11-MAR-2015: Modeling the fall of an object falling with air resistance

Part 1

(Determining the relationship between air resistance force and speed)

Purpose:  The purpose of this portion of the lab is to collect data regarding the velocities of falling coffee filters and relate it to the force of air resistance acting on said coffee filters.  We will use this data and plot it appropriately in order to determine the values of k  and n in the following power-law equation:

   Fresistance = k * v^n

Procedure:  We began by walking over to the design technology building.  Inside, there is a balcony on the second floor which can be easily viewed from the nearby staircase.  We then used video capture software on our MAC systems to record the falling coffee filters (first one, then 2 stacked, up to a total of 5 stacked at a time).  Utilizing the LoggerPro software back in class, we created a reference length distance within the recorded video.  We then plotted points on the video as the object fell (at 1/30th second intervals).  Gathering all this data together, we plotted position vs. time graphs for each individual run.  An example is seen below:

(Position vs. Time graph of first run; a single coffee filter)

Having measured the mass of a single coffee filter (m = 0.00092 kg) we were able to produce a Force vs. Velocity graph.  Such graph is seen below:

(Force vs. Velocity Graph)

It is from this graph, we can see the values of k and n for our power-law equation. 

Where k = 0.01193 and n = 1.951.

Part 2

(Modeling the fall of an object including air resistance)

We gathered and organized all of our data into an Excel spreadsheet in order to determine the terminal velocity of each run (that is, a single coffee filter, to five stacked together).  

(Excel spreadsheet containing all gathered data; this section represents a single filter)

If we scroll down the velocity (v) column, we'll see that it begins to become a constant value as time goes on.  This value, is the value of terminal velocity of the coffee filter.

(Excel sheet for run 1; terminal velocity = 0.866282 m/s)

Conclusion:  To be 100% honest, this particular lab write-up is (when compared to my others) not up to standards; I was sick, as I'm sure was noticed, most of the week this lab occurred.  Therefore, my understanding of exactly what went on during this lab is, somewhat fractured.  I do understand however, the concept of how terminal velocity is represented in the Excel datasheet.