Drag Force on a Coffee 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 a fluid, such as air, it experiences a drag force that opposes its
motion.  This force generally increases with velocity of the object.  In this lab we are going to
investigate the velocity dependence of the drag force.   We will start by assuming the drag force,
FD, has a simple power law dependence on the speed given by
1)  FD  =  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:
NOTE: You will be given a packet of nine nested coffee filters.  It is important that the shape of this
packet stays the same throughout the experiment so do not take the filters apart or otherwise
alter the shape of the packet. Why is it important for the shape to stay the same? Explain and
use a diagram.

1.  Login to your computer with username and password. Start the Logger Pro software, open the
Mechanics folder and the graphlab file. Don’t forget to label the axes of the graph and create an
appropriate title for the graph.  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.  (Be aware other of nearby objects which can
cause reflections.)  Start the computer collecting data, and then release the packet.  What should the
position vs time graph look like?  Explain.
Verify that the data are consistent. If not, repeat the trial.  Examine the graph and using the mouse,
select (click and drag) a small range of data points near the end of the motion where the packet
moved with constant speed.  Exclude any early or late points where the motion is not uniform.
3.  Use the curve fitting option from the analysis menu to fit a linear curve (y = mx + b) to the selected
data. Record the slope (m) of the curve from this fit.  What should this slope represent? Explain.
Repeat this measurement at least four more times, and calculate the average velocity.  Record all
data in an excel data table.
4.  Carefully remove one filter from the packet and repeat the procedure in parts 2 and 3 for the
remaining packet of eight filters.  Keep removing filters one at a time and repeating the above steps
until you finish with a single coffee filter. Print a copy of one of your best x vs t graphs that show the
motion and the linear curve fit to the data for everyone in your group (Do not include the data table;
graph only please).
5.  In Graphical Analysis, create a two column data table with packet weight (number of filters) in one
column and average terminal speed (|v|) in the other.  Make a plot of packet weight (y-axis) vs.
terminal speed not velocity (x-axis).  Choose appropriate labels and scales for the axes of your
graph.  Be 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.  Obtain a printout of your graph for each member of
your group. (Check the % error between your experimentally determined n and the theoretical
value before you make a printout – you may need to repeat trials if the error is too large.)
6.  Since the drag force is equal to the packet weight, we have found the dependence of drag force on
speed.  Write equation 1 above with the value of n obtained from your experiment.  Put a box around
this equation.  Look in the section on drag forces in your text and write down the equation given there
for the drag force on an object moving through a fluid.  How does your value of n compare with the
value given in the text?  What does the other fit parameter represent?  Explain.

Conclusion:

The point of this experiment was to determine through observation and experimentation the effect of drag using the formula k|v|^n by evaluating the value of n with the LoggerPro curve fit analysis. There were several factors to which the experiment may or may not go accordingly; the fact that the coffee filters are very fragile and subject to physical modification and, of course, human error for collecting data, dropping the filters accurately, and fitting the data with a curve fit inaccurately or with a non-optimum value. The result of the trials my group conducted hinted us to believe that the n value was approximately 2. The surface area of the filters is also a dependence factor for the drag calculations, which is why it is very important to keep the filters in pristine condition. In conjunction with the former, we concluded that the more filters you have, the greater the drag because there is more surface area to inhibit an expedited fall.