APPLIED MECHANICS FOR ENGIN

CHAPTER I

DEFINITIONS

1. Introduction. The study of the subject of mecl of engineering involves a study of matter, space, and The subject as presented in this book consists of two I viz., statics, including the study of bodies under the a of systems of forces that are in equilibrium (balan and dynamics, including a study of the motion of bod

2. Force. A body acted upon by the attraction repulsion of another body is said to be subjected t attractive or repulsive force, as the case may be. Fo are usually defined by the effects produced by them for example, we say, a force is something that produ motion or tends to produce motion, or changes or te to change motion, or that changes the size or shape o body. The study of relations between forces and motions produced by them is usually designated as study of Statics and Dynamics. Forces always occur pairs; for example, a book held in the outstretched ha exerts a downward pressure on the hand, and the ha exerts an equal upward pressure on the book.

3. Unit of Force. The unit of force used by enginee in this country and England is the pound avoirdupois.

is sometimes, however, necessary to use the absolute unit of force. This may be defined as follows: The absolute unit of force is that force which acting on a unit mass during unit time will produce in the mass, unit velocity. This absolute unit of force is called a poundal. In France, Germany, and other countries where the centimeter-gramsecond system is used, the engineer's unit of force is the kilogram. The absolute unit of force, in such countries, is the force which acting upon a mass of one gram weight (at Paris) will produce a velocity of one centimeter per second, in a second. Such a unit is called a dyne. ̧

4. Unit Weight. The weight of a cubic foot of a substance will be called the unit weight of the substance and will be represented by 7. Below is given a table of such weights taken at the sea level. It will be seen that the unit weight of a substance divided by the unit weight of pure water gives its specific gravity. (See Table I on opposite page.)

5. Rigid Body. In studying the state of motion or rest of a body due to the application of forces acting upon it, it is not necessary to consider the deformation of the body itself, due to the forces. When so considered it is customary to say that the body is a rigid body. Unless otherwise stated bodies will be considered as rigid bodies in this book.

6. Inertia. The property of a body that causes it to continue in motion, if in motion, or remain at rest, if at rest, unless acted upon by some other force, is called inertia. This is Newton's First Law of Motion. (See Art. 76.)

7. Mass. The mass of a body is the quantity a matter it contains. Mass differs from weight, in tha the weight varies with the position on the surface of the

earth and with the height above the surface, while the mass remains the same. The engineer's definition of mass, viz. that it is equal to the weight divided by the acceleration of gravity (see Art. 76), may be expressed

G M: =

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Both G and g vary for different localities, but the quotient is constant; that is, the quantity of matter in a body is independent of its position with reference to the earth. The weight of a body may be determined by means of the spring balance. Such a balance is the only true measure of weight, since the equal-armed balance gives the same weight regardless of distance from the center of the earth. The equal-armed balance really

measures mass.

8. Displacement. - By the displacement of a body is meant its change from one position to another. A displacement involves a movement in a definite direction. It may be represented by an arrow, the length of the arrow representing the distance moved and the direction of the arrow the direction of the motion. Thus, if a man walks due east one mile and then due north one mile, we might represent his displacement from the original position by an arrow drawn northeast of a length equal to √2 miles. Or, in Fig. 1, if P2 represents a displacement of a body in the direction indicated and P, a subsequent displacement in the direction of P1, then R represents a displacement equivalent to P1 and P2. It is seen that R may be determined by constructing a parallelogram on P1 and P2 as sides and drawing the diagonal. Quantities that may be represented by arrows are known as vector quantities, and the arrows themselves as vectors.

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