The Physics of Gym Elastic: Elastic Force and Energy of a Non-Linear Material

Rodrigo Cutri; Nair Stem; Octavio Mattasoglio

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Conference: 2024 ASEE Annual Conference & Exposition
Location: Portland, Oregon
Publication Date: June 23, 2024
Start Date: June 23, 2024
End Date: July 12, 2024
Conference Session: Engineering Physics and Physics Division (EP2D) Technical Session 2
Tagged Division: Engineering Physics and Physics Division (EP2D)
Permanent URL: https://peer.asee.org/48126

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Paper Authors

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Rodrigo Cutri Maua Institute of Techonology orcid.org/0000-0001-8143-8685

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Cutri holds a degree in Electrical Engineering from Maua Institute of Technology (2001), MSc (2004) and Ph.D. (2007) in Electrical Engineering - University of SÃ£o Paulo. He is currently Titular Professor of Maua Institute of Technology, Professor of the

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Nair Stem prof. Instituto Mauá de Tecnologia

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- Associate Professor at Instituto Maua de Tecnologia - CEUN-IMT
- Graduated at Physics (Bachelor) at IFUSP, Master at Electrical Engineering and Doctor at Electrical Engineering at EPUSP.

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Octavio Mattasoglio Neto Instituto Mauá de Tecnologia orcid.org/0000-0001-7812-8491

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Undergraduate in Physics (1983), master in Science (1989) and phd in Education (1998) all of them from Universidade de São Paulo. Professor of Physics at Mauá Institute of Technology, since 1994 and President of Teacher's Academy of the same Institute,

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Abstract

Aiming to analyze first-year engineering students' previous knowledge regarding elastic force and energy, we chose to characterize an everyday material: gym latex elastics and to compare it to a linear spring characteristic curve. This choice aimed to contextualize the concept being taught, establishing a connection between the students and a familiar non-linear material. There were four types of elastic tubes that were provided to the students, each color can be associated to a specific level of resistance: a) The minimum resistance – yellow one b) Low-intermediate resistance – blue one c) Upper-intermediate resistance – red one, and d) The maximum resistance – black one, according to the manufacturer. The purposed activity can be divided into four stages: pre-class, during class, post-class, and student´s perception. The pre-class and post-class activities (equal for both phases) involved a quiz about elastic force and energy. This quiz included questions that tested low-order thinking skills related to elastic forces (Hooke's Law), high-order thinking skills involving graph interpretation and the non-linear behavior of materials, as well as elastic potential energy. Approximately 350 students participated in this activity. This comparison was necessary because students often enter high school with the misconception that all elastic materials strictly obey Hooke's Law for a long interval of deformation. During the class step, the students were divided into groups of three or four members; each group was assigned to only one specific type of elastic band to discover its level of resistance by means of the characteristic curve (elastic force as a function of deformation) and a spring. The elastic forces in the elastic tubes and in the spring were measured using a PASCO force sensor. The spring constant was about 8.0 N/m, and the characteristic curve was completely linear. For the elastic tubes the forces were measured with an elongation range from 0 to 40 cm in 2.0 cm increments. A comparison among third-degree, second-degree polynomial function and linear fits was performed. The results indicated that, despite achieving a better fit with a third-degree polynomial, it is not the most suitable method for physical interpretation and modeling. According to the literature, these gym elastic curves exhibit three asymptotic lines, allowing for the definition of three different elastic constants for specific regions. To simplify the problem for a first-year course in an introductory graph analysis class, the students approximated the trend line and obtained the elastic constant only for the region of elongation from 2.0 cm to 6.0 cm. The analysis of the three asymptotic regions was not asked in order to not lose the focus on elastic force and the different behavior for linear and non linear materials. A collective construction took place, where each group shared their assigned elastic constant with the entire class, ensuring that all types of elastic tubes were characterized. A qualitative comparison was made between the measured elastic constants (obtained in the interval 2.0 cm to 6.0 cm) and those provided by the manufacturer. The teachers provided explanations about elastic tube behaviors such as elastic hysteresis, the influence of wall thickness on the resistance force. They also compared the results to linear spring. According to our results (utilizing descriptive statistics), a comparison was performed between the scores obtained in the pre-quiz and post-quiz, as shown by the presented data distribution histogram. There was a general improvement from 69.1% to 78.7%. Subsequently, the data were filtered using only the highest scores clusters in the analysis performed by employing data mining (using a software called Orange); otherwise, it wouldn't be possible to interpret the results due to the sparse distribution of clusters and their overlap. Focusing on having a detailed analysis of the types of the questions from both quizzes (elastic forces and high-order thinking skills) and elastic potential energy, an analysis of the students' development was performed by using tree algorithm. Additionally, a qualitative comparison between the measured elastic constants and the manufacturer's predictions showed good agreement, with approximately 97.0% of students correctly identifying the maximum resistance for the black tubes. Regarding student perception, we asked about their thoughts on the activity: a) how much new information they felt it brought, and b) how interesting they found it. Students could rate their responses on a scale from 1 (not interesting or no new information) to 5 (very interesting or a lot of new information). Out of the 246 students who responded, 82.6% found the activity either very interesting or interesting, and approximately 72.4% considered it to have provided new information.

Citation
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Cutri, R., & Stem, N., & Mattasoglio, O. (2024, June), The Physics of Gym Elastic: Elastic Force and Energy of a Non-Linear Material Paper presented at 2024 ASEE Annual Conference & Exposition, Portland, Oregon. https://peer.asee.org/48126

TY - CPAPER
AB - Aiming to analyze first-year engineering students&#39; previous knowledge regarding elastic force and energy, we chose to characterize an everyday material: gym latex elastics and to compare it to a linear spring characteristic curve. This choice aimed to contextualize the concept being taught, establishing a connection between the students and a familiar non-linear material. There were four types of elastic tubes that were provided to the students, each color can be associated to a specific level of resistance: a) The minimum resistance – yellow one b) Low-intermediate resistance – blue one c) Upper-intermediate resistance – red one, and d) The maximum resistance – black one, according to the manufacturer. The purposed activity can be divided into four stages: pre-class, during class, post-class, and student´s perception. The pre-class and post-class activities (equal for both phases) involved a quiz about elastic force and energy. This quiz included questions that tested low-order thinking skills related to elastic forces (Hooke&#39;s Law), high-order thinking skills involving graph interpretation and the non-linear behavior of materials, as well as elastic potential energy. Approximately 350 students participated in this activity. This comparison was necessary because students often enter high school with the misconception that all elastic materials strictly obey Hooke&#39;s Law for a long interval of deformation. During the class step, the students were divided into groups of three or four members; each group was assigned to only one specific type of elastic band to discover its level of resistance by means of the characteristic curve (elastic force as a function of deformation) and a spring.
The elastic forces in the elastic tubes and in the spring were measured using a PASCO force sensor. The spring constant was about 8.0 N/m, and the characteristic curve was completely linear. For the elastic tubes the forces were measured with an elongation range from 0 to 40 cm in 2.0 cm increments. A comparison among third-degree, second-degree polynomial function and linear fits was performed. The results indicated that, despite achieving a better fit with a third-degree polynomial, it is not the most suitable method for physical interpretation and modeling. According to the literature, these gym elastic curves exhibit three asymptotic lines, allowing for the definition of three different elastic constants for specific regions. To simplify the problem for a first-year course in an introductory graph analysis class, the students approximated the trend line and obtained the elastic constant only for the region of elongation from 2.0 cm to 6.0 cm. The analysis of the three asymptotic regions was not asked in order to not lose the focus on elastic force and the different behavior for linear and non linear materials. A collective construction took place, where each group shared their assigned elastic constant with the entire class, ensuring that all types of elastic tubes were characterized. A qualitative comparison was made between the measured elastic constants (obtained in the interval 2.0 cm to 6.0 cm) and those provided by the manufacturer. The teachers provided explanations about elastic tube behaviors such as elastic hysteresis, the influence of wall thickness on the resistance force. They also compared the results to linear spring. According to our results (utilizing descriptive statistics), a comparison was performed between the scores obtained in the pre-quiz and post-quiz, as shown by the presented data distribution histogram. There was a general improvement from 69.1% to 78.7%. Subsequently, the data were filtered using only the highest scores clusters in the analysis performed by employing data mining (using a software called Orange); otherwise, it wouldn&#39;t be possible to interpret the results due to the sparse distribution of clusters and their overlap. Focusing on having a detailed analysis of the types of the questions from both quizzes (elastic forces and high-order thinking skills) and elastic potential energy, an analysis of the students&#39; development was performed by using tree algorithm. Additionally, a qualitative comparison between the measured elastic constants and the manufacturer&#39;s predictions showed good agreement, with approximately 97.0% of students correctly identifying the maximum resistance for the black tubes. Regarding student perception, we asked about their thoughts on the activity: a) how much new information they felt it brought, and b) how interesting they found it. Students could rate their responses on a scale from 1 (not interesting or no new information) to 5 (very interesting or a lot of new information). Out of the 246 students who responded, 82.6% found the activity either very interesting or interesting, and approximately 72.4% considered it to have provided new information.

AU - Rodrigo Cutri
AU - Nair Stem prof.
AU - Octavio Mattasoglio Neto
CY - Portland, Oregon
DA - 2024/06/23
PB - ASEE Conferences
TI - The Physics of Gym Elastic: Elastic Force and Energy of a Non-Linear Material
UR - https://peer.asee.org/48126
ER -