Caroline. When I see any body moving in a circle, I shall remember, that it is acted on by two forces.
Mrs. B. Motion, either in a circle, an ellipsis, or any other curve-line, must be the result of the action of two forces; for you know, that the impulse of one single force, always produces motion in a right line.
Emily. And if any cause should destroy the centripetal force, the centrifugal force would alone impel the body, and it would, I suppose, fly off in a straight line from the centre to which it had been confined.
Mrs. B. It would 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; if a stone, whirled round in a sling, gets loose at the point A, ([plate 3. fig. 2.]) it flies off in the direction A B; this line is called a tangent, 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 of the circle C.
Emily. You say, that motion in a curve-line, is owing to two forces acting upon a body; but when I throw this ball in a horizontal direction, it describes a curve-line in falling; and yet it is only acted upon by the force of projection; there is no centripetal force to confine it, or produce compound motion.
Mrs. B. A ball thus thrown, is acted upon by no less than three forces; the force of projection, which you communicate to it; the resistance of the air through which it passes, which diminishes its velocity, without changing its direction; and the force of gravity, which finally brings it to the ground. The power of gravity, and the resistance of the air, being always greater than any force of projection we can give a body, the latter is gradually overcome, and the body brought to the ground; but the stronger the projectile force, the longer will these powers be in subduing it, and the further the body will go before it falls.
Caroline. A shot fired from a cannon, for instance, will go much further, than a stone projected by the hand.
Mrs. B. Bodies thus projected, you observe, describe a curve-line in their descent; can you account for that?
Caroline. No; I do not understand why it should not fall in the diagonal of a square.
Mrs. B. You must consider that the force of projection is strongest when the ball is first thrown; this force, as it proceeds, being weakened by the continued resistance of the air, the stone, therefore, begins by moving in a horizontal direction; but as the stronger powers prevail, the direction of the ball will gradually change from a horizontal, to a perpendicular line. Projection alone, would drive the ball A, to B, ([fig. 3.]) gravity would bring it to C; therefore, when acted on in different directions, by these two forces, it moves between, gradually inclining more and more to the force of gravity, in proportion as this accumulates; instead therefore of reaching the ground at D, as you suppose it would, it falls somewhere about E.