Two-Dimensional Collision Lab

The Following Information is Provided to the Student

Question: What is the evidence that momentum is conserved in a two-dimensional collision? In what manner does the evidence support the law of momentum conservation?

Purpose: To conduct a vector analysis of a two dimensional collision in an effort to gather convincing evidence that the total system momentum is conserved AND to describe how the evidence supports the law of momentum conservation.

A complete lab write-up includes a Title, a Purpose, a Data section, and a Conclusion/Discussion of Results. The Data section should include a sketch of the experimental results as gathered by the carbon paper impressions (collision location, pre-collision landing location and striker and target sphere post-collision landing location). Actual measurements taken from the large paper should be recorded on your sketch and labeled using the usual conventions (p₁, p₁', p₂', θ₁, θ₂, etc.). A well-organized mathematical analysis should be conducted to show that momentum is conserved (or not conserved) in both the x- and the y-dimensions. Work should be labeled and follow-able. The Conclusion should explain how it is known that total system momentum is conserved; it should also include an error analysis.

Scoring Ruberic

M10.	Two-Dimensional Collision Lab	Score
_____	Included, labeled and organized all parts of the lab report.	_____ / _____
_____	Data section includes an informative sketch; the four strategic locations are shown. Measurements of p₁, p₁', p₂', θ₁, θ₂, are recorded and labeled on the sketch; units are included. Calculations of x- and y-momentum values for the individual objects and for the system are provided for before and after the collision; work is shown in an organized fashion; results are labeled and clearly discernible. Reveals both an understanding of momentum analysis and the ability to organize a complex solution. Results are accurate.
_____	Conclusion/Discussion of Results describes how the evidence suggests that momentum is conserved (or not conserved); actual data values are referenced in an effort to establish the proof. An error analysis is conducted for the total x-momentum; work is shown.

Materials Required

2-D collision apparatus; two identical metal spheres; carbon paper; paper; masking tape; meter stick.

Description of Procedure

The 2-D collision apparatus (described below) is taped to the lab bench. The striker sphere is rolled from rest from the top of the ramp and off the apparatus onto the floor below. Once the approximate landing location is determined, paper is taped to the floor to form a continuous line of paper from the collision location to the landing location. Carbon paper is placed upon the paper and the target sphere is rolled down the ramp about ten times to form a sufficient number of impressions on the paper in order to locate the exact landing location. The exact landing location on the paper is marked and labeled as Striker - before collision. Now the adjustable arm upon which the target sphere rests is moved into position to be struck by the striker sphere. The target sphere is located just barely off the path of the striker sphere so that a glancing collision occurs. The striker sphere is then rolled down the ramp to collide with the target sphere. Once the approximate landing locations of the two spheres is determined, paper is placed at those locations and extended towards the original paper and taped together. Two pieces of carbon paper are placed on top of the paper; the collision is performed about ten times in order to form a sufficient number of impressions on the paper of the landing locations of the two spheres. The two landing locations are marked on the paper and labeled as Striker - after collision and Target - after collision. Finally, the plumb bob is extended downward from the collision location to the paper; the collision location is marked and labeled as Collision Location. Since the distance from the collision location to the three other marked locations are proportional to the velocity, they are also proportional to the momentum (since the spheres have identical mass). These vectors are drawn on the paper and their magnitude and direction is measured and recorded. Component analysis is used to determine the total momentum before (or without) the collision and after the collision.

Alternative Materials and Procedure

The 2-D collision apparatus is relatively simple. It consists of a small ramp with a groove which the sphere rolls down. The ramp gradually levels off at the bottom. The striker sphere rolls along the groove down the ramp to the end of the level section. At the end of the level section of the apparatus is a small resting platform for the target sphere. The resting platform can be rotated into and out of the line of motion of the striker sphere. The entire apparatus could likely be made using thermal pipe insulation purchased from a home store and a little creativity.

Safety Concerns

There is always a higher than usual level of risk associated with working in a science lab. Teachers should be aware of this and take the necessary precautions to insure that working environment is as safe as possible. Student horseplay (especially the use of meter sticks as swords) and off-task behaviors should not be tolerated.

Suggestions, Precautions, Notes

This lab is a difficult lab and may be best suited for your most able classes. Regardless of what level of students perform this lab, it is a lab which deserves an extensive pre-lab and considerable guidance. In the end, results are impressively accurate.
It is important that the striker sphere and the target sphere are aligned at the same height at the moment of the collision. If so, all the momentum of the two spheres immediately after the collision lies in a horizontal plane. Thereafter, gravity acts upon the spheres to cause their fall to the floor. Since gravity doesn't alter the horizontal velocity of the spheres, and since each sphere falls to the ground in the same amount of time, the distance traveled by the spheres is proportional to the velocity and the momentum. If the collision occurs such that one of the spheres is projected slightly upward and the other downward, the time of fall will be different and the above reasoning no longer holds true.
The paper which is placed upon the floor must be all taped to each other; students should not use the tape sparingly. Inform students that momentum should be conserved in this lab, but masking tape should not.
It is helpful during the analysis to define east as the direction which the target sphere was moving before the collision. Thus, the pre-collision momentum was due east.
If the demands of the lab become too overwhelming, consider providing the following tables to assist students in the organization of their measurements and in their analysis: