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.
To determine whether air drag is proportional to the speed or the speed squared, you can analyze the data you gathered during the lab experiment. Here's how you can approach this question:
1. Analyze the individual coffee filter drop: You first dropped a single coffee filter from a height of 1.0 meter. Measure and record the time it took for the filter to fall to the ground.
2. Compare the times: Next, compare the time it took for the single filter to fall with the times it took for the combined filter drop.
a. For the combined filter drop from a height of 1.41 meters, measure and record the time it took to fall to the ground.
b. Similarly, measure and record the time for the combined filter drop from a height of 2.0 meters.
3. Analyze the relationship: Now, let's examine how the times compare.
a. If air drag is directly proportional to the speed, we would expect the times for the combined filter drops to be approximately equal to the time for the single filter drop. This means that the increase in distance does not significantly impact the fall time.
b. If air drag is proportional to the speed squared, we would expect that the times for the combined filter drops to be longer compared to the time for the single filter drop. This is because the squared increase in speed results in a more noticeable impact on the fall time.
4. Interpret the data: Based on your observations, deduce whether the times for the combined filter drops are closer to the time for the single filter drop or significantly longer.
a. If the times for the combined filter drops are closer to the time for the single filter drop, it suggests that air drag is closer to being proportional to the speed.
b. On the other hand, if the times for the combined filter drops are noticeably longer compared to the time for the single filter drop, it indicates that air drag is more likely proportional to the speed squared.
5. Support your answer: To strengthen your explanation, you can include any qualitative or quantitative observations that align with your conclusion. For example, you could mention if you noticed any patterns, changes in speed, or any other details that highlight the relationship between air drag and speed or speed squared.
Remember, the goal is to analyze the data you gathered and interpret it in the context of the expected relationship between air drag and speed.