A treatise on mechanics, applied to the arts; including statics and hydrostatics / By the Rev. H. Moseley ... Published under the direction of the committee of General Literature and Education, appointed by the Society for Promoting Christian Knowledge.

  • Moseley, Henry, 1801-1872.
Date:
1847
Catalogue details

Licence: Public Domain Mark

Credit: A treatise on mechanics, applied to the arts; including statics and hydrostatics / By the Rev. H. Moseley ... Published under the direction of the committee of General Literature and Education, appointed by the Society for Promoting Christian Knowledge. Source: Wellcome Collection.

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    straight line with p3p3. p3p3, when produced, must, therefore, pass through o. The above demonstration applies, strictly, only to that case in which the directions of the forces, when produced, meet at some point within the body; it may, however, be applied to the equally common case, in which they meet at some point without it. For let us sup¬ pose ?! and p2, when produced, to meet in a point o, without the body. Then, although we cannot at present suppose the forces to be applied to the body in o, the body, in fact, not ex¬ isting there, yet we may suppose it to be extended, so as to include that point, without altering the conditions of the equilibrium; provided, that by so extending it we do not in any ■way add to or diminish the forces which already act upon it. The forces and their points of application remaining the same, it is clear, that if they were in equilibrium before, they will be so now. Now conceiving the body to be thus extended, so as to include the point o, the case will resolve itself into that which we have before considered. Applications of the Principle of the Parallelogram of Forces. There is scarcely any case of equilibrium, in which the principle of the composition of forces acting upon a point does not find its application. Out of the variety of illustrations which present themselves, we shall select the following:— 23. Let us suppose a given weight, w, to be supported, as in the accompanying figure, by means of a horizontal beam, a c, abutting in a vertical wall at a, and sustained at its opposite extremity by an oblique stay, bc; and let it be required to determine the thrust* and strain upon the timbers A c and b c, and upon the wall at a and b. Draw b d paral¬ lel to ac, and cd to ab; divide cd into as many equal parts as there are units of weight in w, and find how many such parts there are in c a and c b. The numbers thus obtained will equal * A thrust is that force which, acting in the direction of the length of a timber, tends to compress it. A strain, that which tends to lengthen it.'