The setup for this lab was both easy and difficult. What I mean by this is that a lab technician had already set up the camera, rod stand, firewire cable and glass that we were to conduct the collision on which was the easy part. The difficult came when the camera didn't want to communicate with the laptop we were using so our professor was kind enough to lend us his. Below is a picture of the setup.
After following the instructions to setup our camera, we chose three marbles, two of equal mass and a smaller marble, and weighed them for their masses(seen below). The results were, m1=0.021kg, m2=0.019kg and small=0.005kg. For our first collision, we used the two marbles of equal mass. One we had stationary under the camera and the other we rolled into the stationary at an angle so they would go off in different directions. Next, we collided the stationary large marble with the smaller marble with the same intent of them going in different directions. Since there were groups waiting to use the station, we conducted both our collisions before we analyzed our video.
Seen below is the analysis of our video capture with the segment highlighted being before the collision. The red dots represent the x component of motion for our moving marble and the blue represent the y component. The y-axis is position and the x-axis is time. The velocity components of our moving marble, displayed as the slope of the linearization, are shown in the boxes respectively. These are the initial velocities of the collision. As a reminder the mass of the moving marble, m1, was 0.021kg.
Next below is a picture of the analysis with the highlighted portion being after the collision for m1. As you can see by the slopes, the ball has slowed down and changed direction after the collision.
Displayed below is a picture of the same collision but this time, I have analyzed the motion of m2. Before the collision, m2 was stationary and had no velocity. Now though it has gained some velocity displayed in the boxes as the slopes thanks to the collision. The mass of m2=0.019kg just to remind.
Next, we use our masses and recorded velocities to see whether or not both momentum and energy are conserved after the collision.
Above we can see that momentum is almost conserved in the elastic collision between the two similar marbles. The velocities were obtained from Logger Pro after tracking their motion before and after the collision.
Seen above are the calculations for kinetic energy of the two similar mass marbles. Most of the energy is in the Y direction as we chose to have M1 progress along this axis.
In the next experiment, we used marble M1 and S, a smaller marble.
In the picture above, we can see that M1 is the only marble moving with it's velocities displayed as slopes in the boxes above.
Now displayed above is the velocities of M1 after the collision with the smaller marble.
Seen above are the velocities of S after M1 runs into it.
Above are the calculations for momentum. For this collision, we decided to use M1 again to collide with stationary S. The velocities were obtained from Logger Pro after tracking M1 as it went through the action of colliding with S.
These are the calculations for kinetic energy. For both initial components of kinetic energy, only M1 is moving with velocities obtained from Logger Pro. After the collision, both M1 and S are moving but M1 is moving a little slower while S starts moving after the collision.
In conclusion, since these are considered elastic collisions both momentum and kinetic energy should be conserved. However, kinetic energy can be seen to lose about half its value after the collision. It could have been that M1 was projected too fast and didn't roll but skid along the glass surface creating a small amount of friction that took away from the already small values of kinetic energy. It is also possible that the marbles were not tracked very well when the collisions were examined.
The major sources of error from this lab came from the tracking of the marbles. Although great effort was put into obtaining data, the values that came from the data were less than desirable. Another small source of error came from the weighing of the marbles. The scale used to weigh the marbles was accurate to one gram.
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