Drag Force on a Coffee Filter

Purpose: To examine the effects air drag has on free-falling objects.


Equipment/Materials: Computer with Logger Pro software, lab pro, motion detector, 9 coffee filters, meter stick, and a calculator for averaging values

Procedure & Results: For this particular lab we were to let coffee filters fall vertically onto a motion detector that measured the filters' velocities and displayed on a computer with the Logger Pro software. This procedure was done for a total 45 times, more specifically 9 sets of 5 drops. Beginning with 9 coffee filters, we'd remove one from the stack after a set of 5 drops until we ended up with 1 coffee filter. For each set we were to average all 5 velocity values of the drops to get a number for our power law fit graph that would help us calculate the value of n on the drag force formula:

Drag Force = k | v | ^ n

Which is the main point of this lab. The value of n is actually 2 and once we got all of the average values from our sets we were able to find our value for n and came up with 1.84 +/- 0.159 which if added would give us 1.999. Our graph is as shows:

B is the value n.  Calculating our percent error we got .1%

Of course these values were derived from all of the drop trials we did. Here's an example of one of them:

A sample trial using 9 coffee filters that gave velocity 1.87 m/s

Q & A: 

What should the position vs time graph look like?

-It should look linear due to its physical properties the coffee filter reaches terminal velocity almost instantly.

What should this slope represent? 
-The change in velocity over time.

How does your value of n compare with the value given in text?

-It is actually almost that exact value. Our value of 1.999 is only .001 shy from the actual value of 2.

What is the value of K in the drag force formula?

-The value of K is the surface area.

Conclusion: I wasn't aware of terminal velocity prior to this lab. I now know that it's a velocity that corresponds to free-falling objects and gravity. Terminal velocity occurs when the sum of the drag force on an object equals that of the force gravity and has an acceleration of 0 (or a net force of 0). Also, the time the drag force is reaches is dependent upon the surface area and mass of the object. I do have to be honest though, this lab was pretty boring. There isn't anything exciting about dropping coffee filters 45 times. But although boring, this lab was also pretty darn enlightening. I was happy with our n value of 1.999 since it gave us a percent error of .1%. It's difficult for me to identify any sources of error with the results we got but if I had to mention at least one it would have to be the condition of the coffee filters themselves. After every drop and multiple times of touching them, the filters could have been bent or worn down. In summation, this lab was boring but informative and we did really good on it!