19-Sept-2016: Modeling the fall of an object falling with air resistance

Lab 4: Modeling the fall of an object falling with air resistance
Date: 14 & 19 September 2016
Lab Partner: Richard Mendoza
Name: Andrew Martinez

Introduction: Air resistance applied to an object depending on its speed, shape, and the material. This model can be seen as a power law.

Apparatus:
- 150 coffee filters (mass= 134.2 g)
- Meter stick
- Computer

Procedure:
- Take the coffee filters and measure their mass
- Find a high balcony inside a building to minimize air resistance
- Bring laptop to record with logger pro
- Use a meter stick for a point of reference for the recording
- Drop the filters 5 times recording each instance
- Using logger pro graph each video and find the liner fit to plug into part 2 of excel
- Use excel to find terminal velocity

Part 1 Data
The five graphs seen here are position vs time graphs of each of the five videos. The data was taken by scaling the one meter mark and using dots to follow the distance the filters had moved per frame during free fall. This was then calculated by the computer and put into graph form.

Video 1

Terminal Velocity (Slope): 3.088 m/s

Video 2

Terminal Velocity (Slope): 2.156 m/s
Video 3

Terminal Velocity (Slope): 2.842 m/s
Video 4

Terminal Velocity (Slope): 3.373 m/s
Video 5

Terminal Velocity (Slope): 3.100 m/s
Using a power law Fresistance = kv^n (k=a, b=n)
Terminal Velocities Graph

K= .0001901 +/- 0.0002173
N = 4.476 +/- 0.9853

Part 2
Measured Data
Excel spreadsheet to model the fall of an object with air resistance using the terminal velocities.

The predicted terminal velocity for various coffee filters appears to be 5.5 m/s
Plug it into power law Fresistance = kv^n. 0.0001901*(5.5^4.476) = .39 N

Conclusion: K and N are determined from the linear fits done to the video graphs and the results that appear of the terminal velocity graph. There is an uncertainty in terms of how accurate the graphs are depending on the user accuracy on plotting the dots. Air resistance was found to be .39 N and based on the model it was effective in determining the air resistance. Other might like to use this method because it requires less analytical work.