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LAB 15- Collisions in two dimensions

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Purpose:
Look at a two-dimensional collision between two steel balls or steel and glass ball and determine if momentum and energy are conserved.
Theory:
An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total kinetic energy before the encounter. In this lab we will determine if the momentum and energy are conserved after collision by checking the data collected by the video. The momentum conserve both on the x-axis and the y-axis. So we can determine the change of the momentum in a two-dimensional collision by checking the total momentum in each direction.

Setup:
Set the stationary ball on a leveled glass table. Aim the rolling ball so that it hits the side of stationary ball. Use the phone’s slow motion capture function to collect data as a camera.

Steel ball and steel ball:
We firstly use two steel balls. After getting data from the phone, we use LoggerPro to analyze it. Plot the position verse time so that we can find out the change in two balls’ motion.

X2 and Y2 belong to the stationary ball and others belongs to the moving ball. We can derive the speed by checking the coefficient of time, which is m in the plot.




Vmi
Vsi
Vmf
Vsf
x-axis
0.007914
0.005618
0.1100
-0.07704
y-axis
-0.3435
0.001200
-0.1258
-0.1635
After getting the speed in each directions, we can calculate the change in momentum and energy. The steel ball weighs 67 g.

As we predicted before the experiment, the momentum and the kinetic energy is conserved after the collision.
Then we plot the center of mass with LoggerPro, which are attached below.




The first plot is the plot for the x-axis and second one is for the y-axis. We tried to get the velocity plot in the third and fourth plot but we failed due to the limitation of the LoggerPro. We can derive from those plots the center of mass is scattered.



Steel ball with glass ball
Follow the same steps we can derive the plots for this part.

Vmi
Vsi
Vmf
Vsf
x-axis
0.03314
0.0003901
0.09021
-0.07887
y-axis
-0.5269
0.0003353
-0.1817
-0.4257
The moving ball is made of steel and the stationary ball is made of glass weighed 19.8 g.


As we predicted before the experiment, the momentum and the kinetic energy is conserved after the collision.
Then we check the center of mass with LoggerPro.
As same as the last experiment, the center of mass is scattered.






Conclusion:
We learned how to use LoggerPro to analyze a two-dimensional collision and determine the momentum and kinetic energy. In fact when we examine the equality of momentum and energy, we have quite large errors. Those errors may be due to inelastic collision，the unleveled planet, the friction between ball and planet o

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