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Lab 4- Modeling the fall of an object falling with air resistance

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Purpose
Find the relationship between air resistance and velocity of falling coffee filters.
Process
First, drop those coffee filters at the technology building’s indoor balcony. Take five clips for different amounts of filters. So that we finish the very first step of this lab.
Then use logger pro to analyze the videos, which can give us data needed in the lab. We will get five velocity verse time plots. From it we can derive terminal speeds.
Amount of coffee filters
Terminal speed
1
1.2068
2
1.7117
3
2.1317
4
2.4631
5
2.7491







Data Analyze
Then we should try to match the plot to the formula F= K * V^n.
The matching result shows that K=0.5989 and n=1.958.
With these two values, we can derive a calculating answer for this problem. First we get eight columns named as t, delta v, v, a, delta x, and x. We set the time to 0.01 second, which is a very small time interval, so that we can get a more accurate result. With this simulation, we can get results for the model we derived. The comparing results are followed.


Amount of coffee filters
Terminal speed (actually)
Terminal speed (in simulation)
1
1.2068
1.2115
2
1.7117
1.7262
3
2.1317
2.1233
4
2.4631
2.4594
5
2.7491
2.7563
We can find that those results are similar. The differences may be caused by the calculation error and the error from observation.
Summary

In this lab we learn to use logger pro and photo-capturing system to measure the air resistance when the coffee filter was falling. With terminal speed form different groups, we derive a formula for the falling resistance. With calculating approach, we verify the formula and find its error is acceptable. 

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