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## 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}= [itex]\frac{Δd}{Δt}[/itex]

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=-[itex]\frac{mg}{b}[/itex]k.

We can treat -[itex]\frac{mg}{b}[/itex] 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 = [itex]\frac{Δd}{v}[/itex].

Is this correct? It's hard to think about it when you don't have values.