1. Momentum

2. What do you think?
Imagine an automobile collision in which an older model car from the 1960s collides with a car at rest while traveling at 15 mph. Now imagine the same collision with a 2013 model car. In both cases, the car and passengers are stopped abruptly.
List the features in the newer car that are designed to protect the passenger and the features designed to minimize damage to the car.
How are these features similar?
When asking students to express their ideas, you might try one of the following methods.
(1) You could ask them to write their answers in their notebook and then discuss them.
(2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups.
The most important aspect of eliciting student’s ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally.
Students will mention seat belts and air bags. Hopefully some will be aware of collapsible steering columns, shock absorbing bumpers, fenders and car body parts that collapse easily, padded dashboards, and so on. If you can get a fairly complete list, they may see the common thread in these features. That thread is the ability to extend the amount of time required for the car and the passenger to stop.

3. What do you think? What are some common uses of the term momentum?
In your group, write a sentence using the term momentum.
Do any of the examples provided reference the velocity of an object?
Do any of the examples reference the mass of an object?
This slide provides an opportunity for students to assess their own understanding of momentum. There may be some references to motion, but more likely are comments about how the momentum shifted in a soccer match or other sporting event.

4. p = m·v Momentum momentum = mass x velocity
Momentum (p) is proportional to both mass and velocity.
A vector quantity
SI Units: kg • m/s
Momentum is in the same direction as the velocity.
Students may associate momentum only with velocity, so discuss the fact that a slow moving truck has as much momentum as a car moving at much greater speeds.

5. Momentum and Newton’s 2nd Law
Prove that the two equations shown below are equivalent.
F = ma and F = p/t
Newton actually wrote his 2nd Law as F = p/t.
Force depends on how rapidly the momentum changes.
Have students show that the two equations are equivalent.
To do so, substitute v/t for a in the equation F = ma.
It will now read F = mv/t
Next, point out to the students that the mass of an object does not change while it is accelerating (except in cases such as rockets taking off, where the fuel is being expelled so the mass is decreasing). Therefore, mv = (mv) = p.

6. Notes About A System
Remember conservation of momentum applies to the system
You must define the isolated system

7. Types of Collisions Momentum is conserved in any collision
Inelastic collisions
Kinetic energy is not conserved
Some of the kinetic energy is converted into other types of energy such as heat, sound, work to permanently deform an object
Perfectly inelastic collisions occur when the objects stick together
Not all of the KE is necessarily lost

8. More Types of Collisions
Elastic collision
both momentum and kinetic energy are conserved
Actual collisions
Most collisions fall between elastic and perfectly inelastic collisions

9. More About Perfectly Inelastic Collisions
When two objects stick together after the collision, they have undergone a perfectly inelastic collision
Conservation of momentum becomes

10. Some General Notes About Collisions
Momentum is a vector quantity
Direction is important
Be sure to have the correct signs

11. More About Elastic Collisions
Both momentum and kinetic energy are conserved
Typically have two unknowns
Solve the equations simultaneously

12. Elastic Collisions, cont.
A simpler equation can be used in place of the KE equation
This equation will be used to solve problems dealing with perfectly elastic head-on collisions

13. Summary of Types of Collisions
In an elastic collision, both momentum and kinetic energy are conserved
In an inelastic collision, momentum is conserved but kinetic energy is not
In a perfectly inelastic collision, momentum is conserved, kinetic energy is not, and the two objects stick together after the collision, so their final velocities are the same

14. Problem Solving for One -Dimensional Collisions
Coordinates: Set up a coordinate axis and define the velocities with respect to this axis
It is convenient to make your axis coincide with one of the initial velocities
Diagram: In your sketch, draw all the velocity vectors and label the velocities and the masses

15. Problem Solving for One -Dimensional Collisions, 2
Conservation of Momentum: Write a general expression for the total momentum of the system before and after the collision
Equate the two total momentum expressions
Fill in the known values

16. Problem Solving for One -Dimensional Collisions, 3
Conservation of Energy: If the collision is elastic, write a second equation for conservation of KE, or the alternative equation
This only applies to perfectly elastic collisions
Solve: the resulting equations simultaneously

17. Sketches for Collision Problems
Draw “before” and “after” sketches
Label each object
include the direction of velocity
keep track of subscripts

18. Sketches for Perfectly Inelastic Collisions
The objects stick together
Include all the velocity directions
The “after” collision combines the masses