16 October 2014: Collisions in Two Dimensions Lab 14

Objective:
The purpose of this lab is to study a two dimensional collision and determine if the momentum and energy are conserved.

Set Up and Procedure:

For our lab, there was a smooth leveled glass table. Upon this table, we placed two balls, We aimed a rolling ball to hit a stationary ball while a camera recorded the collision from above. The recorded collision was then saved to a computer to be later analyzed. There were two trials of this collision: one occurred with two identical marble balls, and another occurred with a steel ball and a aluminum ball.












Results:

After the recordings of the collisions took place, we went on to analyze our collisions. This included analyzing the video of the collisions frame by frame to discover data about the balls' position, and velocity.












Here are picture of the video of our two collisions. The first of the two identical marbles about to collide. And the second of the steel ball about to collide with the aluminum ball.

steel ball about to collide into aluminum ball

marble balls about to collide

After the video was analyzed, graphs could be produced of the balls' position and velocity. The resultant graphs looked like this:

Graph of collision of two marbles

Graph of collision of steel and aluminum balls

From these graphs would could find that for the marbles collision:

Mass of Marble 1: 20g

Mass of Marble 2: 20 g

Initial Velocity of Marble 1 (x-direction): 0 m/s

Initial Velocity of Marble 1 (y-direction): 0 m/s

Initial Velocity of Marble 2  (x-direction): -.448 m/s

Initial Velocity of Marble 2 (y-direction): -.560 m/s

Final Velocity of Marble 1 (x-direction): .0754 m/s

Final Velocity of Marble 1 (y-direction):  -.119 m/s

Final Velocity of Marble 2  (x-direction): -.448 m/s

Final Velocity of Marble 2 (y-direction): -.374 m/s

And for the aluminum and steel ball collision:

Mass of Steel Ball: 67 g

Mass of Aluminum Ball: 24 g

Initial Velocity of Steel Ball (x-direction): -.422 m/s

Initial Velocity of Steel Ball (y-direction): -.218 m/s

Initial Velocity of Aluminum Ball  (x-direction): 0 m/s

Initial Velocity of Aluminum Ball (y-direction): 0 m/s

Final Velocity of Steel Ball (x-direction): -.212 m/s

Final Velocity of Steel Ball (y-direction):  -.323 m/s

Final Velocity of Aluminum Ball  (x-direction): .0854 m/s

Final Velocity of Aluminum Ball (y-direction): -.121 m/s

With this information we were able to make calculations to prove energy and momentum were conserved:

Calculations of Marbles Collision

Calculations of Aluminum and Steel Collision

We were also able to create graphs of momentum and energy from the collisions:

Graphs of Marbles Collision

Graphs of Steel and Aluminum Collision

Conclusions:

Our calculations are a bit off since we used grams instead of kilograms to calculate momentum and energy in the trial that utilized a steel and aluminum ball. However it can be seen that neither energy nor momentum was conserved. It can also be seen by the graphs as neither are perfectly stable. Therefore this experiment did not find what it set out to prove that energy and momentum are conserved. However the discrepancies are so small in the calculations, and the fluctuations in the graph are small as well. This means that perhaps energy and momentum went into some unforeseen location. Although it is easy to say momentum and energy will be conserved in theory, there could be some sources of error in the real world. For example, some sources of error could include spinning of the ball, imperfections in the ball and surface, and of course human error.