Applied Mechanics. Made Simple by George E. Drabble PDF

By George E. Drabble

ISBN-10: 0491002084

ISBN-13: 9780491002080

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11. The point P is subjected to three forces equal to the respective string tensions. Vectors representing these forces form a closed triangle. The simple force system is shown in Fig. 11 (b). Now the triangle of forces law states that, if we draw lines parallel to each force in turn, of length proportional to the magnitude of the force, the three lines so drawn will form the closed sides of a triangle. This has been done in Fig. 11 (c) and also in Fig. 11 (d\ the difference being the order in which the forces were drawn.

We start our triangle by drawing our known downward force of 100 newtons. This we may do by drawing a vertical line, say 10 millimetres long, with the arrow pointing downwards. Now we may either draw a line from the bottom of this, parallel to Tu and from the top parallel to T2; or we can draw T2 from the bottom, and 7\ from the top. In either case, the directions of the two forces must be observed, and the line drawn in the corresponding direction. Both alternatives have been drawn in Fig. 12 (c).

These perpendicular distances are hx and h2. As the distance gets smaller, the force must be greater to exert the same moment. Now let us look at a case where there is no obvious turning point. The horizontal beam in Fig. 19 supports forces of 4, 6, 8 and 2 units (say kilonewtons) in the positions shown. It is hung from two points. The forces can be assumed to be the weights of masses attached to the beam (to keep the example simple, we shall pretend that the beam itself has no weight). The forces will cause induced reactions in the supporting wires.

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Applied Mechanics. Made Simple by George E. Drabble

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