Conservation of Momentum

1. Conservation of Momentum The physics version of Before and After…

2. Law of Conservation of Momentum In the absence of net external force, the total momentum of a system remains constant. total initial momentum = total final momentum Rewrite the equation above using mass and velocity

3. ptotal (final) = p total (initial) • Elastic collision – collide and bounce • mv + mv = mv + mv • Inelastic collision – collide and stick • mv + mv = (m + m)v • Recoil – start as one unit and breaks apart • (m + m)v = mv + mv

4. Conservation of Momentum Thinking through the collisions: • Always consider before and after • Momentum is a vector sum • Count the number of objects before the collision and after the collision. • Pay attention to direction • Pay attention to the type of collision Put all of these in a picture or diagram

5. Types of Events Inelastic Collision momentum is conserved kinetic energy is not conserved Collide and stick! Elastic Collision momentum and kinetic energy are conserved Collide and bounce! Recoil • momentum is conserved • kinetic energy is not conserved Start as one unit and break apart

6. Example problem – elastic collision A cue ball with a mass of 1kg moves at 2 m/s towards the 8-ball (same mass). The 8 ball is initially at rest. The balls collide elastically. If the cue ball continues moving in the same direction at 0.2 m/s, what is the velocity of the 8-ball after the collision?

7. Example problem – inelastic collision A 12 kg cart moving east at 5 m/s collides head on and sticks to a 16 kg cart headed west at 7 m/s. Calculate the velocity of the 2 cart system after the collision.

8. Example problem – recoil You mistakenly slide out to the middle of a frozen lake. Fortunately you get to your feet on the surface. In a fit of anger you throw your shoe south at 12m/s. What is your recoil velocity? (Your mass is 60 kg and your shoe’s mass is 1 kg)