12-Sep-2016: Lab 4 Modeling the fall of an object falling with air resistance

1.Title: Lab 4 Modeling the fall of an object falling with air resistance
    Name: Qiwen Ye (Sherry)
    Lab partners names: Eugene, Chandler, Jae Yoo
    Date: 12-Sep-2016

2. Purpose

This lab is divvied into two parts: part 1, we need to determine the relationship between air resistance force and speed. To observe the effect of air resistance on falling coffee filters and in determining how the terminal velocity of a falling object is affected by air resistance and mass, choose which of the two force models best represents the air resistance effect on the falling coffee filter. Part 2, the gold here is to apply the mathematical model we developed in part 1 to predict the terminal velocity of our various coffee filters. 

3. Introduction
We have an expectation the air resistance force on a particular objects depends on the objects's speed , its shape, and the material is is moving through. We modeled this expectation as a power law:

4. Part 1

-- Apparatus/Experimental Procedure
We used the Computer,Vernier Motion Detector, Vernier computer interface, 5 basket-style coffee filters in the lab. We went to building 13 - design technology to do our experiment and use video capture to record the coffee filter movement. At first, Professor Wolf dropped the coffee filter from the balcony inside the building. Then, we used laptop to take a video while the coffee filter is falling in order to record this movement. After that, we went back to the class and analyzed the data that we got. 

-- A list of Data
Here is the coffee filters movement the we got from the video is shown

-- A list of Graphs of Data
Here is the data about 1, 2, 3, 4, 5 and 6 coffee filters falling from the balcony:

-- Explanation/Analysis

In order to obtain the terminal velocity, we created four columns in: time, acceleration, the change of velocity, and velocity. First, we used the dates from part one in order to get five different velocity from one to five coffee filter. Assume 150 coffee is 134.2 gram, we can calculus the weight of coffee filter in order to get the graph about velocity and weight. After that, we got the formula similar to Fresistance=k*v^n, and got k and n. Finally, we used Excel to model the fall of an object with air resistance.

Here is the data that we got from part 1, the velocity and weight for one to five coffee filters. (150 coffee = 0.1342kg).

Here is the graph Velocity vs. Weight

This equation is similar to Fresistance=k*v^n. k: 0.000688  n: 1.366, then we got five different data about different coffee filter.

5. Part 2

-- Apparatus/Experimental Procedure

we used the data from part 1 in order to use Excel to model the fall of an object with air resistance. We stared with the following conditions:

-- A list of Data

One coffee filter:

Two coffee filter:

Three coffee filter:

Four coffee filter:

                         

Five coffee filter:

-- A list of calculated results
The percentage difference of the terminal velocities for one coffee filter is 12.55%. The percentage difference of the terminal velocities for two coffee filters was 6.04%. The percentage difference of the terminal velocities for three coffee filters was 9.09%. The percentage difference for four coffee filters was 17.34%. Lastly, the percentage difference for five coffee filters was 19.68%.

-- Explanation/Analysis
When falling, there are two forces acting on an object, the weigh mg and the air resistance. In the real world, because of the air resistance, an object do not fall in definitely with a constant acceleration. At the terminal velocity, the down force is equal to the upward force.

6. Conclusion
In this lab, we learned how to model the fall of an object falling with air resistance. All of the percentage differences are in the range of the uncertainly displayed in the k and n values, roughly 10% - 20%. In order to lower the human error, we need to do the experiment more time to get more data to analyze the results.