Pub Date : 2023-11-09DOI: 10.1088/1361-6404/ad0b3b
Michele Modestino, Roberto De Luca, Orazio Faella
Abstract We propose a simple experiment designed to justify the arithmetic and geometric mean inequality by means of the laws of thermodynamics. The experiment consists in measuring the entropy variation ΔS in the thermodynamic irreversible process of cooling a metal in water. By considering the metal and water as a single isolated system, the arithmetic and geometric theorem is seen to hold by noticing that ΔS is positive for this irreversible transformation. These interdisciplinary activities may be used to reinforce basic concepts in thermodynamics in high school or first-year college students.
{"title":"A physical point of view on the arithmetic and geometric mean inequality","authors":"Michele Modestino, Roberto De Luca, Orazio Faella","doi":"10.1088/1361-6404/ad0b3b","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0b3b","url":null,"abstract":"Abstract We propose a simple experiment designed to justify the arithmetic and geometric mean inequality by means of the laws of thermodynamics. The experiment consists in measuring the entropy variation ΔS in the thermodynamic irreversible process of cooling a metal in water. By considering the metal and water as a single isolated system, the arithmetic and geometric theorem is seen to hold by noticing that ΔS is positive for this irreversible transformation. These interdisciplinary activities may be used to reinforce basic concepts in thermodynamics in high school or first-year college students.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135192019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-08DOI: 10.1088/1361-6404/ad0aa4
Oliver Davis Johns
Abstract The Feynman demonstration that electromagnetic field momentum is real-even
for static fields-can be made more pedagogically useful by simplifying
its geometry. Instead of Feynman's disk with charged balls on its
surface, this article uses the geometry of a hollow non-conducting
sphere with uniform surface charge density. With only methods available
in a typical upper-division electrodynamics course, the initial field
angular momentum and the final mechanical angular momentum can then
be calculated in closed form and shown to be equal.
{"title":"A Spherical Version of Feynman's Static Field Momentum Example","authors":"Oliver Davis Johns","doi":"10.1088/1361-6404/ad0aa4","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0aa4","url":null,"abstract":"Abstract The Feynman demonstration that electromagnetic field momentum is real-even
for static fields-can be made more pedagogically useful by simplifying
its geometry. Instead of Feynman's disk with charged balls on its
surface, this article uses the geometry of a hollow non-conducting
sphere with uniform surface charge density. With only methods available
in a typical upper-division electrodynamics course, the initial field
angular momentum and the final mechanical angular momentum can then
be calculated in closed form and shown to be equal.
","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135340371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract When optical disks are illuminated, bright-colored lines can often be observed on the surface of them. Starting from the oblique incident grating diffraction model, this paper analyzes the physical mechanism behind the appearance of these colored lines and provides the coordinate expression of the location of the colored lines on the optical disc under the far-field condition. The wavelength distribution of the colored lines on the optical disc under white light illumination is also given by the wave vector relationship of the diffraction process. To verify the theoretical analysis results, an experimental apparatus was designed and constructed to measure the position and color of the colored lines. The experimental data, analyzed through Gaussian process regression and direct comparison, demonstrates a good consistency with the theoretical analysis results.
{"title":"Diffraction patterns of Optical Discs under Far-field condition","authors":"Zhuofan Cai, Shijiang Chen, Boyang Deng, Shuqi Liu, Wei Zhao, Zengming Zhang","doi":"10.1088/1361-6404/ad0aa1","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0aa1","url":null,"abstract":"Abstract When optical disks are illuminated, bright-colored lines can often be observed on the surface of them. Starting from the oblique incident grating diffraction model, this paper analyzes the physical mechanism behind the appearance of these colored lines and provides the coordinate expression of the location of the colored lines on the optical disc under the far-field condition. The wavelength distribution of the colored lines on the optical disc under white light illumination is also given by the wave vector relationship of the diffraction process. To verify the theoretical analysis results, an experimental apparatus was designed and constructed to measure the position and color of the colored lines. The experimental data, analyzed through Gaussian process regression and direct comparison, demonstrates a good consistency with the theoretical analysis results.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135340792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-08DOI: 10.1088/1361-6404/ad0a9e
Art Davis
Abstract This paper was inspired by a recent publication by Redˇ z´ ıc[1] which threw into bold relief the differences between the way Maxwell viewed current and the way Lorentz visualized it. We make the assumption that for a circuit of laboratory dimensions current (and charge perturbation effects in general) can be assumed to propagate instaneously around the loop. Our second fundamental assumption is the commonly accepted one that E is the force per unit charge on a stationary charge. We use these facts to make the usual definition of electromotive force more rigorous and to derive the Lorentz force formula.
{"title":"EMF Revisited","authors":"Art Davis","doi":"10.1088/1361-6404/ad0a9e","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0a9e","url":null,"abstract":"Abstract This paper was inspired by a recent publication by Redˇ z´ ıc[1] which threw into bold relief the differences between the way Maxwell viewed current and the way Lorentz visualized it. We make the assumption that for a circuit of laboratory dimensions current (and charge perturbation effects in general) can be assumed to propagate instaneously around the loop. Our second fundamental assumption is the commonly accepted one that E is the force per unit charge on a stationary charge. We use these facts to make the usual definition of electromotive force more rigorous and to derive the Lorentz force formula.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135340793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-08DOI: 10.1088/1361-6404/ad0aa0
Marco Di Mauro, Pasquale Onorato, L M Gratton, Roberto De Luca, Oriana Fiore, Lars Gislén, Adele Naddeo
Abstract We demonstrate the construction and utilization of an affordable apparatus using readily available materials to accurately measure in a quantitative manner the wavelengths reflected by a compact disc (CD) under skimming light rays. In fact, only a limited number of wavelengths can be revealed when light rays from a white lamp are directed at a CD (or a DVD) in a manner that specifically selects the rays that graze the surface of the horizontally held disc. We compare the results with the ones obtained with a commercial spectrometer, the results are in good agreement among them and with the theoretical predictions.
{"title":"Low-cost measurements of the “resonant” wavelengths reflected by a compact disc under skimming light rays","authors":"Marco Di Mauro, Pasquale Onorato, L M Gratton, Roberto De Luca, Oriana Fiore, Lars Gislén, Adele Naddeo","doi":"10.1088/1361-6404/ad0aa0","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0aa0","url":null,"abstract":"Abstract We demonstrate the construction and utilization of an affordable apparatus using readily available materials to accurately measure in a quantitative manner the wavelengths reflected by a compact disc (CD) under skimming light rays. In fact, only a limited number of wavelengths can be revealed when light rays from a white lamp are directed at a CD (or a DVD) in a manner that specifically selects the rays that graze the surface of the horizontally held disc. We compare the results with the ones obtained with a commercial spectrometer, the results are in good agreement among them and with the theoretical predictions.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135340791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-08DOI: 10.1088/1361-6404/ad0aa3
Benito Vázquez-Dorrı́o, Angel Paredes, Miguel Angel Queiruga-Dios
Abstract Inertial motion looks like accelerated motion when observed from the point of view of a non-inertial reference frame. A non-inertial observer can then describe the trajectories by introducing fictitious forces, like the centrifugal and Coriolis forces, that arise from the coordinate change between reference frames. This well-known fact is part of the typical Physics syllabus for undergraduate scientists and engineers, and a number of interesting classroom demonstrations have been discussed in the literature. We present a complementary possibility for the visualization of the effect of fictitious forces by shining a blue laser beam on a rotating platform covered with a phosphorescent vinyl sheet. The laser can be moved in order to simulate inertial motion in the laboratory frame for the trajectory of the laser spot. This gets immediately imprinted in the rotating phosphorescent material resulting in non-inertial trajectories that can be readily observed and compared to the dynamics governed by fictitious forces. Since friction is not considered, this hands-on activity can be considered as a direct demonstration of the effect of pure fictitious forces in and out the classroom. The approach is simple, inexpensive, fast and non-destructive, and can therefore be very convenient for active lecture demonstrations or individual activities of students. We also describe some educational possibilities of how to use the procedure in the classroom or in the laboratory.
{"title":"Hands-on visualization of the effect of fictitious forces with a laser pointer","authors":"Benito Vázquez-Dorrı́o, Angel Paredes, Miguel Angel Queiruga-Dios","doi":"10.1088/1361-6404/ad0aa3","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0aa3","url":null,"abstract":"Abstract Inertial motion looks like accelerated motion when observed from the point of view of a non-inertial reference frame. A non-inertial observer can then describe the trajectories by introducing fictitious forces, like the centrifugal and Coriolis forces, that arise from the coordinate change between reference frames. This well-known fact is part of the typical Physics syllabus for undergraduate scientists and engineers, and a number of interesting classroom demonstrations have been discussed in the literature. We present a complementary possibility for the visualization of the effect of fictitious forces by shining a blue laser beam on a rotating platform covered with a phosphorescent vinyl sheet. The laser can be moved in order to simulate inertial motion in the laboratory frame for the trajectory of the laser spot. This gets immediately imprinted in the rotating phosphorescent material resulting in non-inertial trajectories that can be readily observed and compared to the dynamics governed by fictitious forces. Since friction is not considered, this hands-on activity can be considered as a direct demonstration of the effect of pure fictitious forces in and out the classroom. The approach is simple, inexpensive, fast and non-destructive, and can therefore be very convenient for active lecture demonstrations or individual activities of students. We also describe some educational possibilities of how to use the procedure in the classroom or in the laboratory.
","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135341012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper we extend some recent works about Doppler effect in surface waves on water. We improve the experimental set up exploring several situations: source in motion with constant velocity and receiver at rest, source at rest and receiver in motion with constant velocity, as well as both source and receiver in motion. Thereby we produce fractional frequency changes of the order of 40-50%, far larger than those obtained by more traditional sound experiments. The experimental set-up, the data collection and the data analysis also allow to highlight some aspects relevant from a didactic point of view, in particular the experimental results clearly show the nonlinearity of the Doppler shift with the moving source velocity.
{"title":"Doppler effect in the ripple tank: further experiments with a moving source","authors":"Michele D'Anna, Tommaso Corridoni, Stefano Sposetti, Federico Corni","doi":"10.1088/1361-6404/ad0aa2","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0aa2","url":null,"abstract":"Abstract In this paper we extend some recent works about Doppler effect in surface waves on water. We improve the experimental set up exploring several situations: source in motion with constant velocity and receiver at rest, source at rest and receiver in motion with constant velocity, as well as both source and receiver in motion. Thereby we produce fractional frequency changes of the order of 40-50%, far larger than those obtained by more traditional sound experiments. The experimental set-up, the data collection and the data analysis also allow to highlight some aspects relevant from a didactic point of view, in particular the experimental results clearly show the nonlinearity of the Doppler shift with the moving source velocity.
","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135340962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-08DOI: 10.1088/1361-6404/ad0a9f
Luis Medrano Navarro, Luis Martin-Moreno, Sergio G Rodrigo
Abstract The research in Artificial Intelligence methods with potential applications in science has become an essential task in the scientific community in recent years. Physics Informed Neural Networks (PINNs) is one of these methods and represents a contemporary technique based on neural network fundamentals to solve differential equations. These networks can potentially improve or complement classical numerical methods in computational physics, making them an exciting area of study. In this paper, we introduce PINNs at an elementary level, mainly oriented to physics education, making them suitable for educational purposes at both undergraduate and graduate levels. PINNs can be used to create virtual simulations and educational tools that aid in understating complex physical concepts and processes involving differential equations. By combining the power of neural networks with physics principles, PINNs can provide an interactive and engaging learning experience that can improve students' understanding and retention of physics concepts in higher education.
{"title":"Solving differential equations with Deep Learning: a beginner's guide","authors":"Luis Medrano Navarro, Luis Martin-Moreno, Sergio G Rodrigo","doi":"10.1088/1361-6404/ad0a9f","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0a9f","url":null,"abstract":"Abstract The research in Artificial Intelligence methods with potential applications in science has become an essential task in the scientific community in recent years. Physics Informed Neural Networks (PINNs) is one of these methods and represents a contemporary technique based on neural network fundamentals to solve differential equations. These networks can potentially improve or complement classical numerical methods in computational physics, making them an exciting area of study. In this paper, we introduce PINNs at an elementary level, mainly oriented to physics education, making them suitable for educational purposes at both undergraduate and graduate levels. PINNs can be used to create virtual simulations and educational tools that aid in understating complex physical concepts and processes involving differential equations. By combining the power of neural networks with physics principles, PINNs can provide an interactive and engaging learning experience that can improve students' understanding and retention of physics concepts in higher education.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135340954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-27DOI: 10.1088/1361-6404/ad0790
Pekka Pirinen, Pascal Klein, Simon Zacharias Lahme, Antti Lehtinen, Lucija Rončević, Ana Susac
Abstract Digital signal processing is a valuable practical skill for the contemporary
physicist, yet in physics curricula, its central concepts are often introduced either
in method courses in a highly abstract and mathematics-oriented manner or in lab
work with little explicit attention. In this paper, we present an experimental task in
which we focus on a practical implementation of the discrete Fourier transform (DFT)
in an everyday context of vibration analysis using data collected by a smartphone
accelerometer. Students are accompanied in the experiment by a Jupyter notebook
companion, which serves as an interactive instruction sheet and a tool for data analysis.
The task is suitable for beyond-first-year university physics students with some prior
experience in uncertainty analysis, data representation, and data analysis. Based on
our observations the experiment is very engaging. Students have consistently reported
interest in the experiment and they have found it a good demonstration of the DFT
method.
{"title":"Exploring digital signal processing using an interactive Jupyter notebook and smartphone accelerometer data","authors":"Pekka Pirinen, Pascal Klein, Simon Zacharias Lahme, Antti Lehtinen, Lucija Rončević, Ana Susac","doi":"10.1088/1361-6404/ad0790","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0790","url":null,"abstract":"Abstract Digital signal processing is a valuable practical skill for the contemporary
physicist, yet in physics curricula, its central concepts are often introduced either
in method courses in a highly abstract and mathematics-oriented manner or in lab
work with little explicit attention. In this paper, we present an experimental task in
which we focus on a practical implementation of the discrete Fourier transform (DFT)
in an everyday context of vibration analysis using data collected by a smartphone
accelerometer. Students are accompanied in the experiment by a Jupyter notebook
companion, which serves as an interactive instruction sheet and a tool for data analysis.
The task is suitable for beyond-first-year university physics students with some prior
experience in uncertainty analysis, data representation, and data analysis. Based on
our observations the experiment is very engaging. Students have consistently reported
interest in the experiment and they have found it a good demonstration of the DFT
method.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136234973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-27DOI: 10.1088/1361-6404/ad0188
Hollis Williams
Abstract The relativistic correction to the precession of the perihelion of Mercury provided key evidence for the accuracy of general relativity as a theory of gravity. This example still has a large amount of potential to introduce students to the power of numerical simulations in theoretical physics, but existing approaches may be too detailed for many students and involve them beginning to learn a programming language at the same time. In this article, we take a simpler approach which uses as little coding as possible. The equation for the orbit of a planet is solved with and without relativistic corrections. It is shown that there is precession of the perihelion in the relativistic case, whereas in the Newtonian case, the orbit does not rotate about the origin. Quantitative information is extracted on the precession of the perihelion of Mercury and shown to match with observations.
{"title":"An elementary approach to simulating the perihelion of Mercury","authors":"Hollis Williams","doi":"10.1088/1361-6404/ad0188","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0188","url":null,"abstract":"Abstract The relativistic correction to the precession of the perihelion of Mercury provided key evidence for the accuracy of general relativity as a theory of gravity. This example still has a large amount of potential to introduce students to the power of numerical simulations in theoretical physics, but existing approaches may be too detailed for many students and involve them beginning to learn a programming language at the same time. In this article, we take a simpler approach which uses as little coding as possible. The equation for the orbit of a planet is solved with and without relativistic corrections. It is shown that there is precession of the perihelion in the relativistic case, whereas in the Newtonian case, the orbit does not rotate about the origin. Quantitative information is extracted on the precession of the perihelion of Mercury and shown to match with observations.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136233036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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