Science for the School and Family, Part I. Natural Philosophy

by Worthington Hooker

Fig. 129.

As liquids and aeriform substances resist solids in motion in proportion to the amount of surface which the solids present to them, so also when they strike against solids they cause motion in them in proportion to the amount of surface acted upon. Thus a violent wind could not move a lump of tin, but could blow along a sheet of it, or tear up a roofing of it if it got beneath. So clouds of sand are raised into the air in the deserts of Africa, although the particles are of the same material as stones, and therefore have the same specific gravity. For the same reason dust, feathers, the down and pollen of flowers, etc., are blown about, although they are heavier than the air. A pebble is moved more easily by a current of water than a stone, because it has a larger surface, in proportion to its weight, to be acted upon by the water. For the same reason sand is moved more easily than pebbles, and fine mud than sand, though stones, pebbles, sand, and mud may all be of the same material. This explains why you will find mud where the current is slow, sand where it is faster, pebbles and stones where it is still faster, and where the current is exceedingly rapid you find nothing but large rocks—sand, pebbles, and stones not being able to resist its force. For the same reason, in the process of winnowing, the chaff is carried away by the wind; while the grain, presenting less surface in proportion to its weight to be acted upon by the air, falls to the floor.

In all the above cases the moving water or air may be considered as acting in opposition to the attraction of the earth, the latter pulling the substance down to the earth, and the former pushing it away from the earth. Of course, the more surface the water or air has to push upon the greater is the effect; and it is to be remembered that the attraction of gravity is as the quantity of matter, without any regard to amount of surface in the body attracted.

194. Relation of Force to Velocity.—It would seem at first thought that the motion produced in any body must be in exact proportion to the force producing it; that is, that twice the force which produces a given velocity would double that velocity, and three times would treble it, etc. This is true where there are no obstacles to motion, as in the case of the heavenly bodies moving in their orbits. But in all motions here upon the earth there are obstacles; and as reaction is always equal to action, the greater the velocity the greater is the reaction of the obstacle. If, therefore, you increase the velocity of any body, you not only have to communicate more motion to it, but you must overcome also the increased reaction. The rate of increase of force for increased velocities has been very accurately ascertained.

A B C D
Fig. 130.

This I will explain. A boat moving from B to A, Fig. 130, we will suppose, displaces a quantity of water represented by the space between the two lines extending from B to A. Now if it move from B to C, it displaces twice the bulk of water B C; and as it is displaced in the same time that B A was, each particle is displaced with twice the velocity. Double the force is required to displace a double portion of water, and to do this with double the velocity the force must be doubled again. So if the boat is made to move three times as far in the same time, that is from B to D, three times the quantity of water is displaced, and each of these three portions, B A, A C, and C D, is displaced with three times the velocity. The force required, then, to do this is nine times that required to carry the boat from B to A in the same time. It is plain, therefore, that with velocities represented by the numbers 1, 2, 3, 4, etc., the forces requisite to produce these velocities must be as the squares of these numbers; viz., 1, 4, 9, 16, etc. This law is a very important one in a practical point of view. For example, it shows us how much larger a quantity of coal is required to produce in steamboats a high velocity than a moderate one. Its application too to the science of gunnery is important.

195. Relation of Shape to Velocity.—The resistance of air or water to a flat surface is greater than to a convex one, because the latter readily turns the particles to the one side and the other. So, also, a concave surface is resisted much more than a flat one, because the particles of the air or water can not so easily escape sideways. Fishes are of a spindle-like and slender shape, that they may have as little resistance as possible from the water. It is for this reason that a fish has no neck, for if it had one the upper portion of its body would, from the resistance of the water striking against it, prove a serious impediment to rapidity of motion. Mankind have in some measure imitated the shape of fishes in their boats and ships. Boats which are intended to bear light burdens and go swiftly are made very long and narrow. The webbed feet of water-fowls, when they are moved forward, are folded up so as to meet with as little resistance as possible; but when they are moved backward they are spread out so as to press against the water a broad concave surface. For the same reason the wings of a bird are made convex upward and concave downward; and when it moves its wing upward it makes it cut the air somewhat edgewise, but in moving it downward it presses directly with the whole concave surface.

196. Friction.—Friction is generally an obstacle to motion. When we roll a ball, the more rough is the surface on which we roll it the greater is the friction and the sooner is the ball stopped. Friction lessens the rapidity of motion in machinery, and to prevent this as far as possible oiling and other expedients are employed. But sometimes friction is a cause of motion, as, for example, the friction of the driving-wheels of a locomotive upon the rails. In this case the wheel pushes backward on the rail at each successive point of contact. To make this clear, suppose a common wheel is deprived of its rim and is made to revolve on the ends of its spokes. The end of each spoke gives a backward push as it strikes the ground. Now the rim of a wheel makes the same pushes, but they are more numerous—they are continuous, being made by all the successive points in the rim. Sometimes the rails of a railroad are too smooth from frost or some other cause, and then sand is thrown upon them to give the locomotive a start. The sand serves to prevent the wheels from sliding by enabling them to get some hold upon the rails in their backward pushes.