Air Resistance and Mass: Jose Rodriguez; Lab Partners: Kevin Tran; Kevin Nguyen: Date Lab Completed: 3/13/17

The focus to this is experiment was split into two parts that were equally important.  The first part was to find a relationship between the force of air resistance towards an object during free-fall and the terminal velocity of the object. The other part was focused on using the data obtained through the experiment to model a formula for the relationship between both variables.

What we tried to measure was the terminal velocity of an object at different speeds so we could use that data to predict an exponential formula to model the relationship between velocity and air resistance.  To accomplish this task, we recorded the professor of our class drop several coffee filters from a fixed height with varying masses so we could record data to create an Excel sheet.  The Excel sheet was composed of velocity, force of air resistance, acceleration, velocity, and position during small time intervals to create several graphs to evaluate the experimental results.  

To begin with, this experiment required the class to walk to the auditorium of the school because we needed a tall enough height to complete it.  We needed the height because we needed to drop different masses of coffee filters from the same height so we could calculate the terminal velocity at different speeds.  We assumed that more mass would result in a faster terminal velocity so that's why we used different masses during the experiment trials.  Fortunately, the professor did the dropping of the coffee filters while one of our lap partners filmed the process so we could later use that data to create the graphs.  Also, the professor luckily did the work of weighing a collection of 50 coffee filters to obtain a mass of 43.9-g so we could calculate the mass per one coffee filter.  As well he obtained a black cloth long enough to measure more than two meter sticks and marked the length of one meter stick with blue tape so we could use that length to calculate the distance within the needed frame of reference.  Once we were done with that part we walked back to class and began to export the data from the videos into logger pro by using the distance reference and a set time interval to begin plotting points on the center mass of the coffee filter(s) during its decent to create a position vs time graph.  With those first variables velocity, acceleration, force net, and displacement were easily obtained through the Excel application.  Lastly, we used the final velocities of each trial per different masses and created a graph of the force of air resistance (which was equal to the product of mass and gravity per coffee filter) vs terminal velocities of each trial, created a parabola curve and obtained an equation for our model formula for the proportionality of air resistance and terminal velocity.  

This is an image of the professor dropping a coffee filter. Note the two pieces of blue tape, this distance is the one he indicated measured one meter.

This is an image that shows the data from the recorded videos of the drop trials.  The time starts at t=0 and the time intervals are 1/30th of a second, but we plotted points for every third frame of the video.

This image is of the position vs time graph and show the section of the plotted graph that we focused into to measure the objects terminal velocity.  That is the slope of the graph towards the end of the fall. 

Yet again, another picture focused into terminal velocity.

This portrays the calculations for velocity, acceleration, net force of air resistance, and distance with the help of Microsoft Excel.  Notice that the highlighted areas indicate terminal velocity of the object because the velocity doesn't increase with time.  Also, the fact that velocity doesn't increase indicates that we choose a small enough time interval. 

          This image indicates how the excel graph was formulated and also the initial mass calculations for each coffee filter.

Our assumed formula was Force of air resistance= Kv^n and as seen in this image we got a value for k of .0032 and n of 2.5114 with the use of the air resistance vs terminal velocity per trial graph with a parabolic graph.  

In conclusion, we did get a final result for our assumed formula for air resistance vs terminal velocity of a free falling object.  But more interesting is the fact that that formula helps prove the hypothesis that the force of air resistance at terminal velocity is equal to the force of the object falling.  I think this is why there is a terminal velocity even possible.  It seems like if not for the force of air against a falling object, then the object might increase it fall speed indefinitely.  Never the less, our experiment did result in a value for our velocity constant of K= .0032 and of the exponent n= 2.5114 that was very accurate in calculating the force for objects of different masses.  Our assumption was correct about the existence of a formula for air resistance even though there was many areas where our calculations were not exact.  For example, the fact that we recorded the objects free-falling with a lab top computer instead of a high powered effective camera and that the distance reference was makeshift could easily add errors of data to our calculations.  In fact, the graph above of the air resistance vs terminal velocities doesn't have all the plots exactly on the curve so this proves that the results are not as accurate as they can possibly get.  Also, the fact that we were inside a building during the drop trial might influence the results slightly because there was less air movement than if we were outside?  Never the less, the results do make some sense because it did prove to me that during an objects free-fall the encountered air resistance becomes equal to the force of the object to point of causing the object to have a constant velocity without acceleration.