10/26/16: Collisions in Two Dimensions

Title: Collisions in Two Dimensions
Purpose:
The purpose of this lab is to look at a two-dimensional collision and determine if momentum and energy are conserved.

Apparatus:

We will set a clear ball on the leveled glass table. We will aim and roll one marble and one steel ball at the stationary ball. We will capture this will a phone in slow motion and then use video analysis to capture the position and velocities of the ball.

Theory:
The idea behind this lab is that momentum should be conserved from before and after the collision. However, since it is difficult to whether momentum is conserved in two dimensions, with the x and y directions, the center of mass is used as a system between the two balls.

Data:
Position of Collision between Metal and Clear Ball

Position of Collision between Marble and Clear Ball

Velocity of Collision between Metal and Clear Ball

Velocity of Collision between Marble and Clear Ball

Graphs/Calculations:
Xcm and Ycm vs Time between Clear and Metal Ball

Xcm and Ycm vs Time between Marble and Clear Ball

Vcm vs Time between Metal and Clear Ball

Vcm vs Time between Marble and Clear Ball

Energy vs Time between Metal and Clear Ball

Energy vs Time between Marble and Clear Ball

Momentum vs Time between Metal and Clear Ball

Momentum vs Time between Marble and Clear Ball

Analysis:
From the graphs, it can be seen that by looking at the x and y components, the position and velocity seem to be all over the place. However, when looking at the center of mass, the positions are almost linear, and the velocities do correspond with each other. The energies and momentum look almost conserved, and it is more obvious between the marble and clear ball than the metal and clear ball.

Conclusion:
Momentum and energy do not look to be perfectly conserved by the graphs, and reasonings behind this may be that the surface that we conducted this experiment on is not perfectly frictionless, meaning that some kinetic energy was changed to friction heat. Another source of error is that when drawing the dots in video capture, the dots were not perfect dots.