Physics II AP
Unit 3: Air Drag Lab
The goal of this lab is to determine how the resistive force of air resistance relates to
the terminal velocity of a coffee filter in free fall.
Background
The drag force has the general form:
Fdrag  bvn
Where b is a constant, and v is the velocity of the object. As an object falls from rest
the velocity increases until the acceleration is zero and the forces are equal in
magnitude.
Mg  b(vt ) n
In this lab, the mass, M, will be comprised of coffee filters and small weights, 1-5
grams or less if necessary. Our goal in this lab is to find n for the drag force and the
constant, b.
Pre-lab Questions
1. Drop one filter and then drop two. Did the two filters seem to fall faster, slower
or at the same rate? What kind of mathematical relationship do you expect will
exist between the velocity of the coffee filter and the number of filters?
2. Based on an educated guess, sketch a graph of velocity vs. time for a group of
filters as they fall to the ground. Do your best to guess approximate shape of the
curve. Also sketch an educated guess of the graph of acceleration vs. time.
v
a
t
t
The Experiment
For each set of coffee filters, take five time trials and then average the results. Keep
increasing the mass of the set of coffee filters by adding small weights until they do
not reach terminal speed. Taking data is quick and accurate using a computer,
PASCO 750 Interfaces, and a motion detector.
1. Plug the USB Link from the 750 into the computer’s USB port and plug in the
power cord. Turn the 750 Interface on so the light is green.
2. Open Data Studio and make sure the interface has been detected then choose
Create an Experiment.
3. A picture of 750 will be on the screen. Click on the number 1. A list of probes
will appear. Choose Motion Sensor. Note it will show the motion sensor with the
cords in the order they must be plugged into port one and two (I believe it is yellow
in 1 and black in 2)
4. Double click on the picture of the Motion Detector and adjust the data sampling
rate to 25 Hertz; 50 Hertz may be better or worse. Adjust as needed during the
experiment.
5. At the top the left column, is the Data window which lists the probes connected
to the interface. Find the Displays window on the bottom left on the screen. Here
you click and drag different displays onto the probe in order to display the data.
Click, hold and drag a “Graph” onto the Motion Detector’s velocity data.
6. Place the Motion Sensor on the floor and point it straight upward.
To measure the terminal velocity, vt, click run and then drop the filters from a
vertical height of at least 2 meters straight onto the motion detector. The motion
detectors have a switch on them; turn it to the narrow beam. Delete any data runs
that were flawed. Fill in the table below.
Weight of filters, W Terminal Speed, vt
(N)
(m/s)
Print out one copy of a velocity vs time graph with several data runs on it.
Analysis
Can you generate a graph using these variables that is linear and whose slope is n,
and whose y-intercept could be used to determine b? Give it a shot and see me
when you have a plan of attack. (Hint: how would you alter the drag equation
Fdrag  bvn , to get a linear relationship?)
Once you know what to plot, use either graph paper or Excel to plot the data and
perform linear regression to determine your value for n and the constant, b. Show
all the steps to determine the values.
Questions
1. According to your data and the following general expression, Fdrag  bv n , how does
the force of air resistance on a coffee filter vary with the velocity of the filter?
2. There are two models for the drag force: one for low speeds and one for high
speeds. At high speeds, the Newtonian drag equation fits:
Fd 
1
 CD Av 2
2
Where ρ: density of fluid; A: cross-sectional area; Cd: drag coefficient.
At low speeds, the Stokes Equation for air resistance (non-turbulent flow) works:
Fd  bv
The constant b depends on the size of the object and the fluid’s viscosity. Does your
experimental results for n favor one model over the other? Justify your answer.
3. If the Newtonian drag force model works, calculate the value for the drag
coefficient of the coffee filter.
4. Refer back to your answers to the preliminary questions. How was your
prediction for the plot of velocity vs time graph different from the actual? Sketch a
velocity vs time graph. Use your knowledge of calculus to sketch an acceleration vs
time graph based on the v vs t data.
5. Look carefully at the velocity vs time plots. Is the average velocity over the data
vi  v f
interval equal to vavg 
? If so, why? If no, then is it closer to the initial velocity
2
or the final velocity?