Footprints provide a way to estimate the relative impact of processes and products on the global climate. Including footprint analysis in a course on energy simultaneously provides students with an understanding of this tool and a quantitative guide to approaches that address climate change. College-level classroom activities for (primarily) process-based life cycle carbon footprinting are discussed.
{"title":"Footprinting in a course on energy","authors":"S. Major","doi":"10.1119/5.0136958","DOIUrl":"https://doi.org/10.1119/5.0136958","url":null,"abstract":"Footprints provide a way to estimate the relative impact of processes and products on the global climate. Including footprint analysis in a course on energy simultaneously provides students with an understanding of this tool and a quantitative guide to approaches that address climate change. College-level classroom activities for (primarily) process-based life cycle carbon footprinting are discussed.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43976644","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}
We give a simple introduction to the properties and use of ultrastable optical cavities, which are increasingly common in atomic and molecular physics laboratories for stabilizing the frequency of lasers to linewidths at the kHz level or below. Although the physics of Fabry–Perot interferometers is part of standard optics curricula, the specificities of ultrastable optical cavities, such as their high finesse, fixed length, and the need to operate under vacuum, can make their use appear relatively challenging to newcomers. Our aim in this work is to bridge the gap between generic knowledge about Fabry–Perot resonators and the specialized literature about ultrastable cavities. The intended audience includes students setting up an ultrastable cavity in a research laboratory for the first time and instructors designing advanced laboratory courses on optics and laser stabilization techniques.
{"title":"A basic introduction to ultrastable optical cavities for laser stabilization","authors":"J. Boyd, T. Lahaye","doi":"10.1119/5.0161369","DOIUrl":"https://doi.org/10.1119/5.0161369","url":null,"abstract":"We give a simple introduction to the properties and use of ultrastable optical cavities, which are increasingly common in atomic and molecular physics laboratories for stabilizing the frequency of lasers to linewidths at the kHz level or below. Although the physics of Fabry–Perot interferometers is part of standard optics curricula, the specificities of ultrastable optical cavities, such as their high finesse, fixed length, and the need to operate under vacuum, can make their use appear relatively challenging to newcomers. Our aim in this work is to bridge the gap between generic knowledge about Fabry–Perot resonators and the specialized literature about ultrastable cavities. The intended audience includes students setting up an ultrastable cavity in a research laboratory for the first time and instructors designing advanced laboratory courses on optics and laser stabilization techniques.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":"128 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139350475","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}
Providing students of introductory thermal physics with a plot of the heat capacities of many low density gases as a function of temperature allows them to look for systematic trends. Specifically, large amounts of heat capacity data not only allow students to discover the equipartition theorem but also point to its limited applicability. Computer code to download and plot the temperature-dependent heat capacity data is provided.
{"title":"Thermal physics in the data age—Students judge the applicability of the equipartition theorem","authors":"J. D. Martin","doi":"10.1119/5.0146298","DOIUrl":"https://doi.org/10.1119/5.0146298","url":null,"abstract":"Providing students of introductory thermal physics with a plot of the heat capacities of many low density gases as a function of temperature allows them to look for systematic trends. Specifically, large amounts of heat capacity data not only allow students to discover the equipartition theorem but also point to its limited applicability. Computer code to download and plot the temperature-dependent heat capacity data is provided.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":"18 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139351763","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}
{"title":"Atom-emitting-a-photon solved on the back of an envelope","authors":"R. Johal","doi":"10.1119/5.0162000","DOIUrl":"https://doi.org/10.1119/5.0162000","url":null,"abstract":"","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46779497","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}
{"title":"Physics writing in the era of artificial intelligence","authors":"M. Antonacci, M. A. Maize","doi":"10.1119/5.0159871","DOIUrl":"https://doi.org/10.1119/5.0159871","url":null,"abstract":"","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43758046","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}
The methods devised by Gustav Mie in 1908 to explain the scattering of electromagnetic waves have a close analogy with quantum-mechanical models developed many years later to describe nuclear scattering. In particular, these models use either a complex index of refraction or a complex nuclear scattering potential to account for attenuation caused by non-elastic scattering. We briefly outline the historical development of these models and give examples illustrating the close analogy between them, their parameters, and the resulting scattering. In both models, the ratio of the incident wavelength to the object size, λ/D, can be determined from the scattering characteristics, allowing the extraction of microscopic particle dimensions. This close analogy allows students to simulate accelerator-based nuclear scattering experiments with table-top optical-scattering experiments.
Gustav Mie在1908年设计的解释电磁波散射的方法与多年后开发的描述核散射的量子力学模型非常相似。特别是，这些模型使用复杂的折射率或复杂的核散射势来解释非弹性散射引起的衰减。我们简要概述了这些模型的历史发展，并举例说明了它们之间的密切相似性、它们的参数以及由此产生的散射。在这两个模型中，入射波长与物体尺寸的比值λ/D可以根据散射特性确定，从而可以提取微观颗粒尺寸。这种紧密的类比使学生能够用桌面光学散射实验模拟基于加速器的核散射实验。
{"title":"The nuclear optical model and its optical-scattering analog: Mie scattering","authors":"F. Becchetti","doi":"10.1119/5.0152813","DOIUrl":"https://doi.org/10.1119/5.0152813","url":null,"abstract":"The methods devised by Gustav Mie in 1908 to explain the scattering of electromagnetic waves have a close analogy with quantum-mechanical models developed many years later to describe nuclear scattering. In particular, these models use either a complex index of refraction or a complex nuclear scattering potential to account for attenuation caused by non-elastic scattering. We briefly outline the historical development of these models and give examples illustrating the close analogy between them, their parameters, and the resulting scattering. In both models, the ratio of the incident wavelength to the object size, λ/D, can be determined from the scattering characteristics, allowing the extraction of microscopic particle dimensions. This close analogy allows students to simulate accelerator-based nuclear scattering experiments with table-top optical-scattering experiments.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44416816","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}
We describe student difficulties in applying the superposition principle in combination with Gauss's law. We addressed these difficulties by developing a tutorial that uses guided inquiry. Students who used this tutorial following lecture-based instruction performed significantly better on these topics than those who did not. Instructors can assign the tutorial as classwork or homework.
{"title":"Helping students apply superposition principle in problems involving spherical, cylindrical, and planar charge distributions","authors":"Jing Li, A. Maries, Chandralekha Singh","doi":"10.1119/5.0127127","DOIUrl":"https://doi.org/10.1119/5.0127127","url":null,"abstract":"We describe student difficulties in applying the superposition principle in combination with Gauss's law. We addressed these difficulties by developing a tutorial that uses guided inquiry. Students who used this tutorial following lecture-based instruction performed significantly better on these topics than those who did not. Instructors can assign the tutorial as classwork or homework.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44473732","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}
The canonical equation for self-inductance involving magnetic flux is examined, and a more general form is presented that can be applied to continuous current distributions. We attempt to clarify and extend the use of the standard equation by recasting it in its more versatile form.
{"title":"Self-inductance and magnetic flux","authors":"D. Castaño, Teresa M. Castaño","doi":"10.1119/5.0098417","DOIUrl":"https://doi.org/10.1119/5.0098417","url":null,"abstract":"The canonical equation for self-inductance involving magnetic flux is examined, and a more general form is presented that can be applied to continuous current distributions. We attempt to clarify and extend the use of the standard equation by recasting it in its more versatile form.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63422990","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}
Chenyang Lu, Bentley Turner, Y. Gui, Jacob Burgess, Jiang Xiao, Can-Ming Hu
We have experimentally demonstrated dissipative coupling in a double pendulum system through observation, which shows three distinctly different patterns of motion over the accessible parameter space. The described dissipative coupling apparatus is easy to manufacture and budget-friendly. The theoretical calculations are also suitable for the undergraduate level. Our experiment can serve as a novel demonstration for ubiquitous dynamic coupling effects encountered in many disparate physical systems. Unlike the well-known spring-coupled pendulums, our experiment employs Lenz's effect to couple the pendulums through electromagnetic damping, which, to the best of our knowledge, has not been demonstrated in the classroom. Our pendulums exhibit level attraction behaviour between two modes, induced by the dissipative coupling. This stands in contrast to the traditionally taught concept of level repulsion (avoided crossing) with spring-coupled pendulums. This experiment showcases distinctly different time domain dynamics of the dissipatively coupled pendulums over the parameter space, characterized by different oscillation patterns, damping rates, and relative phase between the two pendulums, which is a valuable lesson elucidating the dynamics of synchronization in linear systems for undergraduate students.
{"title":"An experimental demonstration of level attraction with coupled pendulums","authors":"Chenyang Lu, Bentley Turner, Y. Gui, Jacob Burgess, Jiang Xiao, Can-Ming Hu","doi":"10.1119/5.0081906","DOIUrl":"https://doi.org/10.1119/5.0081906","url":null,"abstract":"We have experimentally demonstrated dissipative coupling in a double pendulum system through observation, which shows three distinctly different patterns of motion over the accessible parameter space. The described dissipative coupling apparatus is easy to manufacture and budget-friendly. The theoretical calculations are also suitable for the undergraduate level. Our experiment can serve as a novel demonstration for ubiquitous dynamic coupling effects encountered in many disparate physical systems. Unlike the well-known spring-coupled pendulums, our experiment employs Lenz's effect to couple the pendulums through electromagnetic damping, which, to the best of our knowledge, has not been demonstrated in the classroom. Our pendulums exhibit level attraction behaviour between two modes, induced by the dissipative coupling. This stands in contrast to the traditionally taught concept of level repulsion (avoided crossing) with spring-coupled pendulums. This experiment showcases distinctly different time domain dynamics of the dissipatively coupled pendulums over the parameter space, characterized by different oscillation patterns, damping rates, and relative phase between the two pendulums, which is a valuable lesson elucidating the dynamics of synchronization in linear systems for undergraduate students.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48857627","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}
We show that a two-dimensional square lattice of magnets can be studied by placing small cylindrical neodymium magnets inside plastic spherical shells and floating them on water, leaving their magnetic moments free to re-orient within the plane. Experimentally, anti-correlated dipole orientations between nearest neighbors appear to be favored energetically. This motivates the construction of a simplified single-variable energy function for a 2D square lattice of magnetic dipoles. For odd numbers of spheres, this ansatz yields a continuum of dipole configurations with the same energies, matching the observed behavior that the orientation of the dipoles in these lattices can be rotated freely. The behavior of square lattices with even numbers of spheres is strikingly different, showing strongly preferred orientations. While the energy calculated in this simplified model is larger than that of the actual ground state for finite size clusters, its asymptotic value in the limit where the number of spheres goes to infinity is in good agreement with the literature value. Additionally, rectangular arrangements of magnetic spheres with and without a defect are analyzed within the class of the single variable energy function. Simple experimental demonstrations qualitatively reproduce several interesting results obtained from all these analyses.
{"title":"Infinite-fold energy degeneracy in 2D square lattices of magnetic spheres","authors":"K. Kim","doi":"10.1119/5.0121937","DOIUrl":"https://doi.org/10.1119/5.0121937","url":null,"abstract":"We show that a two-dimensional square lattice of magnets can be studied by placing small cylindrical neodymium magnets inside plastic spherical shells and floating them on water, leaving their magnetic moments free to re-orient within the plane. Experimentally, anti-correlated dipole orientations between nearest neighbors appear to be favored energetically. This motivates the construction of a simplified single-variable energy function for a 2D square lattice of magnetic dipoles. For odd numbers of spheres, this ansatz yields a continuum of dipole configurations with the same energies, matching the observed behavior that the orientation of the dipoles in these lattices can be rotated freely. The behavior of square lattices with even numbers of spheres is strikingly different, showing strongly preferred orientations. While the energy calculated in this simplified model is larger than that of the actual ground state for finite size clusters, its asymptotic value in the limit where the number of spheres goes to infinity is in good agreement with the literature value. Additionally, rectangular arrangements of magnetic spheres with and without a defect are analyzed within the class of the single variable energy function. Simple experimental demonstrations qualitatively reproduce several interesting results obtained from all these analyses.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44787412","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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