In this lesson students will use a NetLogo model to analyze the 1-Dimensional collision of 2 cars that is completely elastic, i.e., Kinetic Energy is conserved.
Students will determine the following:
1. How does impulse compare to the change in momentum for an individual car in a collision of 2 cars.
2. How does the momentum of an individual car compare before and after the collision of 2 cars.
3. How does the kinetic energy of an individual car compare before and after the collision of 2 cars.
4. How does the analysis change if both cars are combined into a 2-car system. Both cars will be used to produce a single result.
Students will determine in which case(s) {1-car system, 2-car system, both, or none} the momentum and kinetic energy are considered to be conserved, i.e., the same before and after the collision.
The NGSS standard: HS-PS2-1 Motion and Stability: Forces and Interactions
Analyze data to support the claim that Newton’s second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration.
The NGSS standard: HS-PS2-2 Motion and Stability: Forces and Interactions
Use mathematical representations to support the claim that the total momentum of a system of objects is conserved when there is no net force on the system.
Created by Neil Schmidgall
You will use a NetLogo model to analyze the 1-Dimensional collision of 2 cars that is completely elastic, i.e., Kinetic Energy is conserved.
You will determine the following:
1. How the impulse compares to the change in momentum for an individual car in a collision of 2 cars.
2. How the momentum of an individual car compares before and after the collision of 2 cars.
3. How the kinetic energy of an individual car compares before and after the collision of 2 cars.
4. How the analysis changes if both cars are combined into a 2-car system. Both cars will be used to produce a single result.
You will determine in which case(s) {1-car system, 2-car system, both, or none} the momentum and kinetic energy are considered to be conserved, i.e., the same before and after the collision.
Car0 will always be on the left and Car1 will always be on the right. COE stands for Percent of Energy Conserved in the collision. All calculations will be done by the model. The ' symbol stands for values after the collision. For example, v1 is the velocity of Car1 before the collision and v1' is the velocity of Car1 after the collision. Experiment with the sliders below in order to become familiar with the modeling environment. Click on setup and go to run the model.
A NetLogo collision was done with 2 cars and the elasticity at 100%. The before and after pictures are shown below:
Set up the mass and velocity values as shown below. Run the experiment. Take data from the experiment in order to fill in the remaining cells to quantify this situation where each car is its own system.
Initial Velocities:
red(Car0) = 20 (m/s)
brown(Car1) = -20 (m/s)
What was the change in momentum for the red car? Change in momentum is p' - p. Include units on your answer.
How did the impulse on the red car compare to its change in momentum?
What was the change in momentum for the brown car? Change in momentum is p' - p. Include units on your answer.
How did the impulse on the brown car compare to its change in momentum?
How did the impulse on the red car compare to the impulse on the brown car? Comment on magnitude and direction.
How did the ∆p of the red car compare to the ∆p of the brown car? Comment on magnitude and direction.
What was the change in kinetic energy for the red car? Change in KE would be KE' - KE. Include units on your answer.
What was the change in energy for the brown car? Change in KE would be KE' - KE. Include units on your answer.
Let’s look at the collision again and this time, consider that the system to be analyzed consists of the red and brown car combined. Fill in the appropriate numbers below.
What was the change in momentum for the red & brown car system?
What was the total impulse on the red & brown car system?
What was the change in KE for the red & brown car system? Was the total Kinetic Energy conserved in this collision?
The graphs recording momenta and energies for the situation you just completed are below.
Was this a very elastic collision (one that conserves KE, i.e., one where the KE stays constant)? What part of these graphs and data above allow you to determine that? Please explain fully.
What system approach (Individual Car versus Both cars) constitutes an isolated system(one that conserves p, i.e., one where p' - p = 0)? What part of these graphs and data above allow you to determine this? Please explain fully.
Change the masses and/or initial velocities to create 2 different collisions (Trials) of your choosing. Keep the elasticity at 100%. Analyze these 2 trials by entering values below.
Trial1; One-car system analysis:
Trial1; Two-car system analysis:
Trial2; One-car system analysis:
Trial2; Two-cars System analysis:
Given the results for the elastic collisions you just analyzed, in what type of systems (one-car system, two-cars system, both one-car and two-cars systems, or none of these systems) does Impulse = ∆p?
Given the results for the elastic collisions you just analyzed, in what type of systems (one-car system, two-cars system, both one-car and two-cars systems, or none of these systems) is momentum conserved? That is, p' - p = 0.
Given the results for the elastic collisions you just analyzed, in what type of systems (one-car system, two-cars system, both one-car and two-cars systems, or none of these systems) is KE conserved? That is, KE' - KE = 0.
