October 20, 2016: Collisions in two dimensions

Anthony Betancourt
Lab performed: Oct. 20, 2016
Professor Wolf

Lab #15: Collisions in Two Dimensions

Purpose:

The main objective of this lab is to determine if momentum and energy are conserved between two colliding objects.  The first collision is a steel ball with another steel ball bearing, the second collision is a steel ball with a glass marble.

Procedure:

1. Set up the glass table and a large lab stand with a 90 degree arm that is directly over the center if the glass table.
2. Setup up a camera or use a smartphone on the end of the 90 degree arm.
3. Grab two identical balls and one made of different material and mass.  Make sure they are the same in size.
4. For the first collision, place a ball in the center of the glass. Press record on the camera and roll the second ball toward the ball in the center.  
5. Once a clear video showing the collision between the two balls has been captured, repeat for the second collision with two different mass balls.  
6. When both videos have been captured, upload the videos into quicktime to shorten the length to just before and after the collision.
7. Once the videos are shortened, upload them into logger pro software and analyze each video and trace them.  
8. Logger pro can use the traced dots and place them on a graph of position vs. time
9. After the graphs are created, find the velocities for each ball.
10. Afterwards, you must derive a formula for the x-center of mass and y-center of mass.  Then make a graph of both center of mass vs. time graphs.
11. Determine if momentum is conserved.

Measured Data:

(Video analysis in logger pro software)

(video analysis of same balls; velocities before collision)

(video analysis; velocities after collision)

(glass and steel balls; velocity before collision)

(glass and steel balls; velocity after collisions)

(Sample calculations showing momentum and energy; x direction)

Analysis:

The experiment was fairly easy to perform.  The difficulty comes from the video analysis.  The best solution would be to zoom in on the glass table top with the camera used.  Aside from the technical difficulties, the data gathered was sufficient enough to give information on momentum and energy.  From the graphs we can conclude the velocity of the balls from the slope of the linear fit line in both the x and y direction.  The velocity we achieve can be used in the momentum and energy calculations to see if the experiment did turn out as expected.

Conclusion:

The experiment went as expected beside the difficulty with tracking the ball in logger pro video analysis.  Once the graphs were finished, it was fairly simple to calculate the moment and energy for the balls.  The uncertainties that were ran into included: the logger pro software crashing unexpectedly, aiming the balls correctly to get a good angle after the collisions, the camera set up could have been zoomed in to provide better close up footage, and difficulty in setting up the glass table to be completely.