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Gena Horyn
Block III Physics SL
14 October „11
Lab #2: Air Resistance
Research
The goal of this experiment is to determine via a controlled setup the influence of air resistance
and the extent thereof on downward acceleration. The procedure will involve gauging the
distance and velocity of a fallen object and ascertaining trends as well as deviations from such.
A Vernier motion detector will be set approximately 93 centimetres above a tabletop and a
number of coffee filters, from five to one (the number being the independent variable in this
experiment), will be released from a starting position directly under the detector, free to fall. Theinstrument will collect the velocities and positions at increments of .05 s and output them into a
table.
I predict the acceleration will decrease somewhat with time due to air resistance. Additionally, I
predict subtraction of coffee filters will result in a longer time of fall and thus, presumably,
greater air resistance forces.
Variables
The independent variable is the number of coffee filters used in each trial, varying from one to
five.
The dependent variable is the deviation from freefall acceleration in the velocity regression.
The controlled variables include the calibration of the instruments and the types of the coffee
filters.
Materials
Motion detector
Stand for motion detector; ruler
Computer and logging software
Coffee filters, five
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Procedure
Set up motion detector on stand above table surface
Connect motion detector to computer, initiate logger
Drop coffee filter from height of detector
Record position and velocity data
Repeat using varying numbers of coffee filters
Data
Note well that trial 1 corresponds to 5 filters, trial 2 corresponds to 4, etc.
Also note that the uncertainty in the data is negligible for distance and velocity and very close to
negligible for the time (i.e. at the very least, there is no accuracy standard given by the
instruments; the two-decimal figure may well be merely a convention, given that the other dataare given to six decimal places).
Due to space constraints, note :
All times are in seconds (s)
All distances are in metres (m)
All velocities are in metres per second (ms-1)
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Trial 2: 4 filters
Time Distance Velocity0.5 0.178189 0.199035
0.55 0.182991 0.626261
0.6 0.237013 1.120562
0.65 0.308872 1.372286
0.7 0.381588 1.475567
0.75 0.451217 1.63954
0.8 0.542455 1.852676
0.85 0.641582 1.964628
0.9 0.742252 1.93976
0.95 0.848411 1.6109571 0.928158 0.828821
Trial 3: 3 filters
Time Distance Velocity
0.9 0.178532 0.326708
0.95 0.202027 0.754981
1 0.254163 1.180873
1.05 0.333568 1.354564
1.1 0.393593 1.427261
1.15 0.475398 1.500244
1.2 0.541769 1.598666
1.25 0.631806 1.755779
1.3 0.726303 1.719573
1.35 0.805364 1.586566
1.4 0.903291 1.092455
1.45 0.924042 0.435229
Trial 4: 2 filters
Time Distance Velocity
0.6 0.211631 0.730304
0.65 0.26068 0.935342
0.7 0.310244 1.030906
0.75 0.363923 1.095313
0.8 0.419832 1.143238
0.85 0.4802 1.168487
0.9 0.538339 1.179158
0.95 0.587731 1.363711
1 0.675539 1.526159
1.05 0.751513 1.472899
1.1 0.825773 1.30502
1.15 0.890943 0.93982
1.2 0.927815 0.439326
Trial 5: 1 filter
Time Distance Velocity
0.55 0.196368 0.356053
0.6 0.221235 0.419413
0.65 0.241472 0.428369
0.7 0.259137 0.504591
0.75 0.289492 0.616447
0.8 0.330481 0.580051
0.85 0.344715 0.5949140.9 0.379015 0.783469
0.95 0.428922 0.876937
1 0.474884 0.832442
1.05 0.508669 0.826249
1.1 0.554288 0.860644
1.15 0.599564 0.832633
1.2 0.639695 0.778991
1.25 0.665592 0.923909
1.3 0.734192 1.048913
1.35 0.776895 1.048723
1.4 0.834862 1.067778
1.45 0.900375 0.768225
1.5 0.917011 0.371107
1.55 0.927815 0.137009
0
1
2
3
1 1.5 V e
l o c i t y / m s - 1
Time / s
Trial 1 Velocity
0
2
4
0.5 0.7 0.9 V e l o c i t y / m s - 1
Time / s
Trial 2 Velocity
0
1
2
0.9 1.1 1.3 1.5 V e l o c i t y / m s - 1
Time / s
Trial 3 Velocity
0
1
2
0.6 0.8 1 1.2 V e l o c i t y / m s - 1
Time / s
Trial 4 Velocity
0
1
2
0.5 1 1.5 V e l o c i t y / m s - 1
Time / s
Trial 5 Velocity
Trial 1: 5 filters
Time Distance Velocity
1.1 0.178703 0.450854
1.15 0.212832 0.977169
1.2 0.279202 1.444221
1.25 0.375928 1.585327
1.3 0.439212 1.673649
1.35 0.52822 1.987018
1.4 0.646041 2.137652
1.45 0.754257 2.002072
1.5 0.859387 1.545501
1.55 0.928844 0.729447
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Note well that the following velocity graphs discard some of the data points previously
mentioned, especially the “peaks,” which represent merely the strong deceleration as the filter
approaches the table and do not convey any meaningful information regarding the acceleration.
Therefore, only the initial few points will be used to adulterate the results to the smallest extent
possible.
y = 6.1075x - 6.1028
0
0.5
1
1.5
2
1 1.1 1.2 1.3 1.4
V e l o c i t y / m s - 1
Time / s
Trial 1 Velocity
y = 6.5982x - 3.0002
0
0.5
1
1.5
2
0.45 0.55 0.65 0.75
V e l o c i t y / m s - 1
Time / s
Trial 2 Velocity
y = 3.9663x - 3.0013
0
0.5
1
1.5
2
0.8 1 1.2
V e
l o c i t y / m s - 1
Time / s
Trial 3 Velocity
y = 1.3751x + 0.009
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0.5 0.7 0.9
V e
l o c i t y / m s - 1
Time / s
Trial 4 Velocity
y = 0.9192x - 0.1266
0
0.2
0.4
0.6
0.8
1
0.5 0.7 0.9 1.1
V e l o c i t y / m s - 1
Time / s
Trial 5 Velocity
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This table compares the number of filters used in each respective trial with the average of the
gradient of the linear regression of the segment of the graph most resembling the expected trend.
Filters vs. Air Resistance
Filters Trial Acceleration Deviation
from g
1 5 6.1075 3.6925
2 4 6.5982 3.2118
3 3 3.9663 5.8437
4 2 1.3751 8.4349
5 1 0.9192 8.8908
y = 1.562x + 1.3288
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6
D e v i a t i o n f r o m g ( m
s - 2
)
Filters (#)
Number of filters v. deviation from g
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Conclusions
Several general trends may be seen in evaluating these data.
Firstly, as the velocity graphs show, the acceleration does show a trend of leveling off, seemingly
to terminal velocity; this trend is a result of a force of drag that is increasing directly with the
square of the velocity and opposing the force of gravity.
Secondly, the hypothesis was correct and the greatest air resistance was seen in Trial 5 with onefilter. This may be attributed, at least in part, to structural features; i.e. the non-rigidity of a single
coffee filter makes it somewhat more aerodynamic than a greater number of filters.
Thirdly, as the number of filters increases, so does the absolute value of the deviation from the
accepted value of g (in this specific case, 9.81 ms-2
) and thus the opposing force due to drag.
Viz., if the filters were in true free fall, the graph of their velocity would be a straight line with g
as the gradient.
Fourthly, all of the trials show a velocity spike immediately after the sound portion of the trial.
This may be a result of the proximity to the surface, air currents, and non-vertical movement of the coffee filters; however, there seems to be no conclusive answer as to its cause.
Fifthly, in all of the cases the uncertainties are, for all intents and purposes, negligible, as the
final results use only rather general trends and regressions, reducing propagation of error.
Sixthly, according to the “Number of filters v. deviation from g” graph, adding a single coffee
filter decreases the acceleration of the net force working on the objects in falling by
approximately 1.6 ms-2
.
Evaluation
Although these trends are reasonable and present in all of the trials, the specific instances vary
somewhat. Much of the data was inapplicable due to great variations in acceleration and
inapplicability to actual freefall.
The data collection occurred with high precision; however, certain errors, such as random non-
vertical movement may have occurred and hampered the process.
Otherwise, all of the conclusions are consistent.
Improvements
The experiment would be improved by a normalization of data via repeated testing. Also, some
method of restricting non-vertical movement might be devised to most accurately gauge the
position and velocity.