Collisions in two dimensions: Jose Rodriguez: Lab Completed: 4/24/17 Lab Partners: Kevin Tran; Kevin Nguyen

The purpose of this laboratory experiment was to look at several two-dimensional collisions and determine if momentum and energy were conserved during each trial.

In order to show that momentum and energy was conserved during the two-dimensional collisions we had to measure and record several variables during the collisions and after the collisions.  But since the theory leading the lab was Newton's third law, it made the needed measurements fairly easy to obtain.  For instance, one of the experiments was a collision between two marbles with nearly equal mass and the other was a collision between two marbles of different masses.  So for the collision between the nearly equally massed marbles we measured the each mass with a digital balance and used a flat glassed leveled surface apparatus for the stage of the collisions.  The apparatus was leveled with the use of an iphone and its application called bubble level; the collision was recorded with an extension of the apparatus that holds a phone right above the glassed surface allowing it to capture the collision with a bird's-eye view of the area of impact.  Consequently, we were able to make a graph of the position vs. time of the two marbles during the collision and shortly after with the use of a computer program called logger pro that can use the video captured with the phone to make the graph.  Just as important, logger pro allowed us to calculate the slopes of the graph which is the velocity of that individual marble during and after the collision.  Then, with the masses and the velocities obtained we did manual calculations to determine if the momentum and energy was conserved during the experiment.  As for the collision with the different masses, the procedure was almost identical except for the difference in masses.

Several steps were needed in order to complete this experiment.  To begin with, we first had to level the apparatus that allowed the surface for the collisions and we had to place the phone in the apparatus the gave the phone a bird's-eye view.  The surface was confirmed to be level with the use of the iphone and its application mentioned earlier, and the iphone was confirmed to be positioned right by looking at the phone during the video capture mode.  Then, we measured the mass for each marble with a digital balance the is available in the lab.  After that, we placed one marble in the middle of the camera view and rolled the other into it while the phone recorded shortly before and after the collision for the same massed marbles as well as the differently massed marbles.  With the videos, we used logger-pro to trim the videos, set the origin on the center of mass of the at rest marble, and plot points in respective to the movement of the center of mass for each marble during the experiment to produce an imposed position vs. time graph for each marble before and after the collisions.  Shortly after, we calculated the slope for each marble before and after the collision that gave us the value of the velocity for each marble at these times during the experiments.  Again, the only difference between the experimental procedures was the mass for one marble so the steps for the necessary values was nearly identical except for measuring the mass of the heavier marble.  Lastly, since we had the masses and the velocities for each marble before and after the crash we manually calculated the momentum before and after each experiment to analyze the experiments.

 This is an image of the apparatus that we used as a stage for the collisions. Note the apparatus extension that can hold a phone in a bird's- eye view position.
  

  This is an image of how the logger pro application looks like when one plots the position vs. time for each marble.  Notice that the origin is placed in the center of the marble initially at rest.

 This is another image that illustrates the intended paths of the marbles.

 This is an image of the experiment with the same masses.  The masses are labeled as x and y with the after collision labels of x2 and y2 that are in different colors respectively.  For example, the blue dots correspond to the velocity of the marble that was rolled towards the other so one can see that it makes it way towards the origin where the at rest marble is with an initial velocity of 418.5 meters per second.  Also, the ball at rest has a plot that corresponds to it being still at first because its dots don't move from the x-axis before the collision.

 This is an image of the different masses trial.  Notice again that the initial slope of the ball at rest is 0.

 This is an image of the calculations for the conservation of momentum and energy with the collective data.  Notice that the calculations in the y-direction are not as close in value as the x-direction values.  For instance, the x-direction absolute difference is 1066.2-560.4=505.8 g cm/s and the y-direction is 875.4 g cm/s.

This is an image for the calculations to check for the conservation of momentum and energy with the same masses.  Notice that these values are much closer in value.  For instance, the x-direction absolute difference is 7.2 units and the y-direction is 101.6 units.

In conclusion, the experiment did result in showing that Newton's 3rd law was reliable because we did show that for every action there is an equal and opposite reaction.  Although our calculations proved a significant difference is values for the different mass trial that was concerning.  The absolute difference in the y-direction was alarming because it was 875.4 units of value, and the x-direction difference was 505.8 units different so that added to the concern that we had done something wrong in the experiment.  Simultaneously, the calculations for the trial with the same masses also had a difference with the highest value being in the y-direction of 101.6 units.  Therefore, there was obviously some propagated errors surely somewhere in the procedure.  I think one error may of resulted because we plotted the movement of marbles before and after the collision wrong so that through off the graphs that we made, which in turn gave us wrong values for the initial and final velocities.  Another possible error may of come because we didn't consider the force of friction between the marbles during contact that may of transferred some energy in the form of heat so we couldn't capture it that resulted in the significant difference in before and after momentum value.  Lastly, there was probably some friction between the surface and the marbles during the experiment that we didn't measure that may of lead to the difference in before and after values.