May Soe Moe
Lab Partners: Ben Chen, Steven Castro
26-April-2017
Objective: To determine if momentum and energy are conserved by looking at a two-dimensional collision
Introduction: The conservation of energy states that the total energy before the collision is equal to the total energy after the collision, which stays at a constant. The conservation of momentum states that if there is no net external force acting on objects, the momentum before the collision is equal to the momentum after the collision. We would use two steel balls to have a collision between those two balls for the first part. For the second part, we would use one steel ball and one marble and let them collide each other. For both parts, one ball is to be at rest while another ball moves toward the first ball, which is at rest, and collides. We would take two slow-motion videos of the collisions for both sets of balls. We would use the Logger Pro to trace their direction of motion and put it on a graph. We would get the velocities of the balls before and after collisions by getting the slopes from our graphs. Then we would use that velocities to calculate if the momentum and energy are conserved or not.
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| Our apparatus for this lab |
(1) The glass table for this lab was already set up. We had to make sure if the table was leveled. We could check it by seeing if the ball stays at rest without rolling to the other side. If the ball stays at rest, then it is leveled.
(2) We set up the phone we would use to record the collision at the stand attached to the glass table. The stand is set up so that the phone is in the position of filming the process of collision clearly. The filming was done by using iPhone's slow motion capture feature in the phone's camera.
(3) Before we started filming the collision, we practiced rolling the steel ball toward other to make sure that the first moving steel ball hits the second ball at rest.
(4) Once we felt ready to film, we filmed the collision of two balls. We filmed two videos: One video involving the collision between one steel ball moving and one steel ball at rest, and another video involving the collision between one steel ball moving and one marble at rest.
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| Steel ball and Marble Collision |
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| Steel ball and Steel ball Collision |
(5) After we got the videos, we transferred the videos from our phone to the computer. We opened the video using Logger Pro and trace the direction of the balls before and after collision.
(6) Logger Pro allows us to plot the graph of the motion of the ball by transferring the tracing of the balls' directions.
(7) Once we got the graph, we did linear fit and got the equations for before and after collisions. The slope of those equations would give us the velocities of the balls. Logger Pro can also give us the positions of ball in x and y directions after they collide. So, in the graph, x and x2 are x-directions of motions for two different balls and y and y2 are the y-directions of motions.
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| Two Steel Balls Collision-Before the Collision Positions and Velocities Red line for x-direction, Blue Line for y-direction of Moving Steel Ball Green for x-direction, Brown for y-direction of Stationary Steel Ball |
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| Two Steel Balls Collision- After the Collision Positions and Velocities Red line for x-direction, Blue Line for y-direction of Moving Steel Ball Green for x-direction, Brown for y-direction of Stationary Steel Ball |
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| A Steel Ball and a Marble Collision-Before Collision Positions and Velocities Red line for x-direction, Blue Line for y-direction of Moving Steel Ball Green for x-direction, Brown for y-direction of Stationary Steel Ball |
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| A Steel Ball and a Marble Collision-After Collision Positions and Velocities Red line for x-direction, Blue Line for y-direction of Moving Steel Ball Green for x-direction, Brown for y-direction of Stationary Steel Ball |
(8) One question from our graphs was that how do we know if to certain position is before the collision or after the collision.
(9) We could figure that out by seeing their graphs. Before the collision, one ball was moving with a constant velocity, which we could see x2 moving in a constant slope. X on the graph pretty much stayed constant on a straight line, which we knew it was at rest. After the collision, you could see their slopes change, which means they moved, therefore, after the collision.
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| Data and Calculations for Collision between 2 Steel Balls |
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| Checking if Kinetic Energy is Conserved in between 2 Steel Balls |
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| Data and Calculations for Collision between a Moving Steel Ball and a Stationary Marble |
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| Checking if Momentum and Kinetic Energy are conserved |
I calculated the initial momentum, initial kinetic energy, final momentum, and final kinetic energy of the two steel balls to see if the momentum and kinetic energy were conserved. For conservation of momentum calculation, the difference between initial momentum and final momentum were 0.04325, which is about 5.8%. If we were to approximate our results, then, yes, the momentum of two steel balls are conserved. The percentage for momentum was not big. For conservation of kinetic energy, the initial kinetic energy and final kinetic energy were off by 0.0789, about 36.9%, which is way too off. For the second video, where the steel ball moves toward the stationary marble, I did the same calculations, which can be checked in the pictures above. There were also 2.18x10^-4 or 1.33% difference in initial momentum and final momentum. But this value is really small that we could say the momentum between the steel ball in motion and stationary marble are conserved. When we look at the conservation of kinetic energy calculation, we can see that the difference between initial and final kinetic energy is 8.019x10^-4 or 21.7%. Again, the differences for these can be considered small. But I noticed from our conservation of kinetic energy calculations that the percentages were high for both videos.
Conclusion: These differences in calculations might result from the glass table, which we assumed it was leveled after checking that the balls stay at rest. But the graphs that we got say something else. When I checked the graphs, the velocity of stationary balls were not exactly zero.
The other error could be that we did not click on the same point of the balls when we were doing the video analysis using Logger pro to produce our graphs. That could have affect our accuracy of the results. The other factor to think was that there was kinetic friction between the balls and the glass table when they were rolling on the table, which would turn into heat. We ignored the factor of kinetic friction in this lab. If we approximate our results, then we can say both momentum and kinetic energy are conserved.
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