Partners: Matthew Ibarra, Billy Justin
Date of Lab: 14 September 2016
Lab 5 Modeling the fall of an object falling with air resistance
Mission Statement:To determine the relationship between air resistance force and speed.
Theory: Objects falling or otherwise moving through the atmosphere don't simply experience the force of gravity downwards, but also some kind of air resistance opposite their direction of motion as the object plows through the molecules which comprise the atmosphere.
Experimental Procedure:
For this problem, we reasoned that the force of air resistance is proportional to the velocity of the falling/moving object and would work in the direction opposite the motion of the object. We determined that to best experiment with this concept, we would walk together to a nearby building with a large internal cavity within which we could drop coffee filters without worry of crosswinds. The professor walked up to the balcony and dropped the filters whilst everybody video recorded the descent. There were 5 of these drops, the first being only one coffee filter, the second being two filters cupped together for added weight, continuing up to the 5th drop, which involved 5 filters cupped together, falling against a black cloth backdrop.
When we returned to the classroom, we used LoggerPro to place dots correlating with the position of the falling filter at each frame of its fall, and when finished, the dots were referenced in the creation of a graph showing position v time of the filter. We did the same for the other four videos in our archive, recording the slope of the curve on each graph, the slope of which should be the terminal velocity once we did a curve fit of the later points. Below, I show the aforementioned graphs, together with a fifth graph showing terminal velocity v air resistance.
Lists/Tables/Graphs of Collected Data with Explanation:
Below is the position v time graph for our falling mass system of (2) coffee filters, which fell faster, the terminal velocity being 2.393 m/s.
Below is the position v time graph for our falling mass system of (3) coffee filters, which fell even faster, the terminal velocity being 2.512 m/s.
Below is the position v time graph for our falling mass system of (4) coffee filters, which fell still faster, the terminal velocity being 3.792 m/s.
Below is the position v time graph for our falling mass system of (5) coffee filters, which fell fastest, the terminal velocity being 4.022 m/s.
Below is the (terminal) velocity v air resistance graph
From the above graph showing the relationship between air resistance and terminal velocity, we determined our values for k and n to be 0.007173 plus/minus 0.001746 and 1.263 plus/minus 0.1933, respectively.
Experimental Procedure:
For this problem, we reasoned that the force of air resistance is proportional to the velocity of the falling/moving object and would work in the direction opposite the motion of the object. We determined that to best experiment with this concept, we would walk together to a nearby building with a large internal cavity within which we could drop coffee filters without worry of crosswinds. The professor walked up to the balcony and dropped the filters whilst everybody video recorded the descent. There were 5 of these drops, the first being only one coffee filter, the second being two filters cupped together for added weight, continuing up to the 5th drop, which involved 5 filters cupped together, falling against a black cloth backdrop.
When we returned to the classroom, we used LoggerPro to place dots correlating with the position of the falling filter at each frame of its fall, and when finished, the dots were referenced in the creation of a graph showing position v time of the filter. We did the same for the other four videos in our archive, recording the slope of the curve on each graph, the slope of which should be the terminal velocity once we did a curve fit of the later points. Below, I show the aforementioned graphs, together with a fifth graph showing terminal velocity v air resistance.
Lists/Tables/Graphs of Collected Data with Explanation:
PART 1
Below is the position v time graph for our falling mass system of (1) coffee filters, with the slope of the highlighted, linearly-fit region of the curve being the terminal velocity of the falling mass. For this drop, the terminal velocity reached 2.104 m/s. 
Below is the position v time graph for our falling mass system of (2) coffee filters, which fell faster, the terminal velocity being 2.393 m/s.
Below is the position v time graph for our falling mass system of (3) coffee filters, which fell even faster, the terminal velocity being 2.512 m/s.
Below is the position v time graph for our falling mass system of (4) coffee filters, which fell still faster, the terminal velocity being 3.792 m/s.
PART 2
*Notice I wrote 'weight x2' in D2 for clarity purposes
Now we applied the mathematical model we developed in Part 1 to predict the terminal velocity of any given number of coffee filters. We set up a spreadsheet with various condition columns which would let us adjust values of k, n, the time interval size between points of the object's fall, and the mass of the falling mass.
To model the descent and terminal velocity of our falling mass system containing (1) coffee filter, we set up the spreadsheet shown below.
Notice how m is the mass of just one coffee filter. With the spreadsheet fully fleshed-out, we kept scrolling down until we noticed the acceleration fell to approximately zero, suggesting constant speed henceforth, shown below.
The terminal velocity shown here is approximately 1.172 m/s, which is not quite the 2.104 m/s which we observed.
We then proceeded to double, triple, quadruple, and quintuple the mass to model each of our tested falling mass systems, with the results shown below.
For the (2) coffee filter system, we collected the following information
Here we see the terminal velocity (the velocity when the acceleration is approximately zero) is shown to be 2.029 m/s, which is yet again lower than our observed value of 2.393 m/s.
For the (3) coffee filter system, we collected the following information
For the (4) coffee filter system, we collected the following information
Here we see the terminal velocity is shown to be 3.511 m/s, which is lower than our observed value of 3.792 m/s
. For the (5) coffee filter system, we collected the following information
Here we see the terminal velocity is shown to be 4.189 m/s, which is slightly higher than our observed value of 4.022 m/s.
Conclusion-
While our observed values were still within the same order of magnitude of difference from the calculated values, the difference is still quite significant, with our observed values for the (1), (2), and (4) coffee filter systems being higher than their calculated counterparts while the observed values for the (3) and (5) coffee filter systems were actually lower than their calculated counterparts. These discrepancies can best be attributed to our admittedly arbitrary dot-placement when we were trying to capture the descent of our five different systems of falling masses. While we were as precise as possible with our placements of dots, the combination of blurry video and an inadequate backdrop definitely hindered our ability to properly place the dots along the trail of the falling mass.
In terms of systematic error, LoggerPro malfunctioned only once luckily, and we were able to recover our data. Otherwise, there were no pieces of equipment which were used, thus the aforementioned discrepencies, while not severe in scope, could nonetheless be the result of simple human error.
With regard to the premise of the experiment itself, we confirmed that the air resistance rises with increasing terminal velocity, suggesting that heavier objects experience more air resistance, since the air will become increasingly unable to get out of the way of the descending object quickly enough to allow for continuously-increasing velocity of descent.
While our observed values were still within the same order of magnitude of difference from the calculated values, the difference is still quite significant, with our observed values for the (1), (2), and (4) coffee filter systems being higher than their calculated counterparts while the observed values for the (3) and (5) coffee filter systems were actually lower than their calculated counterparts. These discrepancies can best be attributed to our admittedly arbitrary dot-placement when we were trying to capture the descent of our five different systems of falling masses. While we were as precise as possible with our placements of dots, the combination of blurry video and an inadequate backdrop definitely hindered our ability to properly place the dots along the trail of the falling mass.
In terms of systematic error, LoggerPro malfunctioned only once luckily, and we were able to recover our data. Otherwise, there were no pieces of equipment which were used, thus the aforementioned discrepencies, while not severe in scope, could nonetheless be the result of simple human error.
With regard to the premise of the experiment itself, we confirmed that the air resistance rises with increasing terminal velocity, suggesting that heavier objects experience more air resistance, since the air will become increasingly unable to get out of the way of the descending object quickly enough to allow for continuously-increasing velocity of descent.
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