In this experiment, coffee filters were dropped in order to calcutlate if there is a relationship between the air resistance force of an object and the object's velocity. This was done by taking coffee filters and dropping different quantities of them off of a balcony. The fall was recorded using LoggerPro and analyzed in order to get data values which could then be inserted into excel and analyzed.
To start the expeiment, one coffee filter was dropped off the balcony. LoggerPro was used in conjunction with a camera in order to record the drop and be used for analysis.
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| Example of how the fall trials were recorded. |
The experiment was done five different times each with one more coffee filter added to the amount used in the previous trial until there was a total of five filters. These recordings were then analyzed in the lab room using LoggerPro by marking the location of the filter in each frame of the recording.
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| Example of a marked video in LoggerPro |
By marking the videos, LoggerPro was able to create a position vs time graph using the release point as the origin.
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| Examples of the 1 coffee filter and 5 coffee filters trials along with their respective linear fits. |
After the plots were graphed, exact values were able to be viewed which assisted in the calculations.
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| Values for the coffee filter quantities 1-4 |
In order to continue with the analysis, the k and n values needed to be determined. In order to do this, the force of air resistance and terminal velocity values were required. Air resistance was found under the assumption that when an object reaches terminal velocity, the force of air resistance is equal to the force of gravity as there is no acceleration, according to Newton's Second Law. Velocity was found by taking the slope of the linear trendline of the data plots as seen in the figure above. Using excel, the force and velocity in order to get a graph and power fit. Which was then used to obtain the values for k and n. k was the value of the slope of the graph and n was the value of the power. When looking at the equation of y=0.0055x^1.9247, it is very similar to the equation Fresistance = kv^n.
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Once the k and n values were determined, another excel plot was opened in order to determine the terminal velocities of the filters based on the formula. By organizing the data like the figure below, the terminal velocity is able to be determined.
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Based on the new graph, k= 0.0055 and n= 1.9247. Compared to the experimental values for k and n, these values are very close thus the relationship between force of air resistance and object's velocity is supported.
This experiment could have been improved using better recording equipment as the coffee filter was very difficult to see in the video thus the points could have been slightly off. However, the results were close to the theoretical thus the experiment was successful.
Once the data is inserted, scrolling down, there will be an area where the velocity does not change The highlighted region below is an example of that. That velocity is the calculated terminal velocity. This is done for the five coffee filter trials and compared to the experimental data.
The experimental and calculated values were then compared to see how close the k and n values were.
Based on the new graph, k= 0.0055 and n= 1.9247. Compared to the experimental values for k and n, these values are very close thus the relationship between force of air resistance and object's velocity is supported.
This experiment could have been improved using better recording equipment as the coffee filter was very difficult to see in the video thus the points could have been slightly off. However, the results were close to the theoretical thus the experiment was successful.
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