8-Sep.-14: Modeling The Fall Of An Object Falling With Air Resistence

PURPOSE: To learn how to determine the relationship between Air Resistance, Force, and Speed.


The experiment was conducted indoors on a balcony, for the sake of avoiding any wind interference.

Our test measurement required dropping a coffee filter from about 2 meters and analyzing the fall through logger pro.


We have an expectation that air resistance force on a particular object depends on the object's speed:

After we captured the filter's fall, we marked the position (blue dots) of the filter, frame by frame, as it fell to the ground.
This was the same process used for analyzing the filters that were released from the balcony.





The measurements were then plotted on the position-versus-time graph (below), where the slope of the line represents the average terminal velocity of the coffee filter.




















Once we figured out how to measure and plot the free fall, we took more coffee filters to the top of a balcony.

For the first measurement we dropped 1 filter (1gram),
for the second, 2 filters (2g),
for the third, 3 filters (3g),
for the fourth, 4 filters (4g),
and for the fifth, 5 filters (5g).


We also know that at the filter's terminal velocity, the Force of air resistance is equal to the total weight of the filter(s).




We then found the velocities(slope of x-vs-t graph) for the five rounds of falling filters.

After finding values for velocity in all five rounds, we found a value for acceleration using excel.

Combining all five runs, we plotted the Force (air resistance = Weight) versus Velocity graph.
Getting the graph set into a power fit, we were able to determine values for k and n from our original equation for air resistance.

Converting the equation's variables to the graph's:

k = A = 0.007563 ± 0.001291

n = B = 1.764 ± 0.1816

Later in our work, we realized that the data collected from the fourth run with 4 filters, didn't exactly turn out as expected - this was most likely an overlooked error somewhere during the experiment.

So, for the purpose of our graph and for the purpose of more accurately analyzed results, we told the program to ignore the forth run in our data set and to compute the remain runs.