MECHANICS.—I.
FORCE: ITS DIRECTION, MAGNITUDE, AND APPLICATION.
The aim of these Lessons is to make evident to ordinary intelligent persons, who will take a little trouble, the principles of Mechanics—to treat that subject in a popular way, yet so that the reader may form accurate notions about it, and be enabled to apply it to practice in solving common problems by calculation. We have much to do, but all depends on the way of doing it. The reader I desire to have is the intelligent mechanic or artisan, the country schoolmaster or pupil-teacher, the young student who wants to learn the science through a book without a master, the college B.A. or M.A. whose mechanics was made a mess of in his young days, and would be glad, without again going to a "coach," even late in life to learn it. I should not despair of finding even ladies among my scholars. More faith should be placed in the average human intellect than commonly is. It ought to be possible to teach the sciences of form, and number, and force to more persons than usually learn them. These are the "common things" of life, and a knowledge of the laws which regulate them ought to be within the reach of most people, if only the first principles be properly laid down and explained, consequences deduced from them in a simple and natural order, and language used which they can understand. I ask you, then, to approach the subject without fear. Study simultaneously with these lessons those upon Arithmetic; for, as we proceed, a knowledge of the four Common Rules of Arithmetic and of Proportion will be found essential. Any other mathematics you may require, I shall teach you as we go along, but the amount will be small. Observe: accurate mechanical conceptions, and the power of solving mechanical problems by construction by rule and compass or calculation, are the objects we aim at. First, then, let us ascertain what our science treats of. I believe it may accurately be described as follows:—
Mechanics is the science of force applied to a material body or bodies.
This let me fully explain. Mechanics is concerned about force—that is its great subject. But it considers it only in the consequences which follow its application to a body or bodies which must be material. A force may push through an empty point of space; but, as it can make no impression on that point, Mechanics does not consider it under such circumstances. The body to which it is applied may be of any size, even an atom of matter, sometimes termed "a material point;" and Mechanics does inquire what effect forces have on such atoms. But, in the more common problems, it is concerned about bodies of visible and tangible magnitude, such as a block of stone, a beam of timber, a girder of iron, a cannon ball, the earth itself, the moon, or the sun.
DIAGRAM ILLUSTRATING THE APPLICATION OF FORCE.
This being clearly understood and agreed on, our next question is, What is force? I answer—
Force is the power, or agent, whatever be its nature, by which motion is produced in a body, or a tendency to motion accompanied by strains or pressures in its parts.
For instance, a blow is given by the bat to the cricket ball, or a bolt is fired from a cannon: the blow in the one case, and the exploding gunpowder in the other, furnish forces, the effect of which is the motion of the ball or bolt. Steam enters the cylinder of an engine, and away to work goes the machinery connected with it, moving and printing this Popular Educator. Here again is force, the elasticity of the steam, and its effect is motion. A stone is let loose at the top of a tower, or from a balloon, and it falls to the ground: what makes it fall? The great Earth does, which, by its attraction, pulls the stone towards itself. This attraction is the force producing the stone's motion. And if any of you doubt, or feel any difficulty about this, let him take a magnet and put one of its ends near a few loose iron-filings, scattered over a piece of paper, and he will see how this is possible. The filings will move towards the magnet, and stick to it, in the very same way that the stone moves to, and sticks to, the earth until some person pulls it away by a stronger force. And so likewise does the electrified ball draw towards itself the small pieces of cork or feather we place near it. In all these cases, you see, there is, first, a body, the ball, or bolt, or stone, or iron-filing, or cork; secondly, a force applied to it; and, thirdly, motion produced.
But take now the lamp which hangs from the ceiling. It is at rest; but the earth, by its attraction, is trying to pull it down, and down it would come were we to cut the chain or rod by which it is suspended. Here, then, is force again, but it produces only tendency to motion. But observe further, that although the lamp does not move, the chain that holds it is strained by its weight. And not only is the chain strained, but so is the ceiling joist to which it is attached; and, as this joist rests its ends on the walls, this strain is transmitted to the walls in the form pressures on them. There is thus tendency to motion, strain, and pressure produced as the effect of the force applied by the earth to the lamp, but no motion. And, if any of you feel a difficulty in believing in those strains, let him suppose, instead of the lamp, a ton weight of iron suspended from the ceiling: what will follow? The chain will snap, or the joist, or even ceiling, will give way, and down all will come on the floor. They snap or give way because they are strained beyond their strength. So, in like manner, when a train stands at rest on one of those great iron girder bridges that span our rivers, there is tendency to motion, with strains and pressures; the great Earth below pulls at the train to bring it into the water; but the bridge resists, bears the pressure of the weight on it, and is strained throughout its length besides. A more familiar instance is the struggle of two wrestlers. No one will doubt that in the contest great force is put forth by each. For a moment they are motionless, like statues; the forces are balanced, but the strain on their muscles is terrific. There is in each tendency to motion, caused by the force put forth by the other, but as yet no motion. At last one of the combatants prevails; his force ends in producing motion, and his adversary falls to the ground.
These examples will, I trust, be sufficient to make clear to you the account I have given you of force, namely—that it is the agency by which motion is produced in a material body, or a tendency to motion with pressures or strains. You will now understand the reason why Mechanics is divided into two branches, Statics and Dynamics. Statics is the branch which treats of forces which balances each other, and produce only tendencies to motion with pressures and strains, and is so called from the Latin word sto, which means "to stand," or "be at rest." Forces which thus balance one another are said to be in equilibrio, a Latin expression which denotes the balancing of equal weights; and it is important that you should keep the expression in memory, as we shall have frequent occasion to use it. The other branch, Dynamics, treats of force or forces which do not balance one another, but produce motion, and was so named from the Greek word δυναμις (du'-na-mis), power, under the mistaken notion that there was more power in force when its effect is motion, than when it produces strain. This, we have seen, is not the case; but the term "Dynamics" may, notwithstanding, continue to be used without leading to error. The two branches we may therefore define or describe as follows:—
Statics is the branch of Mechanics in which forces are considered which equilibrate, or balance one another, producing tendencies to motion, with strains and pressures.
Dynamics is the branch of Mechanics in which forces are considered which produce motion.
Now it so happens that, of these branches, Statics is the simpler and easier, and more natural for the student to commence with. Questions about forces which balance each other are not so complicated as those which involve motion. The reason is, that time enters into all problems of motion, but
