10/17/2016 : Collisions in Two Dimensions

Lab #15: Collisions in Two Dimensions

Name:    Charles Xu,

Partner:  Anthony, Michell

Date:      10/17/2016

Statement:

In this experiment, the purpose is to determine if momentum and energy are conserved. We used three different balls, two with the same mass, and the other with smaller mass. 

Summary:

First, we level the glass table so that the ball can be at rest before the collisions. Second, we measure the width of the edge of the glass table so that we are able to set scale later on. 

Third, we set up a smart phone above the glass table and recording videos of collisions in slow motion. Then we use a heavier ball to collide the lighter one at the center. 

Setup for Collision Experiment 

After recording video, we used logger pro to collect data from the videos. 

Data Points for Different Masses Collision

Data Points for Same Mass Collision

We set origin on the video and adjust the x axis so that it lines up with the trace of moving ball before collisions. Then we use add point series to add columns relate to center of mass. 

Then, we plot X center of mass and Y center of mass vs. time graph and velocity of center of mass in x direction and velocity of center of mass in y direction vs. time graph.

X center of mass and Y center of mass vs. time graph (different masses)

X center of mass and Y center of mass vs. time graph(same mass)

 velocity of center of mass in x direction and velocity of center of mass in y direction vs. time graph.(different masses)

velocity of center of mass in x direction and velocity of center of mass in y direction vs. time graph. (same mass)

Energy Conserved

For the calculation, I choose two sets of data. One is the velocity of center of mass at both x and y direction before the collision. The other is the same type of data but after collision. KE = ½m(Vx^2+Vy^2). I plug in the sum of two balls' masses as m, then plug in velocity of x direction and velocity of y direction as Vx and Vy. After calculating both before the collision and after collision, i found that the total energy is almost the same. The difference might occur because of friction.

For calculation the momentum, i use the same data sets as the calculation for energy. I got two numbers that are very close, which means that the momentum conserved in this collision.

Conclusion:

By doing this experiment and the calculation, we find that the momentum and energy were conserved in this collision. In the calculation, there is some difference between initial momentum, energy and final momentum, energy. The possible reason is that we didn't have the perfect data from the video by clicking frame by frame. Another possible reason is the friction between balls and glass.