Importance of the
conceptualization of curve fitting in the determination of the elastic constant
of a spring
Published Instituto Tecnológico
Superior Edwards Quito
- Ecuador Periodicity October - December Vol. 1, Num. 23, 2024 pp. 55-61 http://centrosuragraria.com/index.php/revista Dates of receipt Received: May 02, 2024 Approved: July 19, 2024 Correspondence author gmoya@uagraria.edu.ec Creative Commons License Creative Commons License, Attribution-NonCommercial-ShareAlike
4.0 International.https://creativecommons.org/licenses/by-nc-sa/4.0/deed.es
Galo Fernando Moya Castillo1
Tannia Gabriela Acosta Chávez2
Cleitton Alfredo Yance Tutiven3
Axel Jefferson Córdova López4
Ph,D. Agrarian University
of Ecuador, gmoya@uagraria.edu.ec, https://orcid.org/0009-0006-8872-3570 Ph,D. Agrarian University
of Ecuador: tacosta@uagraria.edu.ec https://orcid.org/0000-0002-4740-2213 Ph,D. University of Guayaquil cleitton.yancet@ug.edu.ec,
https://orcid.org/0000-0001-8554-7838 Ph,D. University of Guayaquil axel.cordoval@ug.edu.ec,
https://orcid.org/0009-0009-2722-8244
Keywords: curve fitting, elasticity, spring, spring
Summary:
Keywords Automation, SMEs,
ESP32 DevKitC V4, Programmable Logic Controller (PLC), PCB, Industry 4.0,
Communication Protocol
Introduction
In the educational environment, physics and engineering education face
ongoing challenges related to the understanding and application of complex
concepts; one of the critical aspects is the proper understanding of curve
fitting in the context of determining the spring rate constant of a spring.
Students and teachers often encounter difficulties in selecting
appropriate fitting models, interpreting the results obtained and understanding
the relationship between the fitted parameters and the physical properties of
the spring. These educational actors play a key role in the transmission and
acquisition of scientific knowledge and the lack of solid understanding in the
conceptualization of curve fitting can negatively affect the quality of
education and training in these areas, impacting the learning of future physics
and engineering professionals.
Schemas and conceptualization are key elements for the understanding of
human learning. In this sense, a concept cannot be reduced to a simple
definition, but must also be associated with specific situations and problems.
In addition, Vergnaud stresses the importance of rational knowledge and how it
always involves some form of operation or action. These two ideas together,
according to Vergnaud, form the basis of effective and meaningful learning
(Mendoza, 2020).
On the other hand, the impossibility of having the indispensable
elements, the difficulties in accessing adequate equipment and materials to
carry out the tests and measurements necessary for the development of
experimental practices, makes the creation of a virtual laboratory viable and
necessary, which organizes the different simulations, video tutorials and
specialized pages; in order to provide the school and the different actors, an
environment that complements or even in some cases replaces the existing
laboratory (Diaz B. , 2021).
In the field of physics and engineering, the accurate determination of
the spring rate of a spring is fundamental to understanding and predicting the
behavior of various mechanical systems. Curve fitting, an essential technique
in the analysis of experimental data, plays a crucial role in this process by
modeling the relationships between the variables involved. The correct
conceptualization and application of this technique are vital to obtain
reliable and consistent results in the measurement of the elasticity constant.
This study explores the importance of the conceptualization of curve fitting in
the determination of the elasticity constant of a spring, addressing both the
problems in the institution and the contribution of this research in the field
of science education.
Methodology
The
present investigation contains a non-experimental design, which consists of
gathering information from observational data on how the significant
understanding of statistics is related to the calculation of the coefficient of
elasticity present in Hooke's law; for this purpose, the test is taken as an
investigative technique, which will consist of a questionnaire of 20 questions,
which will help to check the level of understanding and aptitude related to the
conceptualization of curve fitting and the determination of the constant of
elasticity of a spring.
The
objective of this study is not to evaluate a didactic proposal to improve the
learning of statistics or physics, but to measure both variables in a specific
content and verify if they are related, and thus propose an adequate
pedagogical alternative to the results obtained. That is to say, to carry out a
correlational investigation to indicate if there is a relationship, link or
connection between the variables such as: the conceptualization of curve
fitting with the calculation of the elasticity of a spring.
For
this purpose, a thorough review of books, files and documents was carried out
to obtain formal and supported data that were appropriate for the research and
that ensured the quality and a solid base of the contents evaluated in the
test, which will be applied to 57 fifth semester students of the University of
Guayaquil belonging to the career of Pedagogy of experimental sciences of
Mathematics and Physics, in the real environment of the students, taking
advantage of their learning environment.
In this
sense, a quantitative modality is followed, due to the obtaining of numerical
values and grades obtained in the test; as well as the implementation of
descriptive statistics, with which it will be possible to organize, summarize
and visualize the data collected, by means of tables and graphs that will
differentiate the successes and errors obtained by the students in each of the
questions.
Results
The test was based on the analysis of the level of understanding of the elasticity constant and curve fitting, the results obtained are detailed below. Table 1.
Table 1. Test Results - Elasticity constant
and Curve Fitting
|
QUESTIONS |
ELASTICITY CONSTANT |
QUESTIONS |
CURVE FITTING |
||
|
ACIERTOS |
ERRORS |
ACIERTOS |
ERRORS |
||
|
1 |
21 |
36 |
11 |
20 |
37 |
|
2 |
49 |
8 |
12 |
21 |
36 |
|
3 |
41 |
16 |
13 |
30 |
27 |
|
4 |
32 |
25 |
14 |
24 |
33 |
|
5 |
29 |
28 |
15 |
15 |
42 |
|
6 |
31 |
26 |
16 |
30 |
27 |
|
7 |
27 |
30 |
17 |
21 |
36 |
|
8 |
16 |
41 |
18 |
42 |
15 |
|
9 |
35 |
22 |
19 |
32 |
25 |
|
10 |
39 |
18 |
20 |
30 |
27 |
Source: Test Results
Prepared by: Daisy Criollo
37% of
the students know the correct formula to calculate the constant of a spring,
86% know its unit of measurement, 72% calculate the force applied to the spring
from the constant of elasticity and its deformation, as well as 56% of them
indicate that if the spring is replaced by a stiffer one the constant will
increase, but only 51% infer that it is because they are directly proportional.
On the other hand, 54% carry out the corresponding process to know the
deformation that the spring has had and 47% specify that if a spring is cut in
half its constant will be divided in two. However, only 28% manage to answer
correctly what the value of the constant will be based on the frequency and
mass that supports the elastic body; while 61% of the trainees indicate that if
the spring is stretched beyond its elastic limit it will break and finally, it
is 68% who can find the value of the restoring force. It can be visualized that
35% of the trainees can calculate the estimation of the constant of a spring
based on curve fitting, 37% indicate that in statistics this is a method to
approximate a curve from observed data, 53% indicate that it serves to find the
equation of a curve that fits the data and 42% mention that it is complemented
with the linear regression technique. On the other hand, 26% of the students
know how to differentiate the most appropriate type of curve fitting to
represent data, 53% can indicate the equation that is closest to the data.
Also, when distinguishing the type of curve fitting from graphs, the following
results were obtained: 37% recognize the linear fit, 74% resemble the quadratic
function and 60% the exponential function.
According
to the results obtained and with the correct tabulation for the analysis, a
certified statistical tool was used to determine the validity of the research
instrument, which provided an acceptable value, thus assuring the internal
consistency of the application of the test.
Since
the research is correlational, we sought to find links or relationships between
one variable and another, such as the conceptualization of curve fitting with
the calculation of the constant of a spring, and for this purpose we used the
statistical tool "Pearson's Correlation Coefficient", with which we
obtained a value that shows a moderate correlational tendency between the
variables.
|
Correlations |
|
Pearson's correlation 0.454 p-value 0.001 |
Source: Test applied to students
Prepared
by:
Yance Tutiven Cleitton - Córdova López Axel
Once
the existence of an average correlation between both variables has been proven,
alternatives are sought to teach both contents in the educational environment,
and the following are activities that involve the subjects of study.
Conclusions
The problem
evidenced in the educational institutions regarding the understanding of the
curve fitting technique in the context of determining the elasticity constant
of a spring has been effectively addressed through stepwise didactic
activities. These activities allowed students to investigate and discuss key
concepts such as constants, independent and dependent variables, and the
general formula of the linear equation.
The experimental measurement of the spring under different applied
forces provided a practical and concrete experience that reinforced the
understanding of spring elasticity. Students performed direct measurements of
elongations and forces, this activity demonstrated the relationship between the
applied force and the stretching or compression of the spring, establishing a
solid basis for understanding Hooke's Law. In addition, the variation in spring
length as different masses are applied was addressed, exploring how this
variation affects the spring constant. Students recognized the influence of
mass on the elastic behavior of the spring and analyzed the patterns obtained
from the data collected. In other words, the workshop allowed them to establish
connections between theory and practice, consolidating previously learned
concepts.
The calculation of Pearson's coefficient helped to identify a moderate
correlation between the variables of the study and with this, activities
involving them were designed, evidencing that the students, through the graphic
analysis of the data and curve fitting, were able to visualize and understand
the linear relationship between the applied force and the stretching of the
spring. The use of tools such as graphs and software for fitting reinforced
their analytical skills and their understanding of the theoretical foundations.
Finally, a connection was established between the theoretical estimation and
the experimental values obtained, allowing them to compare and contrast the
results. The application of the theoretical formula to calculate the elasticity
constant and the comparison with the averaged experimental values provided a
broader perspective on the accuracy of the methods used and the possible
sources of error.
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