Drag Force on a Coffee Filter Lab

The purpose of this lab is to observe and study the relationship between air drag forces and the velocity of a falling coffee filter. In order to do this lab the materials needed are:

• Computer with Logger Pro
• Lab Pro
• Motion Detector
• 9 Coffee filters
• Meter Stick

INTRODUCTION

When an object falls, it experiences a drag force that points in the opposite direction of which way the object, such as a ball, is moving. When this drag force reaches its maximum force, which is equal to the Gravitational Force pointing in the opposite direction, it has reached it's terminal velocity. This is a constant velocity because when added, the Drag Force and Gravitational Force leave an Fnet = 0. Even though the Fnet is 0 doesn't mean that there isn't any movement. This just means that there is no acceleration.

When calculating drag for this lab we are going to look at the equation:

F(drag) = k|v|^n

and when you compare this equation to drag equation which is

F(drag) = (1/4)Av^2

where A is the surface area of the object and v is the velocity you can see similarities. In the equation we are going to use in the lab k is equal to (1/4)A because it is a constant that will work for all the trials we are going to do even though we are doing trials of different numbers of filters falling. They all have the same surface area.

PROCEDURE

In order to do this experiment, we set up Logger Pro on the computer and labeled our graph on the x axis as Time (s) and the y axis as Position (m). We set our motion detector on the floor facing up and set the data collection rate on Logger Pro to 30 Hz. We also opened an EXCEL spreadsheet and made column titles for velocity of each trial and row titles for how many filters were used for the experiment. We grabbed 9 filters and stacked them into a packet. You must be careful of not damaging any of the filters because it is very important that we keep the surface area the same because since our k value is constant for all trials our A needs to stay the same to keep this true. 

Once we had our graph and table ready, we clicked the "Collect" button and dropped the 9 filters above the motion detector and recorded the data. We did a linear fit to the part of the Position Vs. Time graph where the coffee filters decreased in position at a constant velocity (when the graph made a straight line) just before they hit the ground. We copied the slope which is the velocity into trial 1 for 9 filters into the spreadsheet and repeated this for a total of 6 times. We then calculated the average velocity of the 6 trials.

This graph is one of the trials that shows the constant slope, or terminal velocity, of the falling filters.

Once doing 6 trials for 9 coffee filters and finding the average, we repeated the experiment for 8 filters instead, then 7 filters until we had 6 trials for each amount of filters until we reached 0 filters.

This is the table of the terminal velocities found for all of our trials that we did.

Once having this information we created a graph in Graphical Analysis of the Number of Filters vs. Average Terminal Velocity. When doing so we got the graph of the function we looked at in the introduction:

F(drag) = k|v|^n

We took a power law fit to show the equation of the graph where the value of k = A and the value of n = B.

CONCLUSION

When interpreting this information we first look at the Position vs. Time graph. There is a time right before it hits the ground when there is a constant change in the position with respect to time. This means that it is in a straight line and we have a constant velocity. This is what we call our terminal velocity or terminal speed.

When we performed a power law fit to the Number of Filters vs. Average Terminal Speed graph we were given an A value and a B value. The A value is equal to the value for k in our equation F(drag) = k|v|^n and the B value is equal to n.

The value for k when we go back to the equation F(drag) = (1/4)Av^2 is the constant (1/4)A. It is a constant because our value for A (surface area) is constant since all of trials we did were equal to eachother. This is because when the filters are stacked the surface area never changes since there are none being added around the bottom one. This means 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

Our B value is equal to n which should be equal to 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 had a fairly high percent error but we can make that number smaller because some things we can take into affect would be was there air currents that were going on in the room. Another would be the filters because since they were stacked some could have caught more air resistance since they could've been hanging off the edge of the bottom one a little bit. 

In this lab I learned how to calculate values of terminal speed of a falling object. We used coffee filters and found their terminal speeds when being dropped from 1.5 m.