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force, line, direction, application, body and action

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STATICS, This subject, called Statics, is a branch of Mechanics. It deals with principles relating especially to forces which act upon bodies at rest, and with their useful applications.

There are two quite different methods of carrying on the discussions and computations. In one, the quantities under con sideration are represented by lines and the discussion is wholly by means of geometrical figures, and computations are carried out by means of figures drawn to scale; this is called the graphical method. In the other, the quantities under consideration are represented by symbols as in ordinary Algebra and Arithmetic, and the discussions and computations are carried on by the methods of those branches and Trigonometry; this is called the algebraic method. In this paper, both methods are employed, and generally, in a given case, the more suitable of the two.

I. Force.

The student, no doubt, has a reasonably clear idea as to what is meant by force; yet it may be well to repeat here a few definitions relative to it. By force is meant simply a push or pull. Every force has magnitude, and to express the magnitude of a given force we state how many times greater it is than some standard force. Convenient standards are those of weight and these are almost always used in this connection. Thus when we speak of a force of 100 pounds we mean a force equal to the weight of 100 pounds.

We say that a force has direction, and we mean by this the direction in which the force would move the body upon which it acts if it acted alone. Thus, Fig. 1 represents a body being pulled to the right by means of a cord; the direction of the force exerted upon the body is horizontal and to the right. The direc tion may be indicated by any line drawn in the figure parallel to the cord with an arrow on it pointing to the right.

We say also that a force has a place of application, and we mean by that the part'or place on the body to which the force is applied. When the place of application is small so that it may be regarded as a point, it is called the "point of application." Thus

the place of application of the pressure (push or force) which a locomotive wheel exerts on the rail is the part of the surface of the rail in contact with the wheel. For practically all purposes this pressure may be considered as applied at a point (the center of the surface of contact), and it is called the point of application of the force exerted by the wheel on the rail.

A force which has a point of application is said to have a line of action, and by this term is meant the line through the point of application of the force parallel to its direction. Thus, in the Fig. 1, the line of action of the force exerted on the body is the line representing the string. Notice clearly the distinction between the direction and line of action of the force; the direction of the force in the illustration could be represented by any horizontal line in the figure with an arrowhead upon it pointing toward the right, but the line of action can be rep resented only by the line representing the string, indefinite as to length, but definite in position.

That part of the direction of a force which is indicated by means of the arrowhead on a line is called the sense of the force. Thus the sense of the force of the preceding illustration is toward the right and not toward the left.


Specification and Graphic Representation of a Force.

For the purposes of statics, a force is completely specified or described if its (1) magnitude, (2) line of action, and (3) sense are known or given.

These three elements of a force can be represented graphically, that is by a drawing. Thus, as already explained, the straight line (Fig. 1) represents the line of action of the force exerted upon the body; an arrowhead placed on the line pointing toward the right gives the sense of the force; and a definite length marked off on the line represents to some scale the magnitude of the force. For ex ample, if the magnitude is 50 pounds, then to a scale of 100 pounds to the inch, one-half of an inch represents the magnitude of the force.

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