10/19/2016 - Collisions in Two Dimensions (Lab 15)

PURPOSE:
To look at a 2-D collision and determine if momentum and kinetic energy are conserved.

THEORY:
In collisions where there are no external forces acting on the system, both momentum and kinetic energy are conserved. In this experiment, we want to see if these principles apply to a collision between two balls on a frictionless surface. To test this, we calculate the kinetic energy (KE = .5mv^2) and momentum (p = mv) before and after the collision. If the before and after values are nearly identical for the respective quantity of motion, then the collision is elastic.

APPARATUS:
We used a leveled glass table as our frictionless surface. For our collision objects, we used a glass marble and a steel ball. To capture the collision in slow-motion, we used a ring stand to suspend a smartphone with the capability to record at 120-240 fps.

EXPERIMENTAL PROCEDURE:

1. Gather appropriate materials.
2. Set up apparatus as shown.
3. Make sure glass table is leveled.
4. Measure length of glass table.
5. Place marble in the center of the table.
6. Set up smartphone to record in slow-motion.
7. Mount phone onto ring stand.
8. Record the two following collisions separately:
9. Aim and roll a steel ball towards the marble.
10. Aim and roll another marble towards the marble.
11. Transfer these video files to LoggerPro.
12. Input your table length measurement to calibrate your video tracer.
13. Adjust the click rate to 4-8 frames.
14. Trace the position of the each ball separately for each collision.
15. Get the velocities of each ball before and after each collision.
16. For each collision data set, create two calculated columns that show the momentum in both the x and y axes.
17. Finally, create graphs for the position and velocity of the center of mass in both the x and y axes.

DATA/GRAPHS:
mass of marble (middle): 19.6 g
mass of second marble: 19.8 g
mass of steel ball: 66.9 g
Length of glass table: 0.625 m

Marble-Marble Collision

Marble-Marble Position Graph

KE-Px-Py for Marble-Marble Collision

CM Position for Marble-Marble Collision

CM Velocity for Marble-Marble Collision

Steel Ball-Marble Collision

Steel Ball-Marble Position Graph

KE-Px-Py for Steel Ball-Marble Collision

CM Position for Steel Ball-Marble Collision

CM Velocity for Steel Ball-Marble Collision

ANALYSIS:
By simulating a collision between two balls with different masses, we were able to analyze their behavior to determine whether or not momentum and energy were conserved. However, instead of doing the calculations by hand, our group decided to derive equations that could be inputted into a calculated column for both momentum (x and y) and kinetic energy for each collision respectively.

KE-Px-Py Equations for LoggerPro

If momentum is conserved, then the the momentum in the x-axis should be equal but opposite to the momentum in the y-axis. In other words, if our graphs for Px vs. t and Py vs. t are nearly identical but opposite in value, then momentum is conserved. If kinetic energy is conserved, then we should expect to see that the KE vs. time graph should be nearly constant.

After analyzing our graphs, it becomes apparent that the momentum for both collisions appear to be conserved. However, it is less apparent to see that the kinetic energy is conserved. The collision between the two marbles yielded a relatively straight line, but the collision between the steel ball and the marble had an erratic line, indicating that the kinetic energy throughout the collision varied greatly.

CONCLUSION:
Our results for this experiment were somewhat bittersweet. On the one hand, we successfully demonstrated that the momentum of both collisions were conserved. On the other hand, we had difficulty verifying the same was true for the kinetic energy of both systems. We assumed that there were no external forces acting on the system, although there is bound to be some inherent uncertainty to this statement. For example, if the glass surface we used was unclean, it could have gathered residue, which could have inadvertently hindered the speed of the ball. Another possible source of uncertainty is human error. The motion tracking software on LoggerPro utilizes human input, which can lead to the imprecise collection of data for the position, velocity, and to that end, all of our momentum and KE computations as well.

GROUP MEMBERS: Xavier C., Billy J., Matthew I.