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Module 2

1. Module 2

1.18. Page 2

Lesson 3

Module 2—The Conservation of Momentum in Isolated Systems

Explore

 

What is the difference between a linear and non-linear interaction? To view an example of a non-linear collision, watch this animation.

 

Is Momentum Conserved in a Non-linear Collision?

 

In the previous lesson you learned about momentum and the law of conservation of momentum in the context of one-dimensional collisions: for any isolated system, the total momentum does not change. In a collision, momentum is conserved. The total momentum before the collision is equal to the total momentum after the collision.

 

Is the same true of two-dimensional collisions?

 

Watch and Listen

 

If you don’t feel very comfortable with vector analysis, you can choose to open and try this animation titled Component Vector Analysis.

 

Module 2: Lesson 3 Assignment

 

Remember to submit the answer to A1 to your teacher as part of your Module 2: Lesson 3 Assignment.

 

LAB 1. A simulation can be used to determine if momentum is conserved in two-dimensional collisions. Use the Collision 2D simulator to help you answer the following questions.

 

Once the simulation is open, follow these steps:

  • Toggle “Show CM” and “Show CM Frame” to the off position ().

  • Leave the “Show Trails” box checked.

  • Move the “Impact Parameter” slider to a value other than zero.

  • Press “Play” and observe the collision.

  • Press “Pause” before either of the objects leaves the viewing area.

  • Press the “Data” button to display the data describing the collision.

Perform one two-dimensional collision; then complete the following table. To generate a new collision, press the “New” button () and move the Impact Parameter slider to any value other than zero. Press the “Data” button () to view the collision information that is required to complete the following table.

 

Collision 1 (sample data)

Object

Mass
(kg)


(m/s)


(m/s)


(m/s)


(kg·m/s)


(kg·m/s)


(kg·m/s)

blue

 

 

 

 

 

 

 

green

 

 

 

 

 

 

 

  1. How would you calculate the total momentum before and after a two-dimensional collision?

  2. Would the same analysis that you used for one-dimensional situations work here?

  3. According to your observations, is momentum conserved in a two-dimensional collision?

According to the data you collected for LAB 1 and using the typical analysis performed for a one-dimensional collision, you should have found that momentum in a two-dimensional collision is not conserved. However, this is contrary to the law of conservation of momentum, which means a new type of analysis must be used for two-dimensional collisions.

 

This new type of analysis is based on the following principles, which apply to two-dimensional interactions:

  • Momentum in the x direction is conserved.

  • Momentum in the y direction is conserved.

Try This

 

TR 1. With the following data from the simulation, carry out a calculation of the total momentum before and after the collision using the analysis method that was just introduced to you.

 

Object

Mass (kg)

Magnitude
(m/s)

Direction
(degrees)

Magnitude (m/s)

Direction
(degrees)

blue ball

5.00

8.00

0

2.80

69.51

green ball

5.00

0.0

0

7.50

−20.49
  1. What is the initial total momentum in the x direction?
  2. What is the initial total momentum in the y direction?
  3. What is the final total momentum in the x direction?
  4. What is the final total momentum in the y direction?

On the next page is an example of how to describe vectors (such as momentum) using components and how to apply the law of conservation of momentum correctly to a two-dimensional collision. You may wish to look at the vector review in Module 1 if you’re feeling a bit rusty on vector analysis.