“Exactly. Have you ever observed what happens during the trundling of a mop? The threads which compose it fly off from the centre, but being confined to it at one end they cannot part from it: while the water which they contain being unconfined, is thrown off in right lines.”
“I have certainly observed what you state,” said Louisa; “the water flies off in all directions from the mop.”
“Yes,” added Tom, “the water was not acted upon by the centripetal force as the threads were, and consequently, there was nothing to check the centrifugal force, which carried the water off in a straight line from the centre.”
“You are not quite correct,” said Mr. Seymour; “the water does not fly off in a right line from the centre, but in a right line in the direction in which it was moving at the instant of its release; the line which a body will always describe under such circumstances, is called a tangent, because it touches the circumference of the circle, and forms a right-angle with a line drawn from that point of the circumference to the centre: but I will render this subject more intelligible by a diagram.
“Suppose a body, revolving in the circle, was liberated at a, it would fly off in the direction ab; if at c, in that of cd; and if at e, in that of ef; and so on. Now, if you draw lines from these several points to the centre of the circle, you will perceive that such lines will form, in each case, a right-angle. In the experiment which you have just witnessed, the surface of the water must have formed, during its revolution, a right-angle with the string, and consequently could not have fallen out of the wine-glass. A knowledge of this law,” continued Mr. Seymour, “will explain many appearances which, although familiar, I dare say, have never been understood by you. You may remember accompanying me to the pottery, to see the operation of the turning-lathe; it was owing to the centrifugal force produced by the rotation of the wheel, that the clay, under a gentle pressure, swelled out so regularly; from a similar cause, the flour is thrown out of the revolving mill as fast as it is ground; and I shall presently show you that you are indebted to this same force for the spinning of your top and the trundling of your hoop. But let us quit this subject for the present, and pursue the stone in its course after it is liberated from the sling. Louisa has justly observed that it described a curve; can you explain why it should deviate from a straight line?”
“Let me see,” said Tom, thoughtfully; “it would be acted upon by two forces, one carrying it forward in a right line, the other bringing it to the earth; it would, therefore, not obey either, but describe a diagonal: but why that diagonal should be a curve I cannot exactly explain.”
“Then I will give you the reason,” said his father. “A stone projected into the air is acted upon by no less than three forces; the force of projection, which is communicated to it by the hand or the sling; the resistance of the air through which it passes, and which diminishes its velocity without changing its direction; and the force of gravity, which ultimately brings it to the ground. Now, since the power of gravity and the resistance of the air will always be greater than any force of projection we can give a body, the latter must be gradually overcome, and the body brought to the ground; but the stronger the projectile force, the longer will those powers be in subduing it, and the farther will the body go before it falls. A shot fired from a cannon, for instance, will go much farther than a stone thrown from your hand. Had the two forces which acted upon the stone, viz. those of projection and gravity, both produced uniform motion, the body must certainly have descended through the diagonal; but since gravity, as you have already learned, is an accelerating force, the body is made to describe a curve instead of a straight line.
“This law, however, will require the aid of a diagram for its explanation. Let X represent the ball at its greatest altitude, X Y the force of gravity drawing it downward; and X Z that of projection. We have here, then, two forces acting in the direction of the two sides of a parallelogram. In passing on to Z, the ball will perform the diagonal X a; and in the next equal space of time, will descend through three times the distance Z a, and will consequently be found at b; while in the next period it will fall through five equal spaces, and pass to c; and in the next period, again, as it must fall seven such spaces, it will reach the ground at d, having described a portion of a curve from X to d, or during the time that the two forces were in simultaneous operation. The same principle will explain the curved ascent of the ball, substituting only the laws of retarded for those of accelerated motion; for it is clear, that the body during its ascent, will be retarded in the same degree in which it was accelerated during its descent.”