1. Momentum, Impulse, and Collisions
Chapter 8
Momentum, Impulse, and Collisions

2. Goals for Chapter 8
To determine the momentum of a particle
To add time and study the relationship of impulse and momentum
To see when momentum is conserved and examine the implications of conservation
To use momentum as a tool to explore a variety of collisions
To understand the center of mass
To study rocket propulsion

3. Introduction
If you watch a football game, you’ll see collisions, tackles, many men colliding at once, maybe just two in an open area. Are these situations different?
Newton told us the forces result in acceleration of a mass. We will now study two new points of view—momentum and impulse.

4. How does momentum relate to mass and velocity?
Understanding momentum begins with the simple relationship that momentum is equal to mass multiplied by velocity.

5. Compare momentum and kinetic energy
The impulse–momentum relationship depends on duration of an impact while the work-energy theorem focuses on the distance of force application.
Refer to Conceptual Example 8.1.
Consider Example 8.2, the figure below at right completes that question.

6. Duration of an impact
Figure 8.6 and Figure 8.7 are both image/diagrams related to sports. They are, in fact, of the same duration. The bottom figure assists the setup of Example 8.3.
Consider Example 8.3.

7. Like energy, momentum also has conservation rules
Refer to Figure 8.8. No forces are at play save those from the astronauts.
Refer to Figure 8.9. Many forces are at work.

8. Don’t forget that momentum is a vector
Refer to Figure 8.10 at right. Then consider Problem-Solving Strategy 8.1. Figure 8.11 below will assist you to work through Example 8.4.

9. Objects colliding along a straight line
Consider the collision in Example 8.5.

10. Now, consider a two-dimensional collision
Considering even just two dimensions makes the problem much more intricate.
Consider Example 8.6.

11. Elastic compared to inelastic

12. Completely (or nearly) inelastic collisions
Cars are designed to crumple and absorb as much energy as possible so the passengers do not need to.
Consider Example 8.7 and Figure 8.17 at right below to help you.

13. The ballistic pendulum
This can be demonstrated with a 4  4 block and a .22 caliber rifle. Most schools now prohibit firearms on campus.
Consider Example 8.8 and Figure 8.18 at right to assist you.

14. A possible simple model for automobile accidents
Refer to Example 8.9 and Figure 8.19 to assist you.

15. Elastic collisions—Figure 8.21
Billiard balls are a very good example of objects that collide elastically.

16. Solve a problem related to the “break”
Consider Example 8.10, referring to Figure 8.24 below.
Refer also to Example 8.11.

17. A two-dimensional elastic collision
Consider Example 8.12.

18. Center of mass
Refer to Example 8.13 considering a water molecule.

19. Many centers of mass

20. Tug-of-war without friction (on the feet)
Refer to Example 8.14.

21. Rocket propulsion is a spectacular application!
Look at Figure 8.32.
Examples 8.15 and 8.16 both foreshadow a NASA career calculation. Graduation isn’t that far away!