Introducing students to a new law is pedagogically challenging. One can just declare it as fact, but it is easier on (at least some) students if we can derive it when possible, or, if not, at least motivate it somehow. The Biot-Savart law is particularly challenging in this respect, because it is only derivable from more advanced formulations (such as Maxwell’s equations), which are in their turn merely stipulated (this is the approach of Feynman et al., for example). The other possibility is simply to declare its empirical truth, without details (see, for example, Griffiths).
{"title":"Motivating the Biot-Savart Law","authors":"A. Drory","doi":"10.1119/5.0084454","DOIUrl":"https://doi.org/10.1119/5.0084454","url":null,"abstract":"Introducing students to a new law is pedagogically challenging. One can just declare it as fact, but it is easier on (at least some) students if we can derive it when possible, or, if not, at least motivate it somehow. The Biot-Savart law is particularly challenging in this respect, because it is only derivable from more advanced formulations (such as Maxwell’s equations), which are in their turn merely stipulated (this is the approach of Feynman et al., for example). The other possibility is simply to declare its empirical truth, without details (see, for example, Griffiths).","PeriodicalId":48709,"journal":{"name":"Physics Teacher","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47758106","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 string shooter is an intriguing device that can be used to demonstrate a number of important physics concepts. It uses a pair of rotating wheels to continuously propel a closed loop of string at constant speed (see Fig. 1). Remarkably, the loop quickly reaches a stable shape, remaining suspended in the air. This surprising behavior may be viewed in a number of YouTube videos. Several models of the device are available commercially, at modest cost, and homemade versions are not difficult to construct. Advanced-level discussions of the underlying physics have recently appeared in the scientific literature. Fortunately, the fundamentals of those analyses can be cast into a form that is accessible to students of introductory-level physics. That is the aim of this paper. Conceptually, the device’s behavior can be explained by considering the forces that act on the string (interestingly, air drag plays a key role) and using the conditions for translational and rotational equilibrium. A more complete analysis, using Newton’s second law, allows the shape of a stationary loop, lying in a vertical plane, to be predicted with remarkable accuracy. The method requires only a minimal amount of calculus.
{"title":"Physics of the String Shooter","authors":"K. Mamola","doi":"10.1119/5.0099300","DOIUrl":"https://doi.org/10.1119/5.0099300","url":null,"abstract":"The string shooter is an intriguing device that can be used to demonstrate a number of important physics concepts. It uses a pair of rotating wheels to continuously propel a closed loop of string at constant speed (see Fig. 1). Remarkably, the loop quickly reaches a stable shape, remaining suspended in the air. This surprising behavior may be viewed in a number of YouTube videos. Several models of the device are available commercially, at modest cost, and homemade versions are not difficult to construct. Advanced-level discussions of the underlying physics have recently appeared in the scientific literature. Fortunately, the fundamentals of those analyses can be cast into a form that is accessible to students of introductory-level physics. That is the aim of this paper. Conceptually, the device’s behavior can be explained by considering the forces that act on the string (interestingly, air drag plays a key role) and using the conditions for translational and rotational equilibrium. A more complete analysis, using Newton’s second law, allows the shape of a stationary loop, lying in a vertical plane, to be predicted with remarkable accuracy. The method requires only a minimal amount of calculus.","PeriodicalId":48709,"journal":{"name":"Physics Teacher","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44613564","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}
Alice Olmstead, Brianne Gutmann, Egla Ochoa-Madrid, Alexander Vasquez, Ciana Pike, D. Barringer
STEM professionals make decisions that impact society in a wide variety of ways. Making thoughtful decisions often requires them to consider a complex set of real-world implications that can impact multiple stakeholders, and there may not be a single “best” solution to be discovered. These decisions can also be political in nature. In contrast, science is often portrayed as being purely objective and apolitical. Physics instruction often reinforces this portrayal by focusing exclusively on physics content knowledge and skills. Some physics programs have been expanding to include technical skills that are relevant in the workforce, and this expansion likely benefits students in their careers. But undergraduate physics programs, and STEM courses generally, rarely prepare students to grapple with the types of complex, ethical decision-making that they will encounter in STEM.
{"title":"How Can We Design Instruction to Support Student Reasoning About Physicists’ Ethical Responsibilities in Society?","authors":"Alice Olmstead, Brianne Gutmann, Egla Ochoa-Madrid, Alexander Vasquez, Ciana Pike, D. Barringer","doi":"10.1119/5.0087490","DOIUrl":"https://doi.org/10.1119/5.0087490","url":null,"abstract":"STEM professionals make decisions that impact society in a wide variety of ways. Making thoughtful decisions often requires them to consider a complex set of real-world implications that can impact multiple stakeholders, and there may not be a single “best” solution to be discovered. These decisions can also be political in nature. In contrast, science is often portrayed as being purely objective and apolitical. Physics instruction often reinforces this portrayal by focusing exclusively on physics content knowledge and skills. Some physics programs have been expanding to include technical skills that are relevant in the workforce, and this expansion likely benefits students in their careers. But undergraduate physics programs, and STEM courses generally, rarely prepare students to grapple with the types of complex, ethical decision-making that they will encounter in STEM.","PeriodicalId":48709,"journal":{"name":"Physics Teacher","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47534607","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}
Yuannan Zheng, Kexun Shen, Xianghe Wang, Xingen Yao
The rainbow is a natural optical scattering and dispersion phenomenon that reveals the visible spectral composition of sunlight in the shape of an arc. People are instinctively attracted by its colorful appearance and curved shape. Hence, there are many serious studies about the rainbow with a long history. Recently, several simple experiments, adopting glass balls, acrylic spheres, spherical flasks, or sessile water drops, have been devised to demonstrate how the rainbow is formed. These works demonstrate the colors and shapes of the rainbow well and explain how the dispersive spectrum is produced by the refraction–reflection–refraction process. However, the influence of the refractive index is rarely illustrated. It is not difficult to see that the refractive index of raindrops and the atmosphere is closely related to the rainbow, especially the viewing angle of it. In this paper, we use spherical lenses with different materials and in different solutions to change the refractive index. Under a collimated light source, the evolution of the viewing angles of primary and secondary rainbows with respect to the refractive index is demonstrated. Experiments with refraction conditions similar to a natural rainbow are also conducted.
{"title":"Rainbows in Different Refractive Indices","authors":"Yuannan Zheng, Kexun Shen, Xianghe Wang, Xingen Yao","doi":"10.1119/5.0086915","DOIUrl":"https://doi.org/10.1119/5.0086915","url":null,"abstract":"The rainbow is a natural optical scattering and dispersion phenomenon that reveals the visible spectral composition of sunlight in the shape of an arc. People are instinctively attracted by its colorful appearance and curved shape. Hence, there are many serious studies about the rainbow with a long history. Recently, several simple experiments, adopting glass balls, acrylic spheres, spherical flasks, or sessile water drops, have been devised to demonstrate how the rainbow is formed. These works demonstrate the colors and shapes of the rainbow well and explain how the dispersive spectrum is produced by the refraction–reflection–refraction process. However, the influence of the refractive index is rarely illustrated. It is not difficult to see that the refractive index of raindrops and the atmosphere is closely related to the rainbow, especially the viewing angle of it. In this paper, we use spherical lenses with different materials and in different solutions to change the refractive index. Under a collimated light source, the evolution of the viewing angles of primary and secondary rainbows with respect to the refractive index is demonstrated. Experiments with refraction conditions similar to a natural rainbow are also conducted.","PeriodicalId":48709,"journal":{"name":"Physics Teacher","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45579781","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":"May u B happy","authors":"B. Korsunsky","doi":"10.1119/10.0018002","DOIUrl":"https://doi.org/10.1119/10.0018002","url":null,"abstract":"","PeriodicalId":48709,"journal":{"name":"Physics Teacher","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49668757","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}
R. Stevens, Karen E. Stevens, Ryan L. Grady, Laura A. Stricker
This paper describes an experimental setup using a coffee mug, a low delta-temperature model Stirling engine, and a gas pressure sensor. The experiment is targeted toward first-year calculus-based physics labs and was designed to be implemented at low cost (approximately $120 for engine and pressure sensor) and minimal modification to off-the-shelf components for an instructor. The gas pressure sensor we used plugs directly into a USB port, and no data acquisition hub was required. Software to operate the sensor is available from the manufacturer at no additional cost. A sample student procedure handout is provided in Appendix B. Modifications for use in high school physics, algebra-based college physics, and upper-division thermodynamics courses are presented in Appendix A. Two simple modifications to the Stirling engine are required: (1) drilling a hole in the top plate of the Stirling engine and gluing a Luer lock fitting over the hole; and (2) 3D printing a spool that is then hot glued to the driveshaft of the Stirling engine. A more advanced experiment can be performed by 3D printing two gears and using a rotary motion sensor to track the phase of the system. A video demonstration of these modifications is provided. Student calculations of work done by the engine show good correlation with predicted theoretical calculations. Students also rated the experimental procedure highly for both interest and understanding.
{"title":"Measurement of Work and Power in a Coffee-Mug Stirling Engine as a First-Year Physics Laboratory","authors":"R. Stevens, Karen E. Stevens, Ryan L. Grady, Laura A. Stricker","doi":"10.1119/5.0073861","DOIUrl":"https://doi.org/10.1119/5.0073861","url":null,"abstract":"This paper describes an experimental setup using a coffee mug, a low delta-temperature model Stirling engine, and a gas pressure sensor. The experiment is targeted toward first-year calculus-based physics labs and was designed to be implemented at low cost (approximately $120 for engine and pressure sensor) and minimal modification to off-the-shelf components for an instructor. The gas pressure sensor we used plugs directly into a USB port, and no data acquisition hub was required. Software to operate the sensor is available from the manufacturer at no additional cost. A sample student procedure handout is provided in Appendix B. Modifications for use in high school physics, algebra-based college physics, and upper-division thermodynamics courses are presented in Appendix A. Two simple modifications to the Stirling engine are required: (1) drilling a hole in the top plate of the Stirling engine and gluing a Luer lock fitting over the hole; and (2) 3D printing a spool that is then hot glued to the driveshaft of the Stirling engine. A more advanced experiment can be performed by 3D printing two gears and using a rotary motion sensor to track the phase of the system. A video demonstration of these modifications is provided. Student calculations of work done by the engine show good correlation with predicted theoretical calculations. Students also rated the experimental procedure highly for both interest and understanding.","PeriodicalId":48709,"journal":{"name":"Physics Teacher","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42986378","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}
Gustavo A. Mendes, Jusciane da Costa e Silva, Gustavo de O. G. Rebouças
Although schools commonly teach that sound waves propagate faster in solids than in liquids and in liquids than in gases, there is no low-cost activity that allows students to investigate if this statement is true or not. Indeed, some existing techniques simply allow them to identify the speed of sound in air and its temperature dependence.
{"title":"Instantaneous Measurement of the Speed of Sound in Air and Water Using Arduino","authors":"Gustavo A. Mendes, Jusciane da Costa e Silva, Gustavo de O. G. Rebouças","doi":"10.1119/5.0118245","DOIUrl":"https://doi.org/10.1119/5.0118245","url":null,"abstract":"Although schools commonly teach that sound waves propagate faster in solids than in liquids and in liquids than in gases, there is no low-cost activity that allows students to investigate if this statement is true or not. Indeed, some existing techniques simply allow them to identify the speed of sound in air and its temperature dependence.","PeriodicalId":48709,"journal":{"name":"Physics Teacher","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42742333","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 “Sadly Cannot” (SC) thermodynamic cycle was introduced by Willis and Kirwan in a paper that appeared in the January 1980 issue of this journal. Comprising but two steps, it appears remarkably simple. First, an ideal monatomic gas is expanded from initial state (P0, V0) to final state (P1, V1) along a path that is a straight line of negative slope in the PV plane, but with (P0, V0) and (P1, V1) chosen to be connected by an adiabat: P0V0γ = P1V1γ, where we set γ = 5/3. The return path is the adiabat, along which there can be no heat energy exchange. The cycle is sketched (not to scale) in Fig. 1. As with all such cycles, all processes are assumed to be quasistatic.
{"title":"A Deeper Look at the Sadly Cannot Thermodynamic Cycle","authors":"B. Reed","doi":"10.1119/5.0090865","DOIUrl":"https://doi.org/10.1119/5.0090865","url":null,"abstract":"The “Sadly Cannot” (SC) thermodynamic cycle was introduced by Willis and Kirwan in a paper that appeared in the January 1980 issue of this journal. Comprising but two steps, it appears remarkably simple. First, an ideal monatomic gas is expanded from initial state (P0, V0) to final state (P1, V1) along a path that is a straight line of negative slope in the PV plane, but with (P0, V0) and (P1, V1) chosen to be connected by an adiabat: P0V0γ = P1V1γ, where we set γ = 5/3. The return path is the adiabat, along which there can be no heat energy exchange. The cycle is sketched (not to scale) in Fig. 1. As with all such cycles, all processes are assumed to be quasistatic.","PeriodicalId":48709,"journal":{"name":"Physics Teacher","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47359970","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}
What is the acceleration of a swing as it passes the lowest point and as it turns at the highest point? What are the forces acting? These were a couple of the questions students were asked to discuss in small groups during their first week at university, as part of a tutorial session. On one occasion, two students were unable to reconcile their different viewpoints without teacher intervention. One of them emphasized that the swing moves fastest at the bottom, and concluded that the acceleration must be zero. The other student claimed that there must be a force, since you feel heavier at the bottom. They noted the contradiction, but failed to recognize that acceleration is the derivative of velocity, not the derivative of speed: For the lowest point, the speed is maximum, but the direction of motion changes. These students had certainly been taught all the elements of physics needed to calculate the force and acceleration, but forgot to make the connection on their own. A small hint from the teacher, reminding them about centripetal acceleration, was sufficient.
{"title":"Serious Physics on a Playground Swing—With Toys, Your Own Body, and a\u0000 Smartphone","authors":"A. Pendrill","doi":"10.1119/5.0074171","DOIUrl":"https://doi.org/10.1119/5.0074171","url":null,"abstract":"\u0000 \u0000 What is the acceleration of a swing as it passes the lowest point and as it turns at the highest point? What are the forces acting? These were a couple of the questions students were asked to discuss in small groups during their first week at university, as part of a tutorial session. On one occasion, two students were unable to reconcile their different viewpoints without teacher intervention. One of them emphasized that the swing moves fastest at the bottom, and concluded that the acceleration must be zero. The other student claimed that there must be a force, since you feel heavier at the bottom. They noted the contradiction, but failed to recognize that acceleration is the derivative of velocity, not the derivative of speed: For the lowest point, the speed is maximum, but the direction of motion changes. These students had certainly been taught all the elements of physics needed to calculate the force and acceleration, but forgot to make the connection on their own. A small hint from the teacher, reminding them about centripetal acceleration, was sufficient.\u0000","PeriodicalId":48709,"journal":{"name":"Physics Teacher","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46543882","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}
Measuring the refractive index (RI) of a liquid without using any fancy equipment has become a popular topic in various STEM classses and events. This article proposes a simple method that has the following properties:
{"title":"A Nonlinear Least-Squares Approach for Estimating the Refractive Index of a Liquid","authors":"J. She","doi":"10.1119/5.0086331","DOIUrl":"https://doi.org/10.1119/5.0086331","url":null,"abstract":"Measuring the refractive index (RI) of a liquid without using any fancy equipment has become a popular topic in various STEM classses and events. This article proposes a simple method that has the following properties:","PeriodicalId":48709,"journal":{"name":"Physics Teacher","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44785228","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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