Conversations on Natural Philosophy, in which the Elements of that Science are Familiarly Explained

by Mrs. Marcet; Thomas P. Jones

Mrs. B. Not in all cases; for the power of gravitation sometimes produces accelerated motion; for instance, a stone falling from a height, moves with a regularly accelerated motion.

Emily. True; because the nearer it approaches the earth, the more it is attracted by it.

Mrs. B. You have mistaken the cause of its accelerated motion; for though it is true that the force of gravity increases as a body approaches the earth, the difference is so trifling at any small distance from its surface, as not to be perceptible.

Accelerated motion is produced when the force which put a body in motion, continues to act upon it during its motion, so that its velocity is continually increased. When a stone falls from a height, the impulse which it receives from gravitation in the first instant of its fall, would be sufficient to bring it to the ground with a uniform velocity: for, as we have observed, a body having been once acted upon by a force, will continue to move with a uniform velocity; but the stone is not acted upon by gravity merely at the first instant of its fall; this power continues to impel it during the whole time of its descent, and it is this continued impulse which accelerates its motion.

Emily. I do not quite understand that.

Mrs. B. Let us suppose that the instant after you have let a stone fall from a high tower, the force of gravity were annihilated; the body would nevertheless continue to move downwards, for it would have received a first impulse from gravity; and a body once put in motion will not stop unless it meets with some obstacle to impede its course; in this case its velocity would be uniform, for though there would be no obstacle to obstruct its descent, there would be no force to accelerate it.

Emily. That is very clear.

Mrs. B. Then you have only to add the power of gravity constantly acting on the stone during its descent, and it will not be difficult to understand that its motion will become accelerated, since the gravity which acts on the stone at the very first instant of its descent, will continue in force every instant, till it reaches the ground. Let us suppose that the impulse given by gravity to the stone during the first instant of its descent, be equal to one; the next instant we shall find that an additional impulse gives the stone an additional velocity, equal to one; so that the accumulated velocity is now equal to two; the following instant another impulse increases the velocity to three, and so on till the stone reaches the ground.

Caroline. Now I understand it; the effects of preceding impulses continue, whilst gravity constantly adds new ones, and thus the velocity is perpetually increased.

Mrs. B. Yes; it has been ascertained, both by experiment, and calculations which it would be too difficult for us to enter into, that heavy bodies near the surface of the earth, descending from a height by the force of gravity, fall sixteen feet the first second of time, three times that distance in the next, five times in the third second, seven times in the fourth, and so on, regularly increasing their velocities in the proportion of the odd numbers 1, 3, 5, 7, 9, &c. according to the number of seconds during which the body has been falling.