Download An Investigation of a Model for Air Resistance

An Investigation of a Model for Air Resistance
Coffee Filter Lab
Introduction: When an object falls near the Earth’s surface it experiences the force of gravity as well as a
drag force due to air resistance. In first year physics, most students are told to “ignore” wind resistance.
This lab is designed to show that a model equation may be tested. One of the simplest models for an object
falling due to gravity is
FDrag  kvn
Newton’s 2nd Law of motion tells us that
Fnet  ma
mg  FDrag  ma
mg  kv n  ma
As the object falls, it gains velocity. This will increase the drag force until the point at which the force of
drag will equal the force of gravity. At this time, the acceleration goes to zero and the object is now in a
state of “Terminal Velocity.”
mg  kv n  ma
mg  kv n  0
n
mg  kvterminal
mg
n
 vterminal
k
mg 1
( ) n  vterminal
k
If the natural log is taken of both sides the equation becomes
mg 1
ln( ) n  ln vterminal
k
1 mg
ln( )  ln vterminal
n
k
1
(ln mg  ln k )  ln vterminal
n
1
(ln m  ln g  ln k )  ln vterminal
n
1
1
ln m  (ln g  ln k )  ln vterminal
n
n
1
ln m  C  ln vterminal
n
1
where C  (ln g  ln k )
n
1
ln vterminal  ln m  C
n
The value of “n” may now be determined if mass “m” and terminal velocity “vterminal” are known.
Objective:
To determine the exponent value of the velocity in drag force for an object falling in the
presence of air resistance.
Fnet  ma
mg  FDrag  ma
Equipment: Coffee Filters (9 soft with corrugations), Vernier Motion Probe, Vernier LabQuest, and PC
with MS Excel or other graphing application.
Procedure:
1. The LabQuest should auto-detect the Motion Probe. Delete the velocity-time graph and
only show the position-time graph. (Graph, Show Graph, Graph 1)
2. You will now begin dropping coffee filters from above the Motion Detector placed on the
floor. The filter should be allowed to fall for at least 6 feet for reasonable data. The filter
will accelerate briefly and then coast downward at terminal velocity. Collect the data. Be
careful not to move around the probe as it is quite sensitive in tracking moving objects.
The person dropping the filter should remain motionless without dropping raised arms
down until filter has reached the ground. If the data looks good, you will now analyze it
by trying to retrieve the terminal velocity. (highlight the section of interest, Zoom In,
Analyze, Curve Fit, Linear)
3. Repeat for m = 1 through 9. This assumes the mass of one coffee filter is 1. We do not
have to find the actual mass of a coffee filter.
4. In this section, you will plot ln(vterminal) vs. ln(m). This should form a linear trend line
representing the equation below:
1
ln vterminal  ln m  C
n
y
=
mx + b
5. Produce a graph that can be used to find the coefficient, n, on the velocity term in the drag
force equation.
Analysis:
Answer the following questions in your formal lab report.
1. What does the slope of your graph represent?
2. Determine the % of error of your slope using the theoretical model having an exponent of “2” in the
equation:
FDrag  kv2
3. Take a closer look at your graph. Was the trend more linear in the beginning, the middle, the end, or
the entire graph? Explain why you think the data may show any areas to be more linear than others
due to experimental flaws. How might you improve this lab using the same lab equipment?