Page images
PDF
EPUB
[blocks in formation]

MECHANICS.

CHAPTER I.

1.

DEFINITIONS AND INTRODUCTORY REMARKS.

Definition of Natural Philosophy.

NATURAL PHILOSOPHY is that branch of Science which treats of the laws of the material universe.

These laws are called laws of nature; and it is assumed that they are constant, that is, that like causes always produce like effects. This principle, which is the basis of all Science, is an inductive truth founded upon universal experi

ence.

Definition of a Body.

2. A BODY is a collection of material particles. When the dimensions of a body are exceedingly small, it is called a material point.

Rest and Motion.

3. A body is at rest when it retains the same absolute position in space; it is in motion when it continually changes its position.

A body is at rest with respect to surrounding objects, when it retains the same relative position with respect to them; it is in motion with respect to them, when it continually changes this relative position. These states are called relative rest and relative motion, to distinguish them from absolute rest and absolute motion. It is highly probable that no object in the universe is in a state of absolute

rest.

Trajectory.

4. The path traced out, or described by a moving point, is called its trajectory. When this trajectory is a straight line, the motion is rectilinear; when it is a curved line, the motion is curvilinear.

Translation and Rotation.

5. When all of the points of a body move in parallel straight lines, the motion is called motion of translation; when the points of a body describe arcs of circles about a straight line, the motion is called motion of rotation. Other varieties of motion result from a combination of these two.

Uniform and Varied Motion.

6. The velocity of a moving point, is its rate of motion. When the point moves over equal spaces in any arbitrary equal portions of time, the motion is uniform, and the velocity is constant; when it moves over unequal spaces in equal portions of time, the motion is varied, and the velocity is variable. If the velocity continually increases, the motion is accelerated; if it continually decreases, the motion is retarded.

Forces.

7. A FORCE is anything which tends to change the state of a body with respect to rest or motion.

If a body is at rest, anything which tends to put it in motion is a force; if it is in motion, anything which tends to make it move faster, or slower, is a force. The power with which a force acts, is called its intensity.

Forces are of two kinds: extraneous, those which act upon a body from without; molecular, those which are exerted between adjacent particles of bodies.

An extraneous force may act for an instant and then cease, in which case it is called an impulse, or an impulsive force; or it may act continuously, in which case it is called an incessant force. An incessant force may be regarded as made up of a succession of impulses acting at equal but exceedingly small intervals of time. When these successive

impulses are equal, the force is constant; when they are unequal, the force is variable. The force of gravity at any given place, is an example of a constant force; the effort of expanding steam, is an example of a variable force.

Molecular forces are of two kinds; attractive, those which tend to draw particles together; repellent, those which tend to separate them. These forces also exert an arranging power by virtue of which the particles of bodies are grouped into definite shapes. The phenomena of crystalization present examples of this action. Molecular forces of both kinds are continually exerted between the particles of all bodies, and upon their variation, in intensity and direction, depend the conditions of bodies, whether solid, liquid, or gaseous.

8.

Classification of Bodies.

Bodies are divided into two classes, solids and fluids. A solid is a body which has a tendency to retain a permanent form. The particles of a solid adhere to each other so as to require the action of an extraneous force of greater or less intensity to separate them. A fluid is a body whose particles move freely amongst each other, each particle yielding to the slightest force. Fluids are divided into liquids and gases, liquids being sensibly incompressible, whilst gases are highly compressible. Many bodies are capable of existing in either of these states according to their temperature. Thus ice, water, and steam, are simply three different states of the same body.

Gravity.

9. Experiment and observation have shown that the earth exercises a force of attraction upon all bodies, tending to draw them towards its centre. This force, which is exerted upon every particle of every body, is called the force of gravity.

When a body is supported, the force of gravity produces pressure or weight; when it is unsupported, the force produces motion. Experiment and observation have shown that the entire force of attraction exerted by the earth upon any body, varies directly as the quantity of matter in the body,

and inversely as the square of its distance from the centre of the earth. This force of attraction is mutual, so that the body attracts the earth according to the same law. Observation has shown that this law of mutual attraction extends throughout the universe, and for this reason it has received. the name of universal gravitation.

Weight.

10. The WEIGHT of a body is the resultant action of the force of gravity upon all of its particles. If the body therefore remain the same, its weight at different places will vary directly as the force of gravity, or inversely as the square of its distance from the centre of the earth.

Mass.

11. The MASS of a body is the quantity of matter which it contains. Were the force of gravity the same at every point of the earth's surface, the weight of a body might be taken as the measure of its mass. -But it is found that the force of gravity increases slightly in passing from the equator towards either pole, and consequently the weight of the same body increases as it is moved from the equator towards either pole; its mass, however, remains the same. If we take the weight of a body at the equator as the measure of its mass, it follows from what has just been said, that the mass will be equal to the weight at any place, divided by the force of gravity at that place, the force of gravity at the equator being regarded as the unit; or, denoting the mass of any body by M, its weight at any place by W, and the force of gravity at that place by g, we shall have

[blocks in formation]

The expression for the mass of a body is constant, as it should be, since the quantity of matter remains the same.

The UNIT OF MASS is any definite mass assumed as a standard of comparison. It may be one pound, one ounce, or any

« PreviousContinue »