. Algebraic force system system may The z-components of the forces x-axis and one along the i/-axis. a collinear the constitute resultant of which is a force along system (6) (a) FIG. 29 The the x-axis.

Force and funicular polygons; the former determines its magnitude and direction; the latter determines a point on its action line. If the force polygon closes, that is, if E coincides with A, the rays AO and OE represent two forces which are equal in magnitude and which have parallel action lines and opposite senses. strings ao The resultant in this case is a couple provided that the funicular does not close. polygon If, however, the funicular polygon also closes, that is if ao and oe coincide, the two forces AO and OE will balance and the resultant of the given system will be equal to zero.

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