481. We can easily determine by trial what effect is produced on the tension of the chain, by placing a weight upon the bridge in addition to the permanent load. Thus an additional stone weight in the centre raises the tension of the spring balance to 100 lbs.; of course the tension in the other chain is the same: and thus we find a weight of 14 lbs. has produced additional tensions of 10 lbs. each in the two chains. With a weight of 28 lbs. at the centre we find a strain of 110 lbs. on the chain.
482. These additional weights may be regarded as analogous to the weights of the vehicles which the suspension bridge is required to carry. In a large suspension bridge the tension produced by the passing loads is only a small fraction of the permanent load.
LECTURE XV.
THE MOTION OF A FALLING BODY.
Introduction.—The First Law of Motion.—The Experiment of Galileo from the Tower of Pisa.—The Space is proportional to the Square of the Time.—A Body falls 16' in the First Second.—The Action of Gravity is independent of the Motion of the Body.—How the Force of Gravity is defined.—The Path of a Projectile is a Parabola.
INTRODUCTION.
483. Kinetics is that branch of mechanics which treats of the action of forces in the production of motion. We shall find it rather more difficult than the subjects with which we have been hitherto occupied; the difficulties in kinetics arise from the introduction of the element of time, into our calculations. The principles of kinetics were unknown to the ancients. Galileo discovered some of its truths in the seventeenth century; and, since his time, the science has grown rapidly. The motion of a falling body was first correctly apprehended by Galileo; and with this subject we can appropriately commence.
THE FIRST LAW OF MOTION.
484. Velocity, in ordinary language, is supposed to convey a notion of rapid motion. Such is not precisely the meaning of the word in mechanics. By velocity is merely meant the rate at which a body moves, whether the rate be fast or be slow. This rate is most conveniently measured by the number of feet moved over in one second. Hence when it is said the velocity of a body is 25, it is meant that if the body continued to move for one second with its velocity unaltered, it would in that time have moved over 25 feet.
Fig. 66.