Drag force on a coffe filter

                                           Drag force  on a coffe filter
                   

Purpose: To study the relationship between air drag forces and the velocity of a falling body.

Equipment: Computer with Logger Pro software, lab pro, motion detector, nine coffee filters, meter stick

Introduction:

When an object moves through air, it experiences a drag force that opposes its

motion. In this lab we are going to investigate the velocity dependence of the drag force.

We will use the equation Fdrag = k |v|n, where the power n is to be determined by the experiment.                

This lab will investigate drag forces acting on a falling coffee filter. Because of the large surface

area and low mass of these filters, they reach terminal speed soon after being released.

Procedure:

Why is it important for the shape to stay the same? Explain and

use a diagram. It is important for the filter to stay the same shape because we need the surface area to be the same.

 

1. We logged into the computer with username and password. Start the Logger Pro software, open the Mechanics folder and the graphlab file. Then we Set the data collection rate to 30 Hz.

2. Place the motion detector on the floor facing upward and hold the packet of nine filters at a minimum height of 1.5 m directly above the motion detector. We started the  collecting data, and then release the packet. What should the

position vs time graph look like? Explain. The coffee filters should decreased in position at a constant velocity (when the graph made a straight line) just before they hit the ground.

3. We then used the curve fitting option from the analysis menu to fit a linear curve (y = mx + b) to the selected data. We then Record the slope (m) of the curve from this fit. What should this slope represent? Explain. The slope should represent terminal velocity.

 We then repeat this measurement at least 8 more times, and calculate the average velocity. And record all

data in an excel data table as shown below.

4. We then carefully remove one filter from the packet and repeat the procedure in parts 2 and 3 for the remaining packets of eight filters.  We keep removing filters one at a time and repeating the above steps until we finish with a single coffee filter. As shown in the above data table. We then print a copy of one of your best x vs t graphs that show the

motion and the linear curve fit as shown below.

5. We then used Graphical Analysis, create a two column data table with packet weight in one

column and average terminal speed (|v|) in the other. We Made a plot of packet weight (y-axis) vs. Terminal speed. Choose appropriate labels and scales for the axes of your

graph. We made sure to remove the “connecting lines” from the plot. Perform a power law fit of the data and record the power, n, given by the computer. We obtain a printout of your graph as shown below:

  We then check the % error between the experimentally determined n and the theoretical value . Our B value is equal to n which is 2 since the original equation shows v^2. Our value for B was 2.21. We can calculate our percent error with the equation:

% error = |(accepted-experimental)/accepted| X 100

% error = |(2-2.21)/2| X 100

% error = 10.5%

We then calculated area as shown below : we can find the surface area of the coffee filters since the k value is constant.

k = A

A = 1.39

k = 1.39

k = (1/4)A

1.39 = (1/4)A

A = 5.56

And finally a calculation for the original equation F(drag) = (1/4)Av^n

A=5.56

V=9.89m/s

N=2.22

=220N

Conclusion: Based on the experimental terminal velocity average was 2.22 and the original was 2 based on are percent error that was 10.5%. We had a high percent error meaning we did not take to account several things including air current in the room . Other things that could have been a factor included filters position on top of each meaning the air that goes between each filter if not properly stacked.