22-April-2015: Collisions in two dimensions Lab

Lab 14: Collisions in Two Dimensions

Purpose: To look at a two-dimensional collision and determine if momentum and energy are conserved.

 

Apparatus:  In this lab, we used a leveled glass table for the experiments. The table had a camera mounted above it; it was used to record the collisions.

Lab Apparatus

 Procedure:
The purpose of this lab is to prove if momentum and energy are conserved in a 2D collision. Therefore, we must run an experiment in which we can calculate both energy and momentum. We achieved this purpose through two experiments. One experiment had colliding masses of roughly the same weight, the other experiment had one lighter mass.

We calculated the energy and momentum of the 2D collisions by using the video capture feature on LoggerPro. First, we plotted the movement of the colliding masses. From here, we were able to determine the initial and final velocities of the masses. Finally, we used energy and momentum equations to determine if they were conserved.

Experiment Setup: We set a stationary ball on the leveled glass table. Then, we aimed the rolling ball so that it hit the side of the stationary ball. The balls then came off at an angle from one another.

  

Experiment 1:

• Steel Ball #1 = 66.9 g
• Steel Ball #2 = 66.8 g  (stationary ball)

We ran the experiment with the masses seen above. Next, we captured video of the collision and tracked the movement of the mass before and after the collisions. We also measured the length of the glass table. This gives LoggerPro a reference so that it can accurately calculate the velocity of the masses.

• Measured Length = 0.587 m

 

 First, we adjusted the axes on the video and then plotted the information on a graph.

 

The graph above shows the positions of the masses in both x & y direction, before and after the collsion.
Next, we took linear fits of each graph to determine the velocity of the mass. Using this method, we found velocities in the x and y direction. We did this since: 
Velocity= Change in Position / Time 

Linear Fits of Graphs

To recap, we now have the mass of each ball and their respective xy-velocities. The only thing that is left is finding the momentum and energy of the collision. Since this a 2D collision, we must calculate momentum for movement in the x and y direction. The same thing follows for energy.
Below you will see the initial and final velocities for each mass, as well as our momentum and energy equations.

For the calculations, the given masses in grams were converted into kg.

 

For momentum:
x direction: Initial momentum of ball 1= Final momentum ball 1+ Final momentum of ball 2
y direction: Initial momentum of ball 1= Final momentum ball 1+ Final momentum of ball 2

For KE:
Initial KE of ball 1= Final KE of ball1 + Final KE of ball 2

As you can see the calculations above determine that both momentum and energy are conserved in a 2D collision with similar masses.

Experiment 2:

• Steel Ball #1: 66.9 g
• Glass Ball: 20.7 g  (stationary ball)

 We ran the experiment with the masses seen above, using the same setup from experiment 1. The same procedure was followed as in experiment 1: taking video, plotting movement of masses, determining velocities, and finding momentum and energy.
Calculations of energy and momentum, as well as determined velocities can be found below:

The initial and final velocities can be found off to the right.
The same momentum and energy equations were used in both experiments. As you can see, the result is the same. Momentum and energy are conserved in a 2D collision with one heavy mass and one lighter mass.

Conclusion:
In this lab, we proved that energy and momentum are conserved in a 2D collision. We achieved this through two experiments; one with roughly the same masses, the other with different masses. Even though, we proved that energy and momentum are conserved in a 2D collision; our calculated values for energy and momentum do not exactly add up. This can be due to the uncertainty or sources of errors within the experiment. There could be human error in plotting the movement of the masses, which would alter the values of  the velocities. We can also assume that in a 2D collision, 100% of the energy and momentum is not conserved, but most of it is. If this is the case, our values are acceptable. Nonetheless, the percentage error in our calculated values is small enough that we can overlook the sources of error within the experiment.