Types of Collisions Elastic Two objects collide and bounce off each other Inelastic Two objects collide and stick together Explosion One object separates into two fragments

m1m1 m2m2 After Collision v1'v1' v2'v2' Two-Dimensional Collisions

Example: A 2.00-kg ball, A, is moving at a speed of 5.00 m/s. It collides in a glancing collision with a stationary ball, B, of the same mass. After the collision, A moves off in a direction 30.0º to the left of its original direction. Ball B moves off in a direction 90.0º to the right of ball A's final direction. How fast are they moving after the collision? Solution: 1. Sketch the before and after states Before A B v A1 v B1 =0 A B After v A2 v B2

2. Draw a momentum vector diagram. Note that p A2 and p B2 form a 90º angle. 90ºp A2 30º p B2 p2p2 3. Perform calculations in one direction (x or y): Determine initial momenta in x direction: p A1 = m a v a1 = (2.00 kg)(5.00m/s) = 10.0 kgm/s p B1 = 0 Find p 2 : p 2 = p 1 = 10.0 kgm/s p A1 p B1

Find p A2x and p B2x. after colliding p A2 x = p 2 cos 30.0° p B2x = p 2 sin 30.0° = (10.0 kgm/s)(0.866) = (10.0 kgm/s)(0.500) = 8.66 kgm/s = 5.00 kgm/s Find final speeds. p A2 m A v A2 = v B2 = p B2 m B = 8.66 kgm/s 2.00 kg = 5.00 kgm/s 2.00 kg = 4.33 m/s= 2.50 m/s 90ºp A2 30 º p B2 p2p2