Drag Lab Using Coffee Filters

[mawr95]

Homework Statement

We are given 3 coffee filters. Using a stopwatch and a meter stick, make measurements to predict how long it would take for those filters to fall down a stairwell. Come up with an experimental method to predict this time.
During the lab, we will be told the number of coffee filters that will be used (1-9), as well as the height of the stairwell.
We are given the formula for the force of drag: F_d = -bv

Homework Equations

F_d = -bv
v_terminal = $\frac{Δd}{Δt}$
F_G = -F_d

The Attempt at a Solution

First, find the average terminal velocity for each number of filters. Drop a filter from a high enough height, that it will reach terminal velocity very early on (like 2m). Record the time that it takes the filter to fall. Repeat this for two filters and three filters. For each number of filters, divide the height it fell by the time it took in order to find velocity.
At terminal velocity, F_net = 0. So, F_G = - F_d.
Therefore, kmg = -bv, where k is the number of filters.
Arrange it so that v=-$\frac{mg}{b}$k.
We can treat -$\frac{mg}{b}$ like a constant because we are only changing the number of filters (k), which affects the velocity (v).
Then could we just divide v by k to find the relationship, since the other terms are constant?
If that was correct, then could we just multiply that relationship by the number of filters being dropped down the stairwell to find their velocity? Once we have the velocity, knowing the height of the stairwel, we can easily find the time to fall. Δt = $\frac{Δd}{v}$.
Is this correct? It's hard to think about it when you don't have values.

 

[PhanthomJay]

Yes, well thought out. The results depend largely upon how closely the drag force behaves in accordance with the given formula F_d = -bv
(a linear relationship), which you should note in your error analysis.

'It's hard to think about it when you don't have values'.

Yeah, I think you should be an engineer. They like to to get rid of the letters and crunch out the numbers as soon as possible to get a 'feel' for the situation.:thumbs:

 

[HallsofIvy]

You say, right at the beginning, that your instructons are "Using a stopwatch and a meter stick, make measurements" and "come up with an experimental method". There is nothing in that that says you are to come up with a formula a-priori. Yes, "it's hard to think about it when you don't have values". That's why the instructions here are to do the experiment to get values!

 

[Chestermiller]

2 m is a pretty long distance to reach terminal velocity. How long is this stairwell? If 2 m is on the same order as the length of the stairwell, you may have to take into account the acceleration phase of the motion. According to your equations, for a given length of stairwell, the time should be inversely proportional to the number of filters. Therefore, the product of the time times the number of filters should be constant. Or, you could plot the time as a function of the number of filters on a log-log plot, and it should yield a straight line with a slope of -1. If not, then you would have to figure out why.

Chet

 

[Nickie]

I would first like to commend you for your attempt at solving this problem using scientific principles. Your approach seems logical and could potentially yield accurate results. However, there are a few things that need to be considered in order to ensure the accuracy of your predictions.

Firstly, it is important to note that the formula for drag force (Fd = -bv) is a simplified version and may not accurately represent the drag force experienced by the coffee filters. This is because the drag coefficient (b) varies with factors such as the shape and size of the object, the density of the fluid (air in this case), and the velocity of the object. Therefore, your predicted terminal velocity may not be entirely accurate.

Secondly, the experiment to find the terminal velocity of the coffee filters may be affected by external factors such as air currents, which could alter the results. In order to minimize these effects, you may need to repeat the experiment multiple times and take an average of the results.

Additionally, the relationship between the number of filters and their velocity may not be linear. This means that simply dividing the velocity by the number of filters may not give an accurate relationship. It would be beneficial to plot a graph of the data collected in order to determine the relationship more accurately.

Finally, it is important to consider the limitations of the experimental setup. For example, the height of the stairwell may not be high enough to allow the filters to reach their terminal velocity. In such a case, the predicted time may not be accurate. It would be beneficial to choose a stairwell with a greater height or to adjust the experimental setup to allow for a longer fall time.

In conclusion, while your approach to predicting the time for the coffee filters to fall down a stairwell using scientific principles is commendable, it is important to consider the limitations and potential sources of error in the experiment. By addressing these factors, you can increase the accuracy and reliability of your predictions.