The Law of Conservation of Momentum When two objects collide, the total momentum of the objects before the collision is equal to the total momentum of the objects after the collision. The momentum lost by object 1 is equal to the momentum gained by object 2.

pi = pf The Equation pbefore collision = pafter collision TOTAL Momentum before = TOTAL Momentum after pi = pf pbefore collision = pafter collision (add momentum of multiple objects)

Conservation of Momentum Inelastic Collisions Elastic Collisions Recoil

Inelastic Collision When two objects collide and remain stuck together (2 objects become 1 object)

Inelastic Collision Velocity of both objects must decrease in order to make up for the increase in mass

Example 1: Inelastic

Elastic Collision When two objects collide and bounce off each other 2 objects  2 objects

Elastic Collision The momentum (velocity) that one object loses must be gained by the 2nd object

Example 2: Elastic Collision A toy truck, with a mass of 15.0 kg, travels along a level tabletop at 1.0 m/s. A miniature car, with a mass of 5.0 kg, speeds headlong toward the toy truck at -0.75 m/s. Immediately after the collision, the 15.0 kg toy truck continues in its original direction at +0.13 m/s. What is the velocity of the 5.0 kg miniature car after the collision? 1.86 m/s

Recoil The equal and opposite force of an object being launched forward Initial momentum is zero (1 object  2 objects)

Example 3: Recoil

Solving Collision Problems Identify how many objects you start with and how many objects you end with Calculate the sum of the momentum before the collision and the sum of the momentum after the collision Set the momentum before equal to the momentum after (if multiple objects, add momentums together)

Suppose that a medicine ball is thrown to a clown who is at rest upon the ice with a velocity of 10 m/s. The clown catches the medicine ball and glides together with the ball across the ice. The mass of the medicine ball is 5 kg and the mass of the clown is 60 kg. What is the total momentum of the system before the collision? What must the total momentum of the system be after the collision? If the clown and the medicine ball move together as a single unit after the collision, what happened to the velocity of the medicine ball? Why?

Figure it Out! A 25 kg car moving to the right at 5.5 m/s collides with a 35 kg car moving to the right at 2 m/s. After the collision, the 25 kg car slows to 1.4 m/s to the right. What is the velocity of the 35 kg car after the collision? 5 m/s to the right A 76 kg boater initially at rest in a stationary 45 kg boat, jumps out of the boat and onto a dock. If the boater jumps with a velocity of 2.5 m/s to the right, what is the final velocity of the boat? 4.2 m/s to the left A 3500 kg truck going 25 m/s east runs into a 550 kg motorcycle stopped at a stop sign. If the truck stops as a result of the collision, how fast will the motorcycle shove forward? 160 m/s east 5 m/s 4.2 m/s 160 m/s