An Elementary Treatise of Natural Philosophy

Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: CHAPTER II. OF STATICS, Or the Equilibrium produced by the composition of several Forces applied to the same material point. 1. When a single force is applied to a material particle, it is evident, that this particle, in virtue of its inertia, ought to move in the direction of the force; but when several...
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Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: CHAPTER II. OF STATICS, Or the Equilibrium produced by the composition of several Forces applied to the same material point. 1. When a single force is applied to a material particle, it is evident, that this particle, in virtue of its inertia, ought to move in the direction of the force; but when several forces act simultaneously, on a material particle, or on a system of such particles, two cases are presented, which it is necessary to distinguish. It sometimes happens that the whole of these forces communicate motion to the system; but it may also happen, that they mutually destroy each other, in which case the system will remain at rest The repose, thus produced, from the compensation of several acting forces, is known by the name of equilibrium; and the science which considers the relation, which these forces must have among themselves, in magnitude and direction, to produce this equilibrium, is called statics. 2. The most simple case of equilibrium, is that in which two equal forces are applied in opposite directions to the same material particle. This particle will then be solicited with equal energy in two opposite directions, and will evidently remain at rest. But if the intensities of the two forces be unequal, the particle will move in the direction of the most powerful, as if solicited only by their difference. 3. An equilibrium can be produced by two forces, only when they'are in direct opposition. As soon as their directions make an angle with each other, their efforts conspire in part, and the particle which they solicit, is put in motion, in a certain direction, which it is necessary to determine. In order to do this, let us begin with the most simple case, which is that wherein the two forces to be combined, have equal intensities. 4. Let M (fig....