Drag Force on a Coffee Filter
Purpose: To study
the relationship between air drag and the velocity of a falling body.
Equipment:
Computer with Logger Pro software, lab pro, motion detector, nine coffee
filters and a meter stick.
Objective: In
this lab we are investigating the drag force experienced by an object moving
through the air, and how this drag force affects velocity. We started with the equation for drag force, Fd = kv^n,
where we set out to find the value of n.
Question 1: Why
is it important for the shape to stay the same?
Because the k, in the equation for drag force, is the cross
section area of the object, if the k changes then so will the drag force.
Procedure: We
started by setting up the equipment for the experiment; this included hooking
up the motion detector to the lab pro and the lab pro to the computer. We placed the motion detector on the floor
and measured a distance of 1.5 meters.
This distance was going to be the distance where we dropped our coffee
filters.
Question 2: What
should the position vs time graph look like?
The should be a flat line at 1.5 meters once it is released
it should decrease faster until the coffee filter reaches its terminal velocity
then it should be decreasing constantly.
After making our predictions we released the pack of nine
coffee filters and made recordings for the position vs time graph. Using the curve fit tool in the Logger Pro
software we were able to fit the linear
curve (y = mx + b) to our recorded data.
This gave us the slope of the position vs time graph. Below is print out
of the position vs time graph.
Question 3: What
should this slope represent?
The slope of a position vs time graph gives the velocity of
the coffee filter pack. In this case
it’s the Terminal velocity, the maximum velocity reached when the upward drag
force is equal the downward gravitation force.
We then repeated the procedure five times total for each
amount of filters, we removed one by one until we only had one filter. After measuring the terminal velocities for
each amount of filters we took the average.
The following is a table of the five trials per amount of filter and the
average terminal velocity in meters per second.
In Graphical Analysis, we created a two column data table in
order to plot our average velocities in a graph. On the y-axis we had the number of filters,
while the x-axis was used to represent the terminal speed. We then performed a Power Law fit on the data
we plotted, doing so gave us the value of n in our equation for drag
force. The value of n we obtained from
the experiment was 1.99 the theoretical (accepted) value is 2. So by experimentation we calculated the value
very close to the accepted the percent difference was calculated as follows ((2
– 1.99)/2) x 100 = .5%.
The equation we obtained after finding the value of n
Fd = kv^1.99
The equation from the text
Fd = (1/4)Av^2
Below is print out of the average velocities
graphed with the value of n calculated
Question 4: How
does the value of n compare with the value given in the text? What does the
other parameter represent?
The value we obtained from the experiment was 1.99, the
value in the text is 2. So by means of
experimentation we were able to verify that the value in the text
accurate. The equation from the
graphical analysis was y = A*x^B, the value of A is the value given in the text
(1/4)A whish is the cross section area of the object, y is the number of
filters.
Conclusion: In
this lab we investigated the relationship between the drag force and velocity
of a falling object. We found that as
the drag force increases the velocity gradually increases. The velocity stops increasing when the drag
force equals the weight of the coffee pack.
At this moment the net force is zero, that is the drag force counter
balances the gravitational force. The
force diagram for the coffee pack would include to vectors of equal magnitude,
one pointing upward (Drag force) and one pointing downward (gravitational
force). The sources of error that
prevented us from getting the exact value of n would be rounding issues, both
on the experimenters end and the computer.
Another possible source of error was that the filters did not fall perfectly
straight all the time, this may have caused the motion sensor not to read
correctly. Not selecting the correct
portion of the graph to do a linear fit may have played a role in getting an
incorrect velocity reading. Also the
shape of the coffee filter may have not been the same throughout the whole
experiment this would affect the drag acting on the filters.
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