Posted by Mary on .
I had to complete a lab where I had to find how much time it took for one coffee filter to fall 1.0 meters. Then I had to drop two filters stuck together from 1.41 and 2.0 meters. There is a question asking if air drag is proportional to the speed or the speed squared and what data did you you gather to support your answer. I do not know how to answer this question.
This is not an ideal experiment for determining the velocity dependence of drag, but you can make some inferences. In this case, a V^2 dependence is expected, if the filters remained horizontal, which they probably will if they are slightly concave with the middle portion down.
The times it takes to fall 1.41 and 2.00 m, if in the same ratio, would indicate that the filters quickly obtain a limiting velocity. You should be able to detemine the limiting velocity from the time it takes to fall those distances. At the limiting velocity, the aerodynamic drag force equals the weight. If the two filters together fall at a limiting velocity that is sqrt2 = 1.41 times faster than a single filter, then since two filters weigh twice as much as one, the drag force must be proportional to the square of velocity.
That may or may not agree with your experiment. Try it and see.
I just realized that the difference in the times required to travel 2.00 m and 1.41 m is a good indication of the time required to travel 0.59 m, after the terminal velocity is achieved. So, divide 0.59 by that time difference for a terminal velocity measurement, and see how that velocity depends upon the number of stacked coffee filters, which is proportional to the drag force.