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In an experiment I performed, I dropped $n$ amount of coffee filters from a constant height and recorded the time $t$ taken for the $n$ coffee filters to reach the ground. In the experiment, the value of $n$ was kept as small as possible. I assumed that the coffee filters reached their terminal velocity directly (for simplicity).

I tried to find a relation between the no. of coffee filters and the time taken for these coffee filters to reach the ground.

I am very certain that $t(n) \propto n^{k}$, however, I am not sure which value the constant $k$ should have. The closest I got was $k=-1/4$.

Does anyone know if my $k$ has a reasonable value?

EDIT: the equation I get in MS Excel when I plot the data directly is: $t(n)=3.2108n^{-0.295}$, where $k=-0.295$. I think I need to find what fraction this value is close to.

EDIT2: I discovered that this value is close to $1/3$. The $R^2$ value is closer to $1$.


The mass of a coffee filter was $2g$, so time can be expressed in terms of mass also.

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this is an empirical constant, other than the obvious fact that k must be negative, no one knows better if -1/3 is reasonable more than you do.

the tool available to you as you correctly used is the R^2 coefficient. but you need to be careful as to what value counts as a statistically good fit. what you can do is provide your number of data points used to construct the model. you mentioned you kept n low--this is not good--it would be the most obvious weak point of your hypothesis/model.

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Thank you for your answer, @gregsan! :) –  Artem Sep 15 '13 at 13:31
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