Lab #4
Modeling the Fall of an Object with air Resistance
Ricardo Gonzalez
Josue Luna
3-13-17
In this experiment we want to prove that air resistance is a factor of all free falling objects, regardless of mass.
1. Introduction
When we have looked at free fall motions in the past, we assumed the motion was ideal and the only force accelerating the object was gravity. We know that that is not always the case. Air resistance is an affecting factor in most cases due to the objects shape, the material it is moving through, and as the objects speed. Likewise, as an object speeds up, the force of air resistance must increase. The equation for air resistance is
F(resistance) = kv^n , v is the velocity, where k is a constant value due to the shape of the object and n is an exponential value that the velocity takes.
F(resistance) = kv^n , v is the velocity, where k is a constant value due to the shape of the object and n is an exponential value that the velocity takes.
2. Procedure
For this experiment, we wanted to track the motion of an object during free fall and graph its components of motion. We used the logger pro software to capture a video of the motion of a single coffee filter. We scaled the distance on the camera with the use of scaled reference points from the height. The distance from one hash to another is exactly 1 meter. By adding the scale and placing points on the video after each selected frame per second, we are able to graph the velocity over time. We did the same procedure for 2, 3, 4, and 5 coffee filters. We created an excel file to find the components of the motion numerically.
3. Data
mass of 50 coffee filters = 43.9 +/- 0.1 g
mass of a single coffee filter = 0.89 +/- 0.002 g
The above photo shows the position vs time graph of 1 coffee filter. Slope = 1.154 m/s
4. Results
The above photo shows the slope of the the weight (y-axis) vs velocities (x-axis).
The photo above and below show our numerical data of 5 filters.
5. Analysis
As we know, the formula of air resistance accounts for two unknowns, k and n. When we graphed the velocities of each group of filters vs the weight (in Newtons) of those filters, we can apply a curve fit. From the curve fit, we can see that the curve is exponential, as the speed increases, so does the force of air resistance. What we mean by this, is that when an object falls, at a certain point, the force of gravity is going to equal the force of air resistance, therefore the object is no longer accelerating and in now at its terminal velocity. A larger mass would be needed with the same object in order for the object to once again accelerate and reach a higher terminal velocity which is evident on our graph. The equation of the line from the curve fit is Ax^B. A in this equation is our constant K value and B is our exponential value of N from our equation of air resistance.
By our values measured and calculated, we created an excel file to numerically show the motion of the coffee filters. I have provided two photos of the excel file that show we have set the motion of the coffee filters with the values of k and n as constants. By looking at the file, we can observe that the terminal velocity of the 1 coffee filter reaches 1.38 m/s, however when we found the velocity using the logger pro software, the graph measured the terminal velocity of 1.154 m/s. Also from the excel file, we can see for the five filters, that the filters approach a terminal velocity of 2.492 m/s while the slope of our position time graph for five filters shows that our terminal velocity is 2.471 m/s. These clear deviations in values are due to the uncertainty from our curve fit. There is a range of values for both our k value and n value. Since these uncertainty values were not taken into account in our numerical representation of the motion, the value found from our logger pro software would have been the better choice for this experiment.
6. Conclusion
In summation, the power law of Air resistance holds true as we proved that constants k and n are derived from our own interpretation of the objects motion as it experiences free-fall. With a certain shape of an object and a certain weight (N), there is a limit the speed that object is able to accelerate too since the force of air resistance is going to increase as speed increases until that force of air resistance is equal to the force of gravity pushing it down. An obvious deviation in our data between the slopes of the position time graphs of each group of filters and the numerical value of the corresponding group was due to percent uncertainty found from our curve fit we graphed.
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