1. Collisions: Elastic & Inelastic
Unit 5.3

2. Collisions
You notice collisions day to day without giving much thought to them.

3. Collisions
There are those in which 2 objects collide and stick together such as an arrow hitting a target. The momentum after would equal their combined momentum before the collision.

4. Collisions
In other collisions, the objects collide and bounce so that they move away with two different velocities such as a tennis ball and a racket. Regardless of the type of collision, the total momentum remains constant.

5. Collisions
However, the total kinetic energy is generally not conserved in a collision because some kinetic energy is converted to internal energy when objects deform.

6. Collisions
In this section, we will examine different types of collisions and determine whether kinetic energy is conserved in each type.

7. Collisions
We will first focus on two extreme types of collisions: elastic & perfectly inelastic.

8. Perfectly Inelastic Collision
When 2 objects collide and move together as one mass, the collision is called perfectly inelastic, such as an arrow and target.

9. Perfectly Inelastic Collision
These types of collisions are easy to analyze in terms of momentum because the objects become essentially one object after collision.

10. Perfectly Inelastic Collisions
The final mass is equal to the combined masses of the two objects and they move with the same velocity after colliding.

11. Perfectly Inelastic Collision
m1v1i + m2v2i = (m1 + m2)vf
When using this equation it is important to pay attention to signs that indicate direction.

12. Perfectly Inelastic Collision
In an inelastic collision, the total kinetic energy does not remain constant when objects collide and stick together.

13. Perfectly Inelastic Collisions
Some kinetic energy is converted to sound energy and internal energy as the objects deform during collision.

14. Collisions
This phenomenon helps makes sense of the special use of the words elastic and inelastic in physics.

15. Collisions
Think of elastic as something that returns to or keeps its shape. Think of an inelastic collision producing objects that deform and lose kinetic energy.

16. Collisions
Therefore in an elastic collision, two objects collide and return to their original shapes with no change in total kinetic energy. After the collision, the two objects move separately.

17. Collisions m1v1i + m2v2i = m1v1f + m2v2f
In an elastic collision, both the total momentum and total kinetic energy remain constant throughout the collision.
m1v1i + m2v2i = m1v1f + m2v2f

18. Collisions
Remember that [v] is positive if an object moves to the right and negative if it moves to the left.

19. Collisions
In the everyday world, most collisions are not perfectly inelastic or elastic. Any collision that produces sound is not perfectly elastic, the sound representing a decrease in kinetic energy.

20. Inelastic Collisions
Elastic and perfectly inelastic collisions are limiting cases, most collisions actually fall into a category between these two extremes: inelastic collisions.

21. Inelastic Collision
In an inelastic collision, the colliding objects bounce and move separately after the collision but the total kinetic energy decreases in the collision.

22. Inelastic Collision
For our purposes, we will consider all collisions in which the objects do not stick together to be elastic collisions.

23. Inelastic Collisions
This means we will assume that the total momentum and the total kinetic energy remain constant in all collisions that are not perfectly elastic.