Conservation of Momentum

By Kyle Miller and Craig Jariz

Purpose

The purpose of this experiment is to again show that momentum is conserved in a collision.

Materials

Ball bearings, a floor, a video recording device, and a video analysis application.

Procedure

Place a ball bearing on the floor, making sure it's stable, and, while recording the event, roll another ball bearing at it making sure they collide. Then, using the video analysis software, points can be plotted for each ball to then determine their respective velocities. Then, calculations can check if momentum was indeed conserved in a collision.

Data

The following data were collected via the video analysis application:

Before

	Ball 1	Ball 2
X (m/s)	0	0.7937
Y (m/s)	0	-0.1222

After

	Ball 1	Ball 2
X (m/s)	0.3666	0.3944
Y (m/s)	0.2726	-0.1728

Calculations

From the above data,

Before

After

Since the balls were of the same size, we can interact with the speeds as if they were actually the balls' momentums. Then, calculating the mean value for the speeds in each direction, before and after:

To calculate the average deviation from the mean, we take the sum of the distances of each part of the data to its corresponding mean and divide by the number of parts of data:

So, the maximum error is about 11% for the difference between the energy before and after the collision.

Observations

Despite the camera shaking a bit, the error was suprisingly low. But, the data was very hard to work with as the ball was decelerating as it was about to enter the collision. Averages of two data points were used, which isn't the best but worked. It was hard using video analysis for the event because the balls looked like little comets and choosing the places to plot points was very error inducing as well.

Conclusions

Since the error is relatively low condsidering circumstances, we can conclude that momentum is, indeed, conserved before, during, and after a collision.