Purpose:
Determining the relationship between air resistance force and speed.
Predicting terminal velocity of the object with a mathematical model.
Theory:
The relationship between the air resistance and speed can be modeled with a power law, but we have two unknowns of K and n.
Apparatus:
We dropped coffee filters from a balcony to the ground, starting with 1, and slowly adding up to 5 coffee filters. We captured this motion with LoggerPro and used video capture to be able to plot position and time to find terminal velocity. We plotted the terminal velocity and applied a power curve to find the unknown constants K and n. This gives us a model to be able to predict the air resistance force. We then set up an Excel model similar to the one in Lab 3 for Non-constant Acceleration to predict the terminal velocity to compare the numerical results to the experimental results.
Data:
Part 1
Part 2
1CF:
2CF:
3CF:
4CF:
Graphs:
Explanation/Analysis:
This is the model we derived from the graph after applying a power fit to the terminal velocities. We did not include the fifth point because it was a stray. It messed up the graph, and the graph looked a lot better when the fifth point was not included.
Conclusion:
The answers we arrived at whether numerically or experimentally were pretty close in value. They were precise to the hundredths place. I think some errors that can be accounted for is when we were trying to plot the points for position versus time, as that was a bit time consuming and tedious, and there are a lot of rooms for error at that step. The coffee filters always tend to disappear towards the end of the video, so some of the points were very hard to plot. Regardless, the answers we arrived at were relatively close to each other.
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