Mass Effects On The Terminal Velocity Of A Coffee Filter Falling In Air

1148 words - 5 pages

1
Mass effects on the Terminal Velocity of a Coffee Filter Falling in Air
February 30
th
, 2012
Written By: Ima Cool Performed with: Notso Lame
Question: How does increasing the mass of a coffee filter falling through air affect the
terminal velocity it reaches?
Design:
The mass of the falling coffee filter, independent variable, will be varied by nesting one
to four filters instead the initial filter. The terminal velocity, dependent variable, will be
read from a velocity-time graph generated from the motion sensor. The shape and
surface area of the filter will be controlled. In addition, all trials will take place from the
same height and within the same medium, air.
Materials: 5 coffee filters
electronic balance (±0.1 g)
computer with Data Studio & motion sensor
thermometer (±0.5
o
C)
30 cm ruler (±0.05cm)
meter stick (±0.5cm)
retort stand
Figure 1: Set-up of Materials used for data collection
motion sensor
coffee
filter
2.0m
lab bench
2
Procedure:
1) Materials were set-up according to Figure 1. Within Data Studio, the motion sensor
was connected and a graphical display of velocity vs time was set-up.
3) Air temperature in the room was measured and recorded with the thermometer. The
air temperature was monitored throughout the data collection for any variations. Using
the electronic balance the mass of each coffee filter was measured. The diameter across
the opening of each coffee filter was measured using the 30 cm ruler.
4) Using the 30cm ruler, a single coffee filter was held 20.0 cm from the motion sensor.
The velocity-time graph was generated and the terminal velocity was recorded. This
process was repeated to generate a total of 3 trials.
5) Step 4 was repeated for 2, 3, 4 and 5 filters, nested inside one another (to maintain
surface area and shape of the filter) to generate the data set in Table 1.
Note: Any trial in which the filter `floated` out of the path of the beam was discarded.
Observations:
Table 1: Several trials of the terminal velocity reached by varying masses of coffee filter
as they fall through air
Trial
Number of
Coffee Filters
Mass of Coffee
Filter
(±0.1g)
Terminal
Velocity
(±0.05m/s)
1
1 1.1
1.34
2 1.30
3 1.36
4
2 2.2
1.70
5 1.90
6 1.87
7
3 3.3
2.11
8 2.05
9 2.08
10
4 4.4
2.59
11 2.64
12 2.55
13
5 5.5
2.75
14 2.56
15 2.89
* The coffee filters were dropped from 2 meters above the floor, the air temperature of
the room stayed at 22.2±0.5
o
C, the surface area of the filter increased slightly over the
trials (diameter from 14.1±0.5 cm to 14.9±0.5 cm) and the mass of each coffee filter was
1.1±0.1g
3
Analysis:
Sample Calculations
To determine the average velocity for the 1.1 g filter:
Ave terminal velocity =
=
= 1.33m/s
Table 2: Average Terminal Velocity of Falling Coffee Filters in Air versus The Mass of the Coffee Filter
Mass of Coffee
Filters
(x10
-3
g)
Average
Terminal
Velocity
(m/s [down])
1.1 1.33
2.2 1.82
3.3 2.08
4.4 2.59
5.5 2.73
Figure 2: Terminal Velocity vs Mass of Coffee Filter
The data was fit to a linear trend as well as a power trend. Since the R
2
value of
the power trend is closer to one, it will be used to find the relationship between the two
variables. From the equation, vT = 1.2657m
0.4548
, it is noted that the exponent of 0.4548
can be approximated as 0.5 which then identifies the relationship between the two
variable as the square root function. Hence the terminal velocity of the coffee filter
varies with the square root of its mass. The mass data was modified according to the
vT = 0.3245m + 1.039
R2 = 0.9742
vT = 1.2657m
0.4548
R2 = 0.9881
0
0.5
1
1.5
2
2.5
3
0 0.001 0.002 0.003 0.004 0.005 0.006
T
e
rm
in
a
l
V
e
lo
c
it
y
(
m
/s
[
d
o
w
n
])
Mass of Coffee Filter (kg)
4
sample calculation below and a graph of terminal velocity versus square root of mass was
generated.
Sample Calculation
To determine the square root of the mass of the 1.1 x 10
3
kg filter:
=
= 0.033 √kg
Table 3: Terminal Velocity versus the square root of the mass
Mass of Coffee
Filters
(x 10
-3
kg)
Square root of the
Mass of the
Coffee Filter
(√kg)
Average
Terminal
Velocity
(m/s [down])
1.1 0.033 1.33
2.2 0.047 1.82
3.3 0.057 2.08
4.4 0.066 2.59
5.5 0.074 2.73
vT= 35.147√m + 0.1557
R2 = 0.984
0
0.5
1
1.5
2
2.5
3
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
T
e
rm
in
a
l
V
e
lo
c
it
y
(
m
/s
[
d
o
w
n
])
√ Mass of Coffee Filters (√kg)
Figure 3: Terminal Velocity vs √Mass for Falling Coffee
Filters
5
Conclusion & Evaluation:
From Figure 2, it is evident that as the mass of the coffee filter increases, the
terminal velocity for the filter increases. Since the R
2
value of the square root line of best
fit was closer to 1, Figure 3 was constructed to show this relationship that the terminal
velocity of the filter varies with the square root of the mass of the filter. Since the data
generated a linear line, with an R
2
= 0.984, very close to 1, this confirms that the
prediction of VT α √m is valid. In addition, it was determined that the equation between
the 2 variables was vT= 35.147√m + 0.1557.
One source of error is attributed to the surface area of the coffee filter. It was
noted that as more coffee filters were nested inside each other, the diameter across the
opening increased. This would cause the measured terminal velocities to be lowered. It
is suggested that this factor could be reduced by starting with 5 nested filters out of the
box and then remove one at a time so that there is no stretch when adding more filters.
A second source of error occurred in the reading of the terminal velocities. A
judgement had to be made where the velocity-time line levelled off. In some of the trials
the lines were erratic. This could cause the terminal velocities to be either larger or
smaller. A solution would be to have the motion sensor set at a higher sampling rate.
In addition, the trials for the 4 and 5 filters, there wasn't enough time for the filters
to completely reach terminal velocity. This may have caused the terminal velocity
measurements to be higher. A solution to this problem would be to use larger coffee
filters with larger surface areas to lower the terminal velocities or to have the filters fall
through a larger distance allowing them to reach their terminal velocity.

RELATED

Desribe and evaluate the filter theory of attraction - A level - Essay

599 words - 3 pages concept that filtering based on similarity in attitudes and complementary of needs as an explanation of attraction. A03; Temporal Validity; One weakness of the filter theory in explaining attraction is that it can lack temporal validity. · Temporal validity is the extent to which the findings of a study can be applied to other historical times and era. · Social demographic variables are reduced as technology has increased. Dating sites like tinder

The study of falling in health care facilities - nbcc nursing - essay

791 words - 4 pages there was a curb beside the car. This accident resulted in the swelling of my ankle for months. Falls is the most common factor that negatively affects our daily living, especially in the healthcare facility falling and falls related injures are one of the main concerns of a patient’s safety, especially in among those 65 years and older. Patient’s safety, efficient patient care and quality patient care are top priority of healthcare organization

In Specific, The Mass Of A Volatile Unknown Liquid Was Discovered With The Use Of The Calorimeter

1015 words - 5 pages This is a standardized lab write up for an American Advanced Placement Chem class dealing with the use of a calorimeter. In specific, the mass of a volatile unknown liquid was discovered with the use of the calorimeter.Experiment Eleven - Heat Effects and CalorimetryIn this lab, molar mass of a volatile liquid was determined through the use of a calorimeter The lab validates the equation Q=S.H * M * T, by using the known or calculable values of

This Essay Discusses The Fair Trade Coffee Movement And The Advantages Of Fair Trade Coffee Over Regular Coffee

1076 words - 5 pages through at theexpense of the large producers, who harm the environment. I told them the information Ilearned about "good work" and stressed that as a Catholic family, it is our responsibilityto do something to assist these people who are denied good work. Finally, I told myparents that Fair Trade Certified coffee is available at three locations in my hometown,two of which they go to on a weekly basis, so they do not even have to go out of theirway to

the effects of a shark in water - biology - essay

463 words - 2 pages can’t deal with any of this any more 2) Ok I get I might have introduced the Idea of us not talking to each other in public, but I eventually was going to have this problem if you put in too much effort realising that Marie doesn’t want your friendship anymore will hurt even more. On this note from all of this I’ve realised that I don’t need anyone’s friendship I just need to focus on my studies games will be blocked from my life this whole

The Effects Of The Great Depression Of 1929 On Democracy In Germany

679 words - 3 pages Effects of Depression on DemocracyThe depression that hit Germany in 1929 is said to have been the most severe depression in modern world history. It devastated the lives of the German republic as well as caused the German Reichstag of 1930 to crumble. However, there were many other reasons for the demise of democracy. These include, but are not limited too, radical right wing extremists challenging democracy, structural problems within the

Impact Of Mass Media In Bangladesh

4181 words - 17 pages used beside Bengali. It is not anymore the signature language of sophistication but it has become a must in an educated person's life. Newspapers, media and internet have made picking up other languages easy. Language is, undoubtedly, the foundation of every culture. Language communicates a culture's most important norms, values, and sanctions to people. When an extraneous culture effects on the language, the impact of mass media is

Analyze The Effects Of The Great Depression On Australia In The 1930s

1231 words - 5 pages , generosity, mateship and resourcefulness commonly seen in Australians today.The Great Depression had a dramatic effect on Australia both economically and socially. It brought about negative effects such as depression, loss and the breaking up of families while also bringing about some goodness like profit for the wealthy and the creation of the Australian attitude which is common today.BIBLIOGRAPHYSpencely G, 1981, "The Depression Decade

A look at imperialism effects on the people of the African Congo - History 10 - Assignment

736 words - 3 pages White King, Red Rubber, Black Death The events of the Congo Free State bear a striking similarity to another major genocide of the twentieth century: the Holocaust. Both are very influential events in our history that we can learn a lot from in order to prevent another tragedy from happening. On the surface, they seem like very different things: a European king exploiting the people of an African country for resources versus the leader of

The Effects Of Lead Poison On Children

2547 words - 11 pages . This problem has been a large issue since the 1920s, when the EPA(Environmental Protection Agency) started making laws on the amount of lead allowed in gasoline.There are many other ways that a child especially under the age of six can be diagnosed to lead poison besides air pollution. One of the most common ways of our past is when a child eats or chews on an object that has lead based paint chips in or on its surface. Parents can easily

Effects Of Globalization On The Environment

584 words - 3 pages Effects of Globalization on the EnvironmentGlobalization has had a huge impact on the world in a number of ways. It has increased the integration of countries' individual economies, the rise in the world trade and multinational companies, and the effect of large amounts of money moving in and out of economies throughout the world. People around the world are more connected to each other than ever before. Information and money flow more quickly

The Effects Of Fairy Tails On Children

1181 words - 5 pages Most of parents read fairy tales to their children and these children enjoy listening fairy tales. However, in fairy tales there are some characters which are taken as a model by children and patterns connecting with some patterns like wedding. In The Green Fairy Book, in 1982, as Lang refering to Lang to emphasises fairy tales to have fun for children but also teach them. Those characters and symbols have active roles on children's behaviour

Air Pollution and it effects. Also Solutions and effectiveness of solutions. - Kulisc - essay

1974 words - 8 pages the SOA formation in the air, petroleum manufacturers should increase the quality of fuel. This can be done by adding hydrogen fuel additives to fuel as it would result in reductions of emissions. In fact, in 2009, British manufacturer, CGON developed Ezero1, a hydrogen additive product which aids in reducing emissions produced by a vehicle engine by up to 80% (Technology, 2018). According to information on the developer’s website, the unit once

Oral History of Media in the 20th century - Mass Communication - Oral history report

1343 words - 6 pages and error with a little bit of frustration locating someone to interview, I settled nicely on a phone conversation with my wife’s step-grandmother. Jerri Rock, who lives in West Virginia, was more than happy to talk with me about the changes throughout her 75 years. She grew up in the southern area of Washington D.C., with what she described as easy parents who enjoyed music and television. I am extremely grateful for her taking the time to talk

Drinking Coffee Somewhere: A Profound Take on Modern America - Pierce College English 101 - Persuasive Essay

1000 words - 4 pages Fernald 2 Tatiana Fernald Dr. Duffy English 101 16 April 2018 Drinking Coffee Somewhere: A Profound Take on Modern America In the time I have had the pleasure of reading ZZ Packer's compilation of short stories in her book, Drinking Coffee Elsewhere, I found several specific elements of her writing and overall story-telling that sheds light on the issues and social dynamics of contemporary America in an accurate and relatable way. Specifically