Linear Momentum Conservation

 

Subject Area

Physics
Age or Grade
9th -12th grade
Estimated Length
90 -120 minutes
Prerequisite knowledge/skills
Newton's Second Law
Description of New Content

The students will be introuduced to the concept of linear momentum, p = mv, and its relation to the true form of Newton's Second Law, Fnet = (change in p)/(change in t). In addition, they will explore the conseuquences of Newton's Second Law cast in this form, focusing particularly on the idea of conservation of momentum.

Goals
  1. For the students to understand the more general form of Newton's Second Law, expressed in the terminology of momentum.
  2. For the students to recognize the difference between situations in which momentum will be conserved and those in which an impulse causes a change in momentum.
Materials Needed
  • Logger Pro or a similar data analysis software
  • Either motion sensors or webcams/cameras compatible with Logger Pro
  • Carts
  • Extra masses

Procedure

 

 

 

Opener

Here's a powerpoint that uses car crashes to motivate the idea of momentum.

Development

Now let's follow through with the implications of possibility #2 (if Fnet = 0, then momentum is conserved) by considering a cannon and a cannonball.

Getting to the actual activity, ask the students if they can see any application of this logic to a two-car collision. Some may make the connection, and some may not.

Splitting the class into groups of two or three, ask the students to simulate a two-car accident using the dynamics carts. They can choose to create a head-on collision, a rear-ending, or any type of collision they like, and they can add masses to the carts as desired to make anything from a "tractor trailer truck" to a "motorcycle". Using either motion sensors or a webcam, ask them to track the momentum of the carts in Logger Pro.

For those who predict momentum will be conserved in the accident, challenge them to prove it. For those who don't make the connection or aren't sure, challenge them to see what they can learn through this activity.

Closure

Clearly the collisions that the students create in the lab cannot compare with the the extremity of a real car accident. Can something as seemingly simple as Newton's 2nd Law really account for the crunching metal and breaking glass that occur in a real accident? In fact, the same video analysis techniques can be used in Logger Pro to analyze a real crash. Here's an example plotting the momentum in a crash test video.
Evaluation
Ask each group of students to come in front of the class and present their results. Students should describe the type of collision that they created, point out the sections of their graph corresponding to before and after the crash occurred, explain how they measured the momenta of the carts, and show whether or not momentum was conserved. If it was not conserved, students should be able to explain why they believe it was not.
Extensions

To further emphasize that this idea governs real car accidents (assuming friction to be negligible over small time frames), point out that momentum convervation is one of the primary tools employed by police in reconstructing car accidents, mainly working backwards to determine the speed of the car(s) involved before the collision.
References

Here are some links to some cool momentum/impulse related car videos found on google:
Linear Momentum Conservation