Download Design Lab

Note: A thumb drive will be very useful for this lab. If you download to a thumb drive, it
is only necessary to print this page for lab.
Pre Lab Questions for Drag Force Design Lab
1. Get 3 of the same, light object with significant surface area (non-cone coffee filters work
best; paper towels or plates work too). Hold a single item in one hand and the other two
items stacked together in the other. Release them from the same height and watch them fall
to the ground. Ignore drift to the right or left. Based on that experiment, would you predict
that there is a mathematical relationship between the maximum speed reached (aka terminal
velocity – vt ) and the mass of that object? For the purposes of this project; both at home and
in the lab, the number of objects can be taken to represent the mass.
2. Draw a free-body diagram (fbd) of an object falling at terminal velocity. Draw the force
arrows at the appropriate relative length for this fbd. Write Newton’s 1st or 2nd Law
(whichever is appropriate) for this situation (Hint: When the object reaches terminal velocity,
it is no longer accelerating).
For the next 2 questions, please attach an additional sheet or complete on the back of this one:
3. Sketch your prediction for a graph of velocity vs. time for a falling object with a nonnegligible drag force.
4. Using equipment that you know is available in the Miramar College physics lab, describe an
experiment that you could do to investigate whether there is a linear relationship between the
number of falling objects and the resulting terminal velocity. You don’t have to give stepby-step instructions, but your description should include the types of probes, software, and
other equipment, and an explanation of how your experiment will achieve your goal.
Additional reading about the drag force can be found in your text.
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Design Experiment to Investigate Drag Force
Due Date: April 17/April 19
SUMMARY
It’s your turn! You and your lab partners will get to design a laboratory experiment that
investigates the relationship between the drag force on a falling object and its velocity. This
is a two-week project. The first week you will work together to write up the design
parameters of the lab. This includes the objective, the equipment, the procedures for data
collection, and the methods of analysis. With the time remaining, you can start to collect data
and refine your procedures. The Logger Pro computer program should be available for you to
download to your home computer. Alternatively, Excel can be used for data analysis at
home. The second week you will actually perform the lab, obtain data and formulate
conclusions that support your objective, or cause you to modify it. This will allow you to
write up a formal lab report.
Grading for this Lab (total of 40 points for the two weeks):
 A thoughtful design of a lab to investigate drag force, using equipment efficiently,
collecting enough data to obtain meaningful values: 20 pts.
 Well-written out lab report with all the sections listed below: 20 pts.
 Plagiarized lab report, from the Internet or other source: 0 pts
 Data which support your hypothesis without any error or ambiguity: PRICELESS!
But not absolutely necessary for a good grade. The emphasis is on following the
principles of the scientific method, as opposed to the hypothesis being absolutely
correct.
INTRODUCTION: When you solve physics problems involving free fall, often you are told to
ignore air resistance and to assume the acceleration is constant and unending. In the real world,
because of air resistance, objects do not fall indefinitely with constant acceleration. One way to
see this is by comparing the fall of a baseball and a sheet of paper when dropped from the same
height. The baseball is still accelerating when it hits the floor. Air has a much greater effect on
the motion of the paper than it does on the motion of the baseball. The paper does not accelerate
very long before air resistance reduces the acceleration so that it moves at an almost constant
velocity. When an object is falling with a constant velocity, we prefer to use the term terminal
velocity, or vT. The paper reaches terminal velocity very quickly, but on a short drop to the floor,
the baseball does not.
Air resistance is sometimes referred to as a drag force. The direction of the drag force is opposite
to the direction of motion. Experiments have been done with a variety of objects falling in air.
These sometimes show that the magnitude of the drag force is proportional to the velocity and
sometimes the magnitude of the drag force is proportional to the square of the velocity. If the
former case were true, it would mean that:
Fdrag = bv (eq.1)
If the latter were true, it would mean that:
Fdrag = cv2 (eq.2)
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In each case, the constants b and c are called the drag coefficients and depend on the size and
shape of the object, as opposed to the mass.
It has always been a challenge in the community college physics lab to determine which of the
above equations is the more accurate description of the relationship between drag force and
velocity. This is because direct measurement of the drag force on a falling object is impractical
to obtain. The experimental designer must choose alternate measurements which both describe
the relationship in question AND can be can be done accurately with available equipment.
QUESTIONS
1a. If equation 1 above is true, write an equation showing the relationship between the
magnitude of the gravitational force and the magnitude of the drag force at terminal velocity for
any object:
_____________ = mg
1b. Now remove all the constants from the above equation (g is a constant on this planet) and
rewrite it as a proportionality:
______________
∝ ___________
2a. If equation 2 above is true, write an equation showing the relationship between the
magnitude of the gravitational force and the magnitude of the drag force at terminal velocity for
any object:
_______________ = mg
2b. Now remove all the constants from the above equation and rewrite it as a proportionality:
______________
∝ ___________
YOUR ASSIGNMENT
With your partners, design an experiment to allow you to choose between the two competing
force models (i.e. Equations 1 and 2) for the drag force on 1 to 5 falling coffee filters. Your
experiment may or may be the one that you described in your pre lab. You must explain in
your objective statement how it will achieve the objective of the assignment.
LIMITATIONS:
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During the lab period, please do not access the Internet. You must agree to this in order
to use a personal computer.
Please do not use lab equipment until you have compiled a legible draft of your
equipment list. You may use the lab computers, but we will not distribute printer cables
until you are ready to print data and graphs.
Due to the extra length of this lab, it cannot be dropped as your lowest grade.
The lab scales do not accurately “mass” 1 coffee filter. You can use number of filters as
an approximation of mass.
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The motion detector has a maximum sample rate of 30 samples per second, which can be
set by clicking on the clock icon. It must be set each time you open a new file, else it will
default to 20 samples per second.
Objective Statement State the objective of your experiment and explain how your
experiment will achieve that objective. Write the draft statement, below:
Equipment (You must have any item you wish to use in your experiment on this list.
This includes everything from computers to stopwatches, and coffee filters). Attach a
piece of paper with your draft list.
Procedure – Number each step. This should be very complete. The type of
information here should include things such as:
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Which probe you will use (e.g. force probe, motion detector)
Whether probe will be at the top or the bottom of the drop (it is ok to drop coffee filters
ONLY on top of a probe from a distance of 2 meters. If it is the former, explain what
method you will use to support the probe
How long will the drop be and how you know your maximum mass will reach terminal
velocity in less than that distance
They type of data you will be taking (position, velocity, force, acceleration, time) and
how you will obtain that data, step by step
How you will recognize whether to keep data, or discard and retry.
DATA TABLES- Here is an example for one filter. Only use the columns you need for your
experiment. You should have a separate data table for each number of coffee filters dropped (no
more than 5). Some raw data will already be listed in columns in Logger Pro, but may be hard to
print. DO NOT print graphs that generate data for falling coffee filters, use tables instead.
One Coffee Filter
Trial #
Position
Terminal Velocity
vT (m/s)
Time of drop (s)
Terminal Velocity2
vT 2(m2/s2)
1
2
3
4
5
6
7
8
9
10
Avg
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ANALYSIS
1. Decide which values will be used to determine if your data better support Equation 1 or
Equation 2. Notice that you are choosing between two different descriptions of the drag
force, neither may not correspond exactly to what you observed.
2. To manually enter and graph data in Logger Pro, disconnect all devices and the LabPro
interface, and bring up a new file. Double click on each column to name it and add
information about units, etc. The first column is for the x-axis (independent variable); the
others are for the y-axis (dependent variable). You may also make graphs with Excel or
another program.
3. For all graphs, include an appropriate title and name all axes. Include all analysis boxes. For
Excel choose the option to print graph equation and R2 error term (this is automatic on
Logger Pro). Decide whether “forcing” your data to have a y-intercept of 0 makes sense for
analysis purposes and if so, make 0,0 your first data point in Logger Pro (Excel has an option
you can choose to automatically do this).
CONCLUSIONS
Discuss results.
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Based on your data and analysis, were you able to determine which of the equations
discussed in the introduction is a better model for the relationship between the drag force
and the velocity of a falling object? If so, what is your conclusion? If not, explain why
not.
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What were the problems associated with your lab design? Were you able to modify your
design and get better data?
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Based on your results, do you think your lab design, if written up as a college-level
“equation verification lab” would be a good lab activity for:
o An engineering mechanics class (like this one!)
o A non-calculus based physics class
Your response should take into account how difficult it is to understand the relationship between
the quantities that you were able to measure and the quantities that you were actually
investigating, as well as how well the data were able to “verify” the equation in question.
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