An Elementary Treatise on Kinematics and Kinetics (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1876 Excerpt: ... separate. At any rate a finite change is almost instantaneously produced in the motion of each, and therefore each must have exerted on the other an impulsive force to produce this change. The two forces thus brought into play are, by Law III., equal and opposite. Let the bodies be smooth spheres, A and A'. Then, since they are smooth, the mutual action between them must be wholly normal, and, since they are spheres, it must be in the line joining their centres, called their line of centres. Then, by Law II., the only change, which takes place in the motion of either, must be in this line. 162. Direct Impact.--In the first place let their centres be moving before impact in this straight line; and therefore after impact the centres will continue to move in it. Let m and ml denote the masses of A and A'. Suppose that they are both moving one way before impact, say from left to right. Let u and u' denote their velocities before impact. The case of one ball meeting the other would be allowed for by changing the sign of one velocity, say u'. Let v and v' denote the velocities after impact. Thus v will be positive, or negative, according as A is moving after impact from left to right, or from right to left. Similarly for v' and A'. Then mu--mv denotes the change in the momentum of A, m'u'--m'v' A'. Let R denote the amount of force exerted by A on A', and therefore--R the amount exerted by A' on A. These produce the above changes. Therefore, Art. 123, mu--mv=--R... (1), m'u'--m'v'=R... (2). These equations are not sufficient to determine v, v' and R. To find a third equation we must consider whether or not the bodies tend to separate after impact, i.e. whether the bodies are elastic or inelastic. I. Inelastic Bodies.--No separation takes p...