an investigation of a model for air resistance lab
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An Investigation of a Model for Air Resistance
This experiment was done to determine the exponential value of the velocity of an object falling in the presence of air resistance. To measure this coffee filters were dropped from a standard height and their velocity was measured by a motion sensor. The value that was collected was 1.6922 which is closest to an exponent of 2. The value was about 5 standard deviations of .076 away from 2. Thus it was concluded that terminal velocity was proportional to v2. The error collected was
Ryan MillerAP Physics
6 December 2010
1. Introduction and Background
This experiment is done in order
to find out whether an object’s terminal
velocity is proportional to v or v2. Also
it is to investigate how air resistance
affects an object and its terminal
velocity. To do this one person drops a
coffee filter from a set height while
another person presses the collect button
on the data collect program (such as
Vernier LabPro) which is connected to
the motion sensor below the filter. This
allows the group to measure the terminal
velocity of the coffee filter as it floats
down to the ground. The equation for
the force of gravity observed on the
coffee filter is:
F = mg
However, the force of the gravity was
being counteracted by the force of the air
resistance and thus the total force
equation or Fnet equation is:
Mg – FDrag = ma
with FDrag being the force caused by the
air resistance (see derivation 1 for a
better equational analysis).
After dropping a total of eight
coffee filters for a total of five trials (at
least) of each number of filters, one has
enough data to make a scatter plot (see
graph 1) of the natural log of the data
and a best fit line. The slope of this line
is then the exponent of v that is
proportional to terminal velocity.
2. Procedure
The main equipment needed for
this experiment is a computer (with
Vernier Logger Pro and Vernier LabPro
software and Microsoft Excel for data
collection / graph making), coffee filters
(8 for testing), and a Vernier Motion
Probe (for measuring velocity).
Then a height needs to be set
from which the coffee filters are dropped
(preferably two meters for accuracy).
Each set of 5 (at least, more if wanted)
trials is then accompanied by an addition
of one more coffee filter. To collect data
we used a Vernier software program
known as LabPro with a motion sensor,
but any data collection connected to a
motion sensor would work.
After the eight coffee filters are
successfully dropped, the data collected
from the drops is then put into excel to
create a natural log graph (see graph 1).
Also the standard deviations and other
statistical data analysis should be found
using excel to help supplement data and
explain one’s findings. Finding the
slope of the best fit line of said natural
log graph indicates which exponent of v
is proportional to terminal velocity.
3. Results
The slope of my best fit line was
1.6922. Thus, the terminal velocity is
more closely proportional to v2.
Although the value that I measured was
about 5 standard deviations away from
the accepted value of 2, the value was
much further from 1 due to the fact that
it was about 10 standard deviations away
from 1. Yet the standard deviations
within my own data were very small,
meaning that my data was not very far
apart within each trial.
4. Error Analysis
There were a total of forty trials
executed with five trials per number of
coffee filter.
The value I determined was
1.6922 which is technically 5 standard
deviations away from the accepted value
of 2. Despite being that many standard
deviations away from the accepted
value, the data that I collected was very
closely correlated and was within not
many standard deviations of itself.
Possible sources of error for this
experiment are numerous. One includes
how each coffee filter was dropped, the
slightest change in shape or crinkle
could change the way the coffee filter
fell and throw the data off. Also any
technical errors within the measuring
device itself could throw the data off
enough to drastically move our value
away from 2. As always, every
measurement taken has a slight error in
it due to rounding by computers and
because of any shortcuts or error taken
or made in graph making and best fit
lines by Microsoft Excel (see derivation
1 for equation and graph 1 for graph).
To top it off, doing the experiment in a
closed environment, such as a school (on
the third level no less) may cause a
change in air density which can change
the speed at which the filter falls, as well
as how much resistance there is.
Graph 1:
Natural Log of Coffee Filters and Air Resistance Graph
y = 1.6922x + 0.8177
-0.5
0
0.5
1
1.5
2
2.5
-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Natural Log of Terminal Velocity
Nat
ura
l L
og
of
Co
ffee
Fil
ters
Derivation 1:
(R = resistive force opposite to motion)= ma (where ma = 0 because velocity is constant)
(y=mx+b is used to as a comparison for the final equation to show that the slope is equal to the exponent of v)
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