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Physics 30: Momentum and Impulse

eMATH Activity

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Elastic Collisions in One Dimension

Purpose:

To explore how the final velocities of two objects are related to their masses and initial velocities when the objects collide in one dimension.

Background:

When two or more objects in an isolated system collide in one dimension, the momentum of the system is always conserved. Using the law of conservation of momentum, we can predict the velocities of each object immediately after collision.

The purpose of this eMATH is to calculate the velocities of two objects immediately after they collide one-dimensionally so that the relationship among mass, initial velocity, and final velocity can be determined.

Instructions:

1. Download and open the accompanying Excel spreadsheet.

This spreadsheet will be used to calculate the final velocities of two objects immediately after a one-dimensional collision. 

For all of the calculations, m2 is initially stationary and m1 has an initial speed of 10.0 m/s.
2.

Start with both objects (m1 and m2) each being 10.0 kg. 

  • Then change m1 to 2.0 kg and press enter. The final velocities of m1 and m2 will be calculated in the spreadsheet.
  • Enter the final velocity values (v1f and v2f) into the table below.  Continue to calculate and record the final velocities for all values of m1 listed in the table.

Analysis:

1.

What do all the values of v1f have in common when the m1 is less than m2? What does this mean in terms of the direction of m1?
2.

What is the value of v1f when m1 is equal to m2?  What is the value of m2? Describe the motion of m1 and m2 in this situation.
3.

What do all the values of v1f have in common when m1 is greater than m2? Interpret this result in terms of the motion of m1 and m2.
4.

Complete the table below using the masses and velocities given.  Record the values of v1f in the second column.  Make a general statement regarding the values of v1f as compared to v1f.
5. Based on this activity, make a general statement about the relationship among m1 and m2 and the final velocities, v1f and v1f.
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