Elastic Collisions in 2D

<h1>Text Preview</h1> <p> Now let's look at each type of collision separately and find the final velocity of the objects. First, let's look at elastic collisions. Consider two balls with masses m1 and m2 and velocities v1 and v2. The initial momentum of the system is the sum of the momentums of the balls: pi = p1i + p2i. After collision, the total momentum of the system is equal to the sum of the momentums of the individual balls after collision The momentum of each ball is equal to its mass times its velocity. Because of conservation of momentum, we can set the total initial and final momentums equal to each other. In an elastic collision, kinetic energy and momentum are both conserved. Thus we can set total initial kinetic energy equal to total final kinetic energy. Examination of equations 1 and 2 shows that they have only 2 unknowns, v1 and v2. Since we have two equations and two unknowns, we can solve for the two velocities. Doing this reveals that v1f is equal to its initial velocity times the difference of the objects' masses divided by the sum of the masses plus twice the mass of the second object times its initial velocity divided by the sum of the masses of the objects. Similarly, we find that v2f is equal to its initial velocity times the difference of the objects' masses divided by the sum of the masses, plus twice the mass of the first object times its initial velocity divided by the sum of the masses of the objects.</p> <p id="TextCopyright">Copyright 2006 The Regents of the University of California and Monterey Institute for Technology and Education</p>