Question
Two balls of equal mass m undergo a collision. Oneball initially stationary. After the collision, the velocities ofthe balls make angles of 31.1 degrees and 48.9 degrees relative tothe original direction of motion of the ball. a) if the initial speed of the moving ball is 2.25 m/s, whatare the speeds of the balls after the collision b) is this collision elastic? justify Two balls of equal mass m undergo a collision. Oneball initially stationary. After the collision, the velocities ofthe balls make angles of 31.1 degrees and 48.9 degrees relative tothe original direction of motion of the ball. a) if the initial speed of the moving ball is 2.25 m/s, whatare the speeds of the balls after the collision b) is this collision elastic? justify
Explanation / Answer
a)when two balls of equal mass m undergo a collision and theballs travel at different angles after the collision then thecollision is elastic.This is because the mometum and kinetic energyin this collision are conserved. By the property of eastic collision we have v1 - v2 = u2 -u1 in x direction: v1x - v2x = u2x -u1x or v1 * cos1 - v2 *cos2 = u2 - u1 (sinceu2x = u2 and u1x =u1) the initial velocities are u1 = 0,u2 =2.25 m/s and the angles are 1 = 31.1oand 2 = 48.9o or v1 * cos(31.1o) - v2 *cos(48.9o) = u2 - u1 or 0.856v1 - 0.657v2 = 2.25 - 0 or 0.856v1 - 0.657v2 = 2.25------------(1) or 0.856v1 - 0.657v2 = 2.25 - 0 or 0.856v1 - 0.657v2 = 2.25------------(1) in y direction: v1y - v2y = u2y -u1y or v1 * sin1 - v2 *sin2 = u2 - u1 (sinceu2x = u2 and u1x =u1) or v1 * sin(31.1o) - v2 *sin(48.9o) = u2 - u1 or 0.516v1 - 0.753v2 = 2.25 - 0 or 0.516v1 - 0.753v2 = 2.25--------------(2) solving equations (1) and (2) for v1 andv2 we get the speeds of the balls after thecollision. b)the collision is elastic.This is because the twoballs fly off at different angles after the collision.Thecollision is inelastic when the two balls stick together after thecollision.In this case the total momentum before and after thecollision is conserved but the kinetic energy is not conservedafter the collision. or 0.516v1 - 0.753v2 = 2.25 - 0 or 0.516v1 - 0.753v2 = 2.25--------------(2) solving equations (1) and (2) for v1 andv2 we get the speeds of the balls after thecollision. b)the collision is elastic.This is because the twoballs fly off at different angles after the collision.Thecollision is inelastic when the two balls stick together after thecollision.In this case the total momentum before and after thecollision is conserved but the kinetic energy is not conservedafter the collision.