How to Compute the Experimental Value of G Frome the Slope Value
The measurement of the acceleration of gravity, g, is usually conducted in the science laboratory, especially in Physics subject. In contrast to the traditional method using a set of ticker timer, we propose a simple method to determine the magnitude of g using a smartphone, unused A4-sized papers, and a pencil. We use the smartphone application called Phyphox, operating in Timers and Acoustic Stopwatch mode to measure the time between two acoustic events. We then fold unused A4-papers together and put a pencil over them. After that, we flick the folded papers so that the pencil falls down. The first jingle from flicking causes the Acoustic Stopwatch to start whereas the second jingle from hitting of pencil on the floor makes it to stop. Through the measured time read by Acoustic Stopwatch and the height of folded papers, we are able to calculate the average of magnitude of the gravitational acceleration at the 5 different heights via (i) arithmetic mean, (ii) graphing by hand, and (iii) graphing by excel. Based on our observation of a free-falling object, we found that the magnitude of g at Bangkok equals to 9.760 m/s2. Comparison with the standard value of 9.783 m/s2 measured by the National Institute of Metrology (Thailand), our experimental value for gravity agrees well with the standard value which offers very good accuracy with a percentage of error of about 0.23%. We envisage that this work is not only economical, and can hence be conducted in places with limited access to laboratory tools, but also provides learning opportunities for students in hands-on practicing and data analysis.
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International Journal of Advanced Science and Technology
Vol. 29, No. 7s, (2020), pp. 884-889
884
ISSN: 2005-4238 IJAST
Copyright ⓒ 2020 SERSC
Measuring the Acceleration of Gravity Using a Smartphone,
A4-Papers, and a Pencil
Aungtinee Kittiravechote and Thanida Sujarittham
1Program of General Science, Faculty of Education, Bansomdejchaopraya Rajabhat University,
Bangkok 10600, Thailand , aungtinee.ki@bsru.ac.th
2Program of General Science, Faculty of Education, Bansomdejchaopraya Rajabhat University, Bangkok
10600, Thailand or Thailand Center of Excellence in Physics, Commission on Higher Education, 328 Si
Ayutthaya Road, Bangkok 10400, Thailand, thanidasu@gmail.com
Abstract
The measurement of the acceleration of gravity, g, is usually conducted in the science laboratory, especially in
Physics subject. In contrast to the traditional method using a set of ticker timer, we propose a simple method to
determine the magnitude of g using a smartphone, unused A4-sized papers, and a pencil. We use the smartphone
application called Phyphox, operating in Timers and Acoustic Stopwatch mode to measure the time between two
acoustic events. We then fold unused A4-papers together and put a pencil over them. After that, we flick the folded
papers so that the pencil falls down. The first jingle from flicking causes the Acoustic Stopwatch to start whereas
the second jingle from hitting of pencil on the floor makes it to stop. Through the measured time read by Acoustic
Stopwatch and the height of folded papers, we are able to calculate the average of magnitude of the gravitational
acceleration at the 5 different heights via (i) arithmetic mean, (ii) graphing by hand, and (iii) graphing by excel.
Based on our observation of a free-falling object, we found that the magnitude of g at Bangkok equals to 9.760
m/s2 . Comparison with the standard value of 9.783 m/s2measured by the National Institute of Metrology
(Thailand), our experimental value for gravity agrees well with the standard value which offers very good
accuracy with a percentage of error of about 0.23%. We envisage that this work is not only economical, and can
hence be conducted in places with limited access to laboratory tools, but also provides learning opportunities for
students in hands-on practicing and data analysis.
Keywords—Gravitational acceleration, laboratory tool, Physics teaching, smartphone.
I. INTRODUCTION
For students enrolled in secondary school, practicing with scientific experiment to understand the truth of nature
is an important learning process [1], especially for development of practical skill and scientific reasoning skill [2],
[3]. One experiment that all students must conduct is to determine the acceleration of gravity using ticker timer [4],
[5]. By attaching one end of the paper strip to the object and another end of that to the carbon paper of ticker timer,
later, allowing such object to fall freely under the force of gravity, these cause the needle of ticker timer presses
onto the carbon paper and spots as black dots arranged on the paper strip with the time between two adjacent dots
equally to 1/50 second. After that, students must record the distance measured between two adjacent dots, and then,
calculate the average speed between two adjacent dots. Consequently, for the analysis of experimental results,
students are assigned to plot the relationship between the average speed and time, draw a straight line called the
line of best fit, and then calculate the slope of the line of best fit in which equals to the magnitude of the
gravitational acceleration at the Earth's surface, together with the percentage of error from the experiment.
Because of the development of technology, smartphones today come with various sensors (such as microphone,
camera, thermometer, gyroscope, proximity sensor, digital compass, and barometer, etc.) to facilitate a better user
experience [6]. This opens up new perspectives on using smartphones as the laboratory devices [7]. For example,
smartphone can be used as an angle meter to read the angle of the ramp tilted relative to the horizontal plane which
is useful in reporting the coefficient of friction [8], or it can even be an acoustic stopwatch to count the time taken
from start to stop using sound which benefits for measuring the speed of sound in the air [9].
Toward this end, we are therefore interested in utilizing the smartphone as a tool to determine the magnitude of
International Journal of Advanced Science and Technology
Vol. 29, No. 7s, (2020), pp. 884-889
885
ISSN: 2005-4238 IJAST
Copyright ⓒ 2020 SERSC
gravitational acceleration (g), instead of ticker timer. We use the smartphone application called Phyphox,
operating in Timers and Acoustic Stopwatch mode to record the time between two acoustic events. We then fold
unused A4-papers together and put a pencil over them. After that, we flick the folded papers so that the pencil falls
down. The first jingle from flicking causes the Acoustic Stopwatch to start whereas the second jingle from hitting
of pencil on the floor makes it to stop. Next, we record the time read from the Acoustic Stopwatch and the height of
folded papers after repeating the experiment at least 3 times. Finally, we perform the same procedure at the 5
different heights and calculate the average of magnitude of the gravitational acceleration through (i) arithmetic
mean, (ii) graphing by hand, and (iii) graphing by excel. In comparison with the theoretical value of g= 9.783 m/s2
at Bangkok, provided by the National Institute of Metrology (Thailand), we found the experimental values for
gravity agree well with the standard value: g = 9.713 m/s2, 9.752 m/s2, and 9.760 m/s2through the employment of
arithmetic mean, graphing by hand, and graphing by excel, respectively, for data analysis.
II. THEORY
Free fall is an example of a vertical motion with constant acceleration. Free-falling object is not only limited to
releasing object in the hand, but also included in throwing up and down. This is because as soon as the object
moves away from the hand, there is only the force of gravity exerted on it. Although the air resistance takes place
along the motion, it might be negligible at a position near the earth's surface.
The rate of speed's change of free-falling object is defined as the gravitational acceleration which is denoted by
the symbol of
. For simple calculation, the magnitude of
is equivalent to 9.8 m/s2 . However,
in practical
depends on the location of mensuration, e.g., the magnitude of
at London and Bangkok is reported as 9.812 and
9.783 m/s2 , respectively [10].
As mentioned before, free fall is one-dimensional motion under constant acceleration. Accordingly, the equation
of motion is
(1)
where the parameters s , u ,t , and aare, respectively, the distance, the initial speed, the time, and the acceleration. If
the experiment is designed by dropping the object
, the
equation is reduced to
(2)
As shown by the above equation, through the measurement of the height and the time of travel for free-falling
object, we are able to determine the acceleration of gravity.
III. METHOD
A. Materials and equipment
The necessary materials and equipment composed of 1 smartphone with Phyphox application, 1 pencil or pen,
4 sheets of unused A4-sized papers, 1 tape or glue, 1 scissors, and 1 ruler or tape measure or meter stick. A
calculator, a graph paper, and a computer with excel program are optional for data analysis.
B. Procedure
The experiment is conducted as follows. Folding A4-sized papers together into a shape that the pencil can be
placed on as shown in Fig. 1. Opening the Phyphox application, selecting the Timers mode, and then choosing
the Acoustic Stopwatch function. Adjusting the threshold with a value in between 0.3 to 0.5 a.u. Pressing the
Play button shown by the triangle symbol (the time appears 0.000 s). Flicking the folded paper so that the pencil
falls down as shown in Fig, 2. The first jingle from flicking causes the Acoustic Stopwatch to start whereas the
second jingle from hitting of pencil on the floor makes it to stop. Recording the time read from the Acoustic
Stopwatch and the height of folded papers after repeating the experiment at least 3 times. Performing the same
procedure again at the 5 different heights. Finally, calculating the average of magnitude of the gravitational
acceleration through (i) arithmetic mean, (ii) graphing by hand, and (iii) graphing by excel.
International Journal of Advanced Science and Technology
Vol. 29, No. 7s, (2020), pp. 884-889
886
ISSN: 2005-4238 IJAST
Copyright ⓒ 2020 SERSC
Fig. 1. Setting the height of free fall experiment using the unused A4-sized papers folded into various shapes that
the pencil or pen can be placed on.
Fig. 2. Time series of the free fall experiment
C. Data analysis
Arithmetic mean of the gravitational acceleration is determined from the average value of gat the 5 different
heights as
International Journal of Advanced Science and Technology
Vol. 29, No. 7s, (2020), pp. 884-889
887
ISSN: 2005-4238 IJAST
Copyright ⓒ 2020 SERSC
(3)
Each height must follow the equation of motion as
(4)
Likewise, to find the average value of gusing the graph, this can be done by plotting the relationship between
height in meter (Y-axis) and squared time in second2(X-axis). The line of best fit from all data results in a
straight line that passes through the origin with its slope of half of the magnitude of g, in other word, gis equally
to twice of the slope.
Furthermore, to enhance the efficiency of our analysis, we use the excel program to interpret the data and
provide the line of best fit with its corresponding linear equation. We noted that after generating the graph with
scatter plot, we find the line of best fit from the following commands: Layout, Analysis, Trendline, More
Trendline Options, choose Linear, tick Set Intercept = 0.0, and tick Display Equation on chart.
Finally, to estimate the percentage of error, this can be obtained from the equation ,
,%100%
Theory
TheoryExperiment
g
gg
Error
(5)
where gTheory represents the magnitude of the gravitational acceleration at Bangkok which equals to 9.783 m/s2
[10].
IV. RESULT AND DISCUSSION
The time of free-falling object recorded by the Acoustic Stopwatch at the 5 different heights as well as the
corresponding magnitude of acceleration of gravity from (4) are presented in Table 1.
TABLE I: EXPERIMENTAL RESULTS USING THE ACOUSTIC STOPWATCH
Acceleration
of Gravity
(m/s2)
In order to evaluate the magnitude of the gravitational acceleration measured by a smartphone, we analyze the
experimental result with the 3 different methods as follows.
A. Calculation of g via arithmetic mean
Through (3) and (5), the magnitude of acceleration of gravity identified in the previous section is averaged and
becomes 9.713 m/s2 with 0.72% of error compared with standard value of 9.783 m/s2.
B. Calculation of g via graphing by hand
The averaged magnitude of acceleration of gravity from experiment is obtained through graphing data by hand,
as shown in Fig. 3. Plotting the relationship between height in meter (Y-axis) and squared time in second2
(X-axis) gives a linear line of best fit. The slope of the straight line is approximately 4.876 m/s2which results in
the magnitude of the gravitational acceleration of 9.752 m/s2. The measured value of gis thus within 0.32% of
the theoretical quantity.
International Journal of Advanced Science and Technology
Vol. 29, No. 7s, (2020), pp. 884-889
888
ISSN: 2005-4238 IJAST
Copyright ⓒ 2020 SERSC
Fig. 3. Obtaining the averaged magnitude of acceleration of gravity (g) using the graphing data by hand. The plot
between height (Y-axis) and squared time (X-axis) shows a linear line of best fit with its slope (or gradient) of half
of the magnitude of g.
C. Calculation of g via graphing by excel
To enhance the analysis effectiveness, the averaged magnitude of acceleration of gravity is further deduced from
graphing using excel. As shown in Fig. 4, the dependence of the height on the squared time performs the linear
relationship with its corresponding equation,
(6)
This provides the magnitude of the gravitational acceleration of 9.760 m/s 2. Comparison of the experimental
value with our measure displays an accuracy of 0.23%.
Fig. 4. Enhancing the effectiveness of data analysis to determine the magnitude of the gravitational acceleration (g)
via graphing by excel. The result shows that the measured value of the magnitude of g is twice of the slope and
becomes 9.760 m/s2with 0.23% of error.
As shown in the data analysis with 3 methods that composed of arithmetic mean, graphing by hand, and
graphing by excel, the magnitude of the acceleration of gravity are found to be 9.713 m/s2, 9.752 m/s2, and 9.760
m/s2 , respectively. Compared to the theoretical value of gat Bangkok (9.783 m/s2), three experimental results
International Journal of Advanced Science and Technology
Vol. 29, No. 7s, (2020), pp. 884-889
889
ISSN: 2005-4238 IJAST
Copyright ⓒ 2020 SERSC
give the accuracy of 0.72%, 0.32%, and 0.23% which implied that our method is suitable for classroom
experiment to measure the gravitational acceleration with high accuracy. To this end, we highlight our work for
determining the gravitational acceleration using smartphone which is simple to conduct for students.
V. CONCLUSION
In this paper, we propose a simple method to measure the acceleration of gravity based on the observation of a
free-falling object using the smartphone instead of the usually employed with ticker timer. Regarding the best of
our experimental result, the magnitude of the gravitational acceleration at Bangkok is found to be 9.760 m/s2 , this
method offers very good accuracy, with a percentage of error of about 0.23%. Our experimental value for gravity
agrees well with the standard value in which reported as 9.783 m/s2measured by the National Institute of
Metrology (Thailand). We envisage the advantage of this experiment that it is not only economical, and can hence
be conducted in places with limited access to laboratory tools, but also provides learning opportunities for students
in hands-on practicing and data analysis.
ACKNOWLEDGMENT
We are grateful for the financial support by the Research and Development Institute, Bansomdejchaopraya
Rajabhat University and by Chevron Enjoy Science Project.
REFERENCES
[1] P. Turiman, J. Omar, A. M. Daud, and K. Osman, "Fostering the 21st century skills through scientific literacy
and science process skills," Procedia Soc. Behav. Sci. , vol. 59, pp. 110-116 , 17 October 2012.
[2] C. Zimmerman, "The development of scientific reasoning skills," Dev. Rev., vol. 20, no. 1, pp. 99-149, March
2000.
[3] P. A. Kirschner, "Epistemology, practical work and academic skills in science education," Sci. Educ., vol. 1,
no. 3, pp. 273-299, September 1992.
[4] IOP Institute of Physics. (2019). Finding average acceleration with a ticker-timer. Avaiable:
https://spark.iop.org/finding-average-acceleration-ticker-timer
[5] Institute for the Promotion of Teaching Science and Technology. (2017). Thailand National Core Curriculum
of Basic Education in 2008. Avaiable:
http://physics.ipst.ac.th/wp-content/uploads/sites/2/2019/02/SciCurriculum_2560.pdf
[6] B. Jarosievitz, "Enjoy physics classes with your own devices," in IOP Conf. Series: Journal of Physics: Conf.
Series, 2018, pp. 012014-1-10.
[7] Khairurrijal, E. Widiatmoko, W. Srigutomo, and N. Kurniasih, "Measurement of gravitational acceleration
using a computer microphone port," Phys. Educ., vol. 47, no. 6, pp. 709-714, 2012.
[8] M. Oprea and C. Miron, "Mobile phones in the modern teaching of physics," Romanian Rep. Phy, vol. 66, no.
4, pp. 1236-1252, 2014.
[9] S. Hellesund, "Measuring the speed of sound in air using a smartphone and a cardboard tube," Phys. Educ.,
vol. 54, no. 3, pp. 035015-1-5, 4 April 2019.
[10] National Institute of Metrology (Thailand). (8 November 2018). The measurement of gravity in Thailand and
its importance. Avaiable: http://www.nimt.or.th/main/?p=21307
ResearchGate has not been able to resolve any citations for this publication.
- Beata Jarosievitz Dr.
Introducing the latest educational technology trends has accelerated enormously in the past few years; therefore, the use of personal devices, especially smart phones, tablets, laptops has increased considerably also in the educational processes. Many researchers used M-learning for different purposes (Hsu & Ching, 2013), but only a few of them used it for physics teaching experiments (Crompton, Burke, Gregory & Gräbe, 2016; Jarosievitz, 2016; Kuhn & Vogt, 2013). The use of M-learning devices in experiments is based on the rich set of built-in sensors in smart phones (Kuhn & Vogt 2013; Staacks, 2016). However, beside the devices themselves, also free applications and teachers' (instructors') expertise is required. In this work some meaningful use of M-learning during physics lectures will be presented. Some of the key terms describing the quality of the measurement have also been discussed with the students, and will be presented here. After the conclusion of the measurements, students used their own devices as clickers, and answered the questions synchronously and anonymously through an on-line assessment system.
A method has been developed to measure the swing period of a simple pendulum automatically. The pendulum position is converted into a signal frequency by employing a simple electronic circuit that detects the intensity of infrared light reflected by the pendulum. The signal produced by the electronic circuit is sent to the microphone port and recorded as a 16-bit wave file by common software. The wave file is then processed to obtain the signal period as a function of time by timing all zero crossings. From the obtained signal period as a function of time, an average value of the period is calculated. Using the calculated average period, it was found that the gravitational acceleration is (9.77 ± 0.03) m s−2. Noting that the G-type La Coste & Romberg G928 gravimeter obtains a gravitational acceleration of 9.78 m s−2, the present method offers very good accuracy, with a percentage error of about 0.1%.
To overcome the challenges of the twenty first century in science and technology sector, students need to be equipped with the 21st century skills to ensure their competitiveness in the globalization era. They are expected to master the 21st century skills apart of just being excelled in their academic performance. Therefore, it is crucial to incorporate 21st century skills in science education. 21st century skills comprised of four main domains namely digital age literacy, inventive thinking, effective communication and high productivity. Scientific literacy is one of the skills required in digital age literacy. It means knowledge and understanding of the scientific concepts and processes required for personal decision-making, participation in civic and cultural affairs, and economic productivity. Scientific literacy is important in our modern society since they are many issues related to science and technology. Basic science process skills include observing, classifying, measuring and using numbers, making inferences, predicting, communicating and using the relations of space and time. While the integrated science process skills consist of interpreting data, operational definition, control variables, make hypotheses and experimenting. Science students have been cultivated by scientific literacy and science process skills through science classes. With these two skills, it is hoped that the science students have developed some skills needed in 21st century skills. This paper will further explain about the 21st century skills, scientific literacy and science process skills. It also explains about the intersection of science process skills and 21st century skills in science education.
- Paul Kirschner
This article discusses the inherent flaws in considering and using the epistemology of the natural sciences as equivalent to a pedagogic basis for teaching and learning in the natural sciences. It begins with a discussion of the difference between practising science and learning to practice science. It follows with a discussion and refutation of three commonly held motives for using practicals in science education. It concludes with the presentation of three new, better motives for their use.
- M. Oprea
- Cristina Miron
Nowadays, smartphones have become an indispensable part of students' lives. Used mainly for communication purposes and for entertainment applications, their educational uses are almost universally ignored by teachers and students alike. The greatest challenge for a physics teacher is to unlock the great potential of these devices during the teaching process and shed new light on the diverse and enticing ways in which students could grasp a better understanding of physics through the simple use of their pocket-fitting gadgets. Hence, the purpose of this article is to show how smartphones operating on Android may take physics classes to the next level, as they can be used both as data collection systems and as data processing systems through their inbuilt sensors (such as the accelerometer, magnetometer, gyroscope, and the location and proximity sensor). With the help of open-source applications, these sensors enable the device to perform a series of measurements, such as the acceleration and speed of a moving person or vehicle, to establish the user's location through the method of trilateration or to measure the angle value of a slope. Therefore, along with the functions of smartphones themselves, the numerous free applications available on Google PlayStore are a precious educational resource for a modern physics teacher and deserve to be explored in a thorough study which will show a new and more comprehensive way to approach the teaching of physics.
- Corinne Zimmerman
The purpose of this article is to provide an introduction to the growing body of research on the development of scientific reasoning skills. The focus is on the reasoning and problem-solving strategies involved in experimentation and evidence evaluation. Research on strategy use in science has undergone considerable development in the last decade. Early research focused on knowledge-lean tasks or on tasks in which subjects were instructed to disregard prior knowledge. Klahr and Dunbar (1988) developed an integrated model of scientific discovery that has served as a framework to study the interaction of conceptual knowledge and the set of cognitive skills used in scientific reasoning. Researchers now take a more integrated approach, examining the development and use of strategies in moderately complex domains in order to examine the conditions under which subjects' theories (or prior knowledge) influence experimentation, evidence evaluation, and belief revision. Recent findings from integrated studies of scientific reasoning have the potential to inform and influence science education and conceptualizations of science as both academic skill and content domain.
Thailand National Core Curriculum of Basic Education
Institute for the Promotion of Teaching Science and Technology. (2017). Thailand National Core Curriculum of Basic Education in 2008. Avaiable: http://physics.ipst.ac.th/wp-content/uploads/sites/2/2019/02/SciCurriculum_2560.pdf
How to Compute the Experimental Value of G Frome the Slope Value
Source: https://www.researchgate.net/publication/340756218_Measuring_the_Acceleration_of_Gravity_Using_a_Smartphone_A4-Papers_and_a_Pencil
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