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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-22 1:24 |
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Conference: Bucharest University Faculty of Physics 2018 Meeting
Section: Physics Education
Title:
Experimental data processing with Excel spreadsheets for the study of the elastic hysteresis
Authors:
Ionel GRIGORE(1), Daniela STOICA(1), Mihai POPESCU(1)
Affiliation:
1)"Ion Luca Caragiale" National College, Ploieşti, Romania
E-mail
grigore_1965@yahoo.com
Keywords:
spreadsheets, elastic hysteresis, elastic constant, interpolation, numerical integration, physics education
Abstract:
This paper shows how experimental data can be processed with Excel spreadsheets for the study of the elastic hysteresis. The experimental data presented come from an elastic band with 60% rubber in its composition. The input data used are the undeformed initial length of the elastic body and the values of the body length in deformed state, corresponding to the values of the applied force. The hysteresis phenomenon is emphasized by the graphical representation of the displacement according to the applied force, at loading, when the applied force is increasing and, at unloading, when the applied force is reduced. The facilities of the spreadsheet allow the approximate mathematical modeling of hysteresis by finding the proper interpolation function of the experimental data in the variation domain of the applied force. With the interpolation function found, for the two cycles of the hysteresis, the energy dissipated in heat by friction of the elastic body was calculated. For this we have implemented the trapezoidal rule in the spreadsheet to evaluate the area delimited by the elastic hysteresis loop. Also, starting from the mathematical modeling of the hysteresis, we have graphically plotted the dependence of the elastic constant on the applied force at extension and at relaxation. The use of spreadsheets in the study of the elastic hysteresis presents a series of advantages in the classroom with the students. Thus, by easily processing the data with the mathematical modeling tools in the spreadsheet, the students can take a first step in clarifying the difference between linear elasticity and nonlinear elasticity.
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