Collisions

1. Collisions Collision – Two objects make contact with each other exerting equal but opposite forces. The contact forces will cause the momentum of each object to change. • Collisions can be classified under two different categories • Elastic collisions • Inelastic collisions - Momentumandkinetic energy are conserved - Momentum is conserved Total energy is still conserved for both cases. - Momentumandkinetic energy are conserved Elastic collisions • Two rigid objects will rebound off of each other. • No loss of kinetic energy • No sound emitted • No light emitted • No deformation of either object • No heat generated No real world collision is perfectly elastic, but this is a close approximation for a collision between two rigid objects. The closest would be atomic interactions. and

2. Let us examine an elastic collision between two different spheres. Just after collision Just before collision v2 v1 v’1 v’2 m1 m2 m1 m2

3. Substitute separately back into the initial momentum conservation equation, to obtain two new equations for the velocity after impact. These two equations are only valid for perfectly elastic collisions!!

4. Inelastic collisions - Momentum is conserved • Collisions between any two objects where: • Sound is emitted • Light is emitted • Heat is generated • Deformation of at least one object occurs • Merging of two objects Just before collision v2 v1 v’ m1 m2 Let us examine an inelastic collision between two different spheres. Just after collision m1+ m2 Kinetic energy is not conserved!

5. You are given two carts, Aand B. They look identical, and you are told that they are made of the same material. You place Aat rest on an air track and give Ba constant velocity directed to the right so that it collides with A. After the collision, both carts move to the right, the velocity of Bbeing smaller than what it was before the collision. What do you conclude? 1. Cart Ais hollow. 2. The two carts are identical. 3. Cart Bis hollow. 4. need more information

6. If ball 1 in the arrangement shown here is pulled back and then let go, ball 5 bounces forward. If balls 1 and 2 are pulled back and released, balls 4 and 5 bounce forward, and so on. The number of balls bouncing on each side is equal because 1. of conservation of momentum. 2. the collisions are all elastic. 3. neither of the above

7. Most people are familiar with the standard "collision balls" apparatus. Six identical steel balls are suspended in a row; lifting one of the end balls and releasing it causes the one on the opposite side to move away, then fall back, causing the original ball to do the same, etc. The motion satisfies all of the requirements of conservation of energy and linear momentum during the various collision processes. Now suppose that we modify this apparatus so that one of the balls (the fourth from the left) is made from aluminum rather than steel, and therefore no longer has the same mass. In this case, how will the collision balls apparatus work? In particular, will it work the same way as the equal mass collision ball apparatus? Will the ensuing motion be one ball moving up on one side, then the other side, back and forth? (1) Yes! (2) No!

8. A cart moving at speed v collides with an identical stationary cart on an air track, and the two stick together after the collision. What is their velocity after colliding? 1. v 2. 0.5 v 3. zero 4. –0.5 v 5. –v 6. need more information

9. If all three collisions in the figure shown here are totally inelastic, which bring(s) the car on the left to a halt? 1. I 2. II 3. III 4. I, II 5. I, III 6. II, III 7. all three