Mr. Seymour answered this question, by observing that, if the hand possessed the same degree of feeling as the face, they would both suffer equally under the conflict. “If,” continued he, “you strike a glass bottle with an iron hammer, the blow will be received by the hammer and the glass; and it is quite immaterial whether the hammer be moved against the bottle at rest, or the bottle be moved against the hammer at rest, yet the bottle will be broken, though the hammer be not injured; because the same blow which is sufficient to shiver the glass is not sufficient to break or injure a lump of iron. In like manner, the blow that is sufficient to pain your sensitive face, and make your ears tingle, will not occasion the least annoyance to the obtuse hand of your preceptor. The operation of this law,” continued Mr. Seymour, “will be exemplified in every step of our progress. When the marble, as it rolls along, strikes any obstacles, it receives, in return, a corresponding blow, which will be found to influence its subsequent direction. The peg of the top, as it rubs on the ground, is as much influenced by the friction, as if a force were actually applied to it when in a state of rest; and when we consider the forces by which the kite is made to ascend into the air, you will learn, from the same law, the nature of that advantage which you derive from running with it.”
The vicar observed that the subject of Momentum might be introduced, and advantageously explained, upon this occasion.
“Momentum,” said Tom; “and pray what is that?”
“It is a power,” replied his father, “intimately connected with motion; and, therefore, as your friend, the vicar, justly remarks, may be very properly introduced before we quit that subject.--It is the force with which a body in motion strikes against another body.”
“That,” observed Tom, “must of course depend upon the velocity of the body’s motion.”
“Undoubtedly, my dear; the quicker a body moves, the greater must be the force with which it would strike against another body; but we also know that the heavier a body is, the greater also will be its force; so that momentum, you perceive, must have a relation to both these circumstances, viz. velocity, and weight; or, to speak more correctly, the momentum of a body is composed of its quantity of matter, multiplied by its quantity of motion: for example, if the weight of a body be represented by the number 3, and its velocity also by 3, its momentum will be represented by 3 x 3 = 9; so that, in producing momentum, increased velocity will always compensate for deficiency of matter, and a light body may thus be made a more effective force than a heavy one, provided that its velocity be proportionally increased; thus, a small ball weighing only two pounds, and moving at the rate of five hundred feet in a second, will produce as much effect as a cannon ball of ten pounds in weight, provided it moved only at the rate of one hundred feet in the same time.”
“Let me see,” cried Tom, “whether I understand your statement. We must multiply, as you say, the weight by the velocity; the weight of the small ball you state at two pounds, and it travels at the rate of five hundred feet in a second; then its momentum must be a thousand. The weight of the great ball is ten pounds, its velocity only a hundred feet, then its momentum must also be a thousand; because, in both cases, the sums multiplied into each other will give the same product.”
“Exactly: and thus you perceive that the small ball becomes an exact balance to the larger one; the first making out in motion what it wanted in matter, while the latter makes out in matter what it wanted in motion. I wish you to keep this law of Momentum in your remembrance; upon it depends the action of all the mechanical powers[(8)], as they are termed.”
“I have heard,” said Louisa, “that a feather might be made to produce as much havoc as a cannon shot, if you could give it sufficient velocity.”
“Unquestionably: but there is a practical difficulty in the attempt, from the resistance of the air, which increases, as you have already seen in the experiment of the paper and penny-piece (p. 30), as the weight of a body decreases. Were it not for this resistance of the air, a hailstone falling from the clouds would acquire such a momentum, from its accelerated velocity, as to descend like a bullet from a gun, and destroy every thing before it; even those genial showers which refresh us in the spring and summer months, would, without such a provision, destroy the herbage they are so well calculated to cherish. Had the elephant possessed the mobility of the beetle, it would have overturned mountains. From this view of the subject of Momentum,” continued Mr. Seymour, “you will easily understand why the immense battering rams, used by the ancients, in the art of war, should have given place to cannon balls, of but a few pounds in weight. Suppose, for example, that the battering ram of Vespasian weighed 100,000 pounds, and was moved, we will admit, with such a velocity, by strength of hands, as to pass through 20 feet in one second of time, and that this was found sufficient to demolish the walls of Jerusalem, can you tell me with what velocity a 32-pounder must move to do the same execution?”