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By P. Sandori
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Extra info for Logic of Machines and Structures
Example text
All seems perfectly logical and a suitable experiment will confirm the result obtained in this way. However, there is a gap between the law of the . inclined plane and the triangle of forces derived bum it when it comes to forces pulling in arbitrary directions. The triangle of forces is supposed to be 51 52 ,he Inclined Plane - ~ ... ' ~ ~. 13 The stumbling block: this triangle of forces was never proved by Simon Stevin. 12 ",0 The triangle of forces in its most general form. r to the tri Isolate the jib as a fI-ee body (Fig. 18). Neglecting the self-weight of the jib and saddle, we find that there are just three forces acting on the body. Two of these, the pull T of the cable and the weight W of the load, intersect at point N. The force R acting on the . bealing A must pass through the same point. The vector triangle gives us the magnitudes of the support forces right away. The support reaction R is further resolved into its components, showing the large horizontal compo nent R" that has to be resisted by the jib bealing. Stevin obviously knew about the parallelogram; he arrived at the construction by combining two triangles and pointed out that I' H' one triangle was sufficient since side HI was the same length as side CK and side IK equal to side He. But the parallelogram, as derived from dynamics by Newton, provides the logical basis for using the triangle: the triangle is only half of the parallelogram. On the other hand, Stevin would most probably have rejected Newton's line of reasoning in stating the parallelogram rule.