First Principles of Mechanics

In our last number we introduced a pendant ball by way of illustrating the action, reaction, and counteraction of gravity and inertia. And in consideration of the vast importance of a thorough knowledge of these principles we have procured for this number a cut representation of the pendant ball, which we have introduced, and shall endeavour to be more explicit in our theoretic explanations.

If the ball is suspended by a cord or wire from the hook A, the ball will in consequence of the force of gravity, assume a position directly under the hook, and hold the cord by which it is suspended, in a position at right angles with the horizon.

The reason of this is that the ball by its weight, or the force of gravity, tends towards the centre of the earth, and its present position is precisely in a direct line between the hook and the earth's centre; and at the point nearest to the centre, that the ball can possibly approach while thus suspended. Now if this ball be moved horizontally or rather curvilinearly to C, and then let go, being restrained by the cord from descending according to its inclination, directly toward the earth, it naturally seeks the lowest possible point, and thus returns rapidly to its first position. In this instance, gravity in moving the ball from C to L, has overpowered inertia, and in consequence of this motion, inertia has become momentum; and now that the ball has approached the lowest point, and the influence of gravity with regard to the motion of the ball, being diminshed in consequence of it s direction being at this point nearly horizontal, the momentum, which the ball has acquired in its descent thus far, now carries it past this point L, and before the increasing resistance of gravity shall have been sufficient to stop the ball by overcoming this momentum, the ball will have approached to D. Then again gravity predominates and hurries the ball to L, and again momentum drives it forward to E, a little short of its starting point.--Again gravity returns the ball to L, and momentum pushes it forward to F. In this manner gravity and momentum continue the strife of alternate ascendency, till the ball has vibrated to the points G. H. I. J. and K, and finally rests at L. In the vibration of the ball, as above described, the alternate influence of gravity and momentum, are so uniform and equally balanced, that were it not for the resistance of the atmospheric air, and some little friction in the play of the cord, the motion would be prepetual. It is the uniformity of action which gives regularity to the movement of the pendulum of a clock, by which the other movements of a clock are also regulated. But the velocity of the ball, in its vibrations, depends much on the length of the cord or wire by which it is suspended. If this cord be but one foot in length, the ball will perform twice as many vibrations in a given time, as it will with a cord four feet long. The reason of this difference is, that when the cord is longer, the inclination of the curve at the extremity of the vibration is less, and consequently the force of gravity in the direction of the motion is less; and of course requires more time to overcome the inertia of the ball, in putting it in motion, and momentum in stopping it. If the distance from the hook, or point of suspension to the centre of the ball be 39 1-7 inches, the vibration will be 00 per minute. The time required for each vibration of the ball does not much depend on the extent of its motion-the space over which it passes in either direction-whether it be one foot or two feet, more or less; for if the extent of its motion be greater, the inclination of its direction at theextremities of its vibration, is also greater, an consequently the direct force of gravity being greater, the velicity of the ball from point to point is also greater, and nearly if not precisely in proportion to the distance over which it moves. Hence may be seen the peculiar adaptability of the pendulum for measuring time.