13-March-2017: Lab 4: Modeling the fall of an object falling with air resistance

Lab 4: Modeling the fall of an object falling with air resistance

Author: Tian Cih Jiao

Lab Partners: Weisheng Zhang, Kitarou

Date: March 13, 2017

Purpose of the lab:

The purpose of the lab is to determine the relationship between air resistance force and speed. Based on the theoretical model we create, the falling of an object including air resistance is modeled by applying the mathematical model developed in the first part to predict the terminal velocity of various coffee filters.

Theory/Introduction:

Summary of apparatus/experimental procedure:

Measured data:

We capture video for coffee filter in build 13. Then we add points on the video then we get a position verse time graph.

The slope of this line is the velocity of the filter. Then we get five of the same process for all filters. Following picture is the third coffee filter's linear fit graph.

This lab is to find air resistance. So we should find a point of time, the gravitational force equals to air resistance. Then the velocity is the terminal velocity. By applying power fit (F = a * v^b), we get the following:

As a = 0.006143066 +/- 0.00009901, b = 1.987616 +/- 0.1687 (in this case, k = a, n = b), the mathematical model we developed was:

F = 0.006143066 * v^1.987616

Since air resistance force is related to the mass of the object, we measured the mass of 50 coffee filters in order to minimize the impact of propagated uncertainty.

let dt = 0.0001 so that v won't change too much. Then use the formula to find the terminal velocity for each case.

One of the case (6 filters):

The final predicted value is 2.9082054 which is very close to what we got in the LoggerPro which is 2.876. Then we do the same process for the other four times. Here is a summary of predicted and analyzed results:

Percent error = (Analyzed results – Predicted results) / Predicted results * 100%

Analysis: 

After comparing the result of real and predicted, we find that they are very close. There are many factors that would affect the errors. When we add points for the video, we might be not very accurate. And also the falling is not ideal free-fall.

Conclusion:

In this lab, we capture 5-6 times filter falling and add points for each video to get position verse time graphs. Then we get the lab terminal velocity. Then we use mathematical model to get ideal terminal velocity result which is very close to ours result.