Coffee filter experiments
Hypothesis
The coffee filters will reach their terminal velocity quickly when dropped and to figure this out we will be solving the drag equation for the exponent (n).
Time-Velocity Graph
We will be testing the following equations:
M * a = M * g - F_drag
F_drag = bv^n
ln v_f = (1/n) ln m + ( (1/n)(ln g - ln b) )
Design of the experiment
To discover exponential equations, we needed an experiment that would show us an exponentially increasing variable with another increasing controlled variable. In this case we decided to drop coffee filters from the balcony of the school's hallway. We were going to drop one, two, three, and four coffee filters at a time for 10 trials per each amount, recording the amount of time it takes to fall the specific distance. So this required two people, one person to drop and the other to play with the stopwatch and come up with numbers.
Data and observations
Data
|
|
1
|
2
|
3
|
4
|
|
1
|
5.65
|
2.87
|
2.78
|
2.16
|
|
2
|
4.75
|
3.31
|
3.50
|
2.59
|
|
3
|
4.89
|
2.72
|
2.72
|
2.81
|
|
4
|
4.78
|
3.03
|
2.82
|
2.75
|
|
5
|
4.63
|
3.15
|
2.72
|
2.80
|
|
6
|
4.56
|
3.22
|
3.25
|
2.31
|
|
7
|
4.81
|
3.18
|
3.75
|
2.56
|
|
8
|
4.68
|
3.28
|
2.83
|
2.91
|
|
9
|
4.89
|
3.40
|
2.93
|
2.16
|
|
10
|
4.65
|
3.22
|
2.68
|
2.56
|
Observations
The coffee filters quickly crumpled up, especially when throwing them in a shoe onto the balcony.
Calculations
Conclusions
The hypothesis was correct and here's the exact value that we calculated.
We also found that it would have been more effective if we started dropping four at a time, so that there would be no structural impairment to the filters and they would have dropped at the same rate. There's a calculation that we can do to show that the effects of the structure influenced the amount of time that it took to fall. Each time that we dropped a single coffee filter, out of the set of 40, there was a certain amount of "structural degradation" that we could label with the variable delta C and multiplied over each trial for each filter, by the near the ends of the rounds, the filters would be falling at a comparatively similar rate that would make it match the actual exponential curve that we came up with in the calculations section.
Discussion
