Joseph C. Amato, John Essick, Harvey Gould, Claire A. Marrache-Kikuchi, Raina Olsen, Beth Parks, Donald Salisbury, Jan Tobochnik
Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite Search Site Citation Joseph C. Amato, John Essick, Harvey Gould, Claire A. Marrache-Kikuchi, Raina Olsen, Beth Parks, Donald Salisbury, Jan Tobochnik; In this issue: June 2023. American Journal of Physics 17 May 2023; 91 (6): 413–. https://doi.org/10.1119/5.0155778 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAmerican Association of Physics TeachersAmerican Journal of Physics Search Advanced Search |Citation Search
查看图标查看文章内容图表和表格视频音频补充数据同行评审分享图标分享Twitter Facebook Reddit LinkedIn工具图标工具转载和许可引用图标引用搜索网站引用Joseph C. Amato, John Essick, Harvey Gould, Claire A. marracher - kikuchi, Raina Olsen, Beth Parks, Donald Salisbury, Jan Tobochnik;本期:2023年6月。《美国物理学杂志》2023年5月17日;91(6): 413 -。https://doi.org/10.1119/5.0155778下载引文文件:Ris (Zotero)参考管理器EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex工具栏搜索搜索下拉菜单工具栏搜索搜索输入搜索输入自动建议过滤您的搜索所有内容美国物理教师协会美国物理杂志搜索高级搜索|引文搜索
{"title":"In this issue: June 2023","authors":"Joseph C. Amato, John Essick, Harvey Gould, Claire A. Marrache-Kikuchi, Raina Olsen, Beth Parks, Donald Salisbury, Jan Tobochnik","doi":"10.1119/5.0155778","DOIUrl":"https://doi.org/10.1119/5.0155778","url":null,"abstract":"Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite Search Site Citation Joseph C. Amato, John Essick, Harvey Gould, Claire A. Marrache-Kikuchi, Raina Olsen, Beth Parks, Donald Salisbury, Jan Tobochnik; In this issue: June 2023. American Journal of Physics 17 May 2023; 91 (6): 413–. https://doi.org/10.1119/5.0155778 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAmerican Association of Physics TeachersAmerican Journal of Physics Search Advanced Search |Citation Search","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135626054","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 develop a simple model to investigate the orientation-dependence of the drag force acting on a magnet falling inside a vertical conducting pipe. We approximate the magnet by a point magnet and the pipe by a two-dimensional cylindrical surface. Independent of the magnet's orientation, the drag force is proportional to its velocity: F→d=−kv→. We show that the coefficient k→ of the horizontally oriented magnet is about 2/3 of the coefficient k↑ for the vertically oriented magnet. If the magnetic moment makes an angle θ with the vertical direction, the drag coefficient k can be expressed as k=k↑ cos2θ+k→ sin2θ. When the magnet falls with a non-vertical orientation, a local charge distribution is induced in the pipe, which plays a role as important as that of the time-varying magnetic field due to the falling magnet in generating the eddy currents. The model's predictions are compared with experimental results.
{"title":"A magnet falling inside a conducting pipe: Dependence of the drag force on\u0000 the magnet orientation","authors":"Chang Hyeon Lee, Byung-Yoon Park","doi":"10.1119/5.0062860","DOIUrl":"https://doi.org/10.1119/5.0062860","url":null,"abstract":"We develop a simple model to investigate the orientation-dependence of the drag force acting on a magnet falling inside a vertical conducting pipe. We approximate the magnet by a point magnet and the pipe by a two-dimensional cylindrical surface. Independent of the magnet's orientation, the drag force is proportional to its velocity: F→d=−kv→. We show that the coefficient k→ of the horizontally oriented magnet is about 2/3 of the coefficient k↑ for the vertically oriented magnet. If the magnetic moment makes an angle θ with the vertical direction, the drag coefficient k can be expressed as k=k↑ cos2θ+k→ sin2θ. When the magnet falls with a non-vertical orientation, a local charge distribution is induced in the pipe, which plays a role as important as that of the time-varying magnetic field due to the falling magnet in generating the eddy currents. The model's predictions are compared with experimental results.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43840496","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}
Sarah Frances Whiting developed innovative and influential laboratory work in her introductory astronomy classes at Wellesley College in the late 1800s and early 1900s. Whiting was strongly influenced by Edward Pickering and the early physics laboratory education at the Massachusetts Institute of Technology. This article explores the early development of laboratory work in astronomy education at Wellesley and Whiting's underlying philosophy of education. By laboratory work, Whiting meant day-time work, including work with astronomical photographs and spectroscopy. Her pedagogy was encapsulated in her phrase “to sharpen the pencil sharpens the mind,” which referenced the importance of a student's familiarity with tools as well as the role of drawing in astronomical work. Whiting further modeled her instruction after the work being conducted at the Harvard College Observatory in order to prepare her students for potential future employment as astronomers.
{"title":"Sarah Frances Whiting, pioneer of laboratory instruction in astronomy","authors":"J. Behrman","doi":"10.1119/5.0131617","DOIUrl":"https://doi.org/10.1119/5.0131617","url":null,"abstract":"Sarah Frances Whiting developed innovative and influential laboratory work in her introductory astronomy classes at Wellesley College in the late 1800s and early 1900s. Whiting was strongly influenced by Edward Pickering and the early physics laboratory education at the Massachusetts Institute of Technology. This article explores the early development of laboratory work in astronomy education at Wellesley and Whiting's underlying philosophy of education. By laboratory work, Whiting meant day-time work, including work with astronomical photographs and spectroscopy. Her pedagogy was encapsulated in her phrase “to sharpen the pencil sharpens the mind,” which referenced the importance of a student's familiarity with tools as well as the role of drawing in astronomical work. Whiting further modeled her instruction after the work being conducted at the Harvard College Observatory in order to prepare her students for potential future employment as astronomers.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45699527","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 problem of determining minimal time trajectories in a plane constrained by an upper bound on the magnitude of the acceleration vector is reexamined. In the previous work [Am. J. Phys. 49(7), 685–688 (1981)], a stationary solution of a functional, applied over curves in two-dimensional velocity space, was used to find explicit expressions for what was claimed to be a minimum turn time trajectory. In this paper, this work is furthered by a formal demonstration that the turn time associated with this trajectory is indeed lower than that corresponding to any other smooth trajectory. Supporting evidence for this claim is provided by numerical procedures, which are developed to allow comparisons between the turn times of competing trajectories across a range of parameter values of the turn width, the initial speed, and the magnitude of the acceleration vector.
{"title":"Optimal trajectories for symmetric turns","authors":"S. Kaczkowski","doi":"10.1119/5.0114235","DOIUrl":"https://doi.org/10.1119/5.0114235","url":null,"abstract":"The problem of determining minimal time trajectories in a plane constrained by an upper bound on the magnitude of the acceleration vector is reexamined. In the previous work [Am. J. Phys. 49(7), 685–688 (1981)], a stationary solution of a functional, applied over curves in two-dimensional velocity space, was used to find explicit expressions for what was claimed to be a minimum turn time trajectory. In this paper, this work is furthered by a formal demonstration that the turn time associated with this trajectory is indeed lower than that corresponding to any other smooth trajectory. Supporting evidence for this claim is provided by numerical procedures, which are developed to allow comparisons between the turn times of competing trajectories across a range of parameter values of the turn width, the initial speed, and the magnitude of the acceleration vector.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45769847","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 drop a circular disk magnet through a thin coil of wire, record the induced voltage, and compare the results to an analytic model based on the dipole approximation and Faraday's law, which predicts that the difference between the voltage peak magnitudes corresponding to the entry and exit of the magnet should be in proportion to z0−1/2, where z0 is the initial height of the magnet above the center of the coil. Agreement between the model and experimental data is excellent. This easily reproduced experiment provides an opportunity for students at a range of levels to quantitatively explore the effects of magnetic induction.
{"title":"Modeling the induced voltage of a disk magnet in free fall","authors":"Nolan Samboy","doi":"10.1119/5.0141862","DOIUrl":"https://doi.org/10.1119/5.0141862","url":null,"abstract":"We drop a circular disk magnet through a thin coil of wire, record the induced voltage, and compare the results to an analytic model based on the dipole approximation and Faraday's law, which predicts that the difference between the voltage peak magnitudes corresponding to the entry and exit of the magnet should be in proportion to z0−1/2, where z0 is the initial height of the magnet above the center of the coil. Agreement between the model and experimental data is excellent. This easily reproduced experiment provides an opportunity for students at a range of levels to quantitatively explore the effects of magnetic induction.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45025737","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 perform phase-sensitive detection with an inexpensive microcontroller, the Teensy 3.5. The programming and pricing of this microcontroller is similar to that of commonly used Arduino microcontrollers, but the Teensy 3.5 offers superior hardware performance. Our Teensy-based phase-sensitive detector can operate either with an external reference signal or by internally generating a reference signal. Additionally, we have developed an open-source graphical user interface for controlling the instrument. We demonstrate that our phase-sensitive detector exhibits good linearity in amplitude and phase, even with 25 mV signals dominated by larger-amplitude noise. We also use our phase-sensitive detector in a simple laboratory measurement: determining the distance dependence of the intensity of a light-emitting diode (LED) with the room lights on. Our instrument is a useful tool for teaching students about phase-sensitive detection and can be a viable low-cost alternative to commercial lock-in amplifiers.
{"title":"Flexible, low-cost phase-sensitive detection for the undergraduate laboratory with a Teensy microcontroller","authors":"J. Fung, Christopher L. Weil","doi":"10.1119/5.0126691","DOIUrl":"https://doi.org/10.1119/5.0126691","url":null,"abstract":"We perform phase-sensitive detection with an inexpensive microcontroller, the Teensy 3.5. The programming and pricing of this microcontroller is similar to that of commonly used Arduino microcontrollers, but the Teensy 3.5 offers superior hardware performance. Our Teensy-based phase-sensitive detector can operate either with an external reference signal or by internally generating a reference signal. Additionally, we have developed an open-source graphical user interface for controlling the instrument. We demonstrate that our phase-sensitive detector exhibits good linearity in amplitude and phase, even with 25 mV signals dominated by larger-amplitude noise. We also use our phase-sensitive detector in a simple laboratory measurement: determining the distance dependence of the intensity of a light-emitting diode (LED) with the room lights on. Our instrument is a useful tool for teaching students about phase-sensitive detection and can be a viable low-cost alternative to commercial lock-in amplifiers.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41354448","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 possibility of stating the second law of thermodynamics in terms of the increasing behaviour of a physical property establishes a connection between that branch of physics and the theory of algebraic inequalities. We use this connection to show how some well-known inequalities, such as the standard bounds for the logarithmic function or generalizations of Bernoulli's inequality, can be derived by thermodynamic methods. Additionally, we show that by comparing the global entropy production in processes implemented with decreasing levels of irreversibility but subject to the same change of state of one particular system, we can find progressively better bounds for the real function that represents the entropy variation of the system. As an application, some new families of bounds for the function log (1+x) are obtained by this method.
{"title":"Finding and improving bounds of real functions by thermodynamic arguments","authors":"Andrés Vallejo","doi":"10.1119/5.0121919","DOIUrl":"https://doi.org/10.1119/5.0121919","url":null,"abstract":"The possibility of stating the second law of thermodynamics in terms of the increasing behaviour of a physical property establishes a connection between that branch of physics and the theory of algebraic inequalities. We use this connection to show how some well-known inequalities, such as the standard bounds for the logarithmic function or generalizations of Bernoulli's inequality, can be derived by thermodynamic methods. Additionally, we show that by comparing the global entropy production in processes implemented with decreasing levels of irreversibility but subject to the same change of state of one particular system, we can find progressively better bounds for the real function that represents the entropy variation of the system. As an application, some new families of bounds for the function log (1+x) are obtained by this method.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46505404","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}
When learning about potential energy functions, students are sometimes told that the potential energy function is analogous to that of a particle sliding along a frictionless roller coaster track or wire confined to a vertical plane with peaks and valleys of the track corresponding to unstable and stable equilibrium points. However, motion along a track with height z(x) is a constrained two-dimensional motion, not a one-dimensional motion, so the exact nature of this analogy may be unclear. We show that the horizontal motion of a point mass sliding along a frictionless track z(x) and subject to a uniform gravitational field is equivalent to the motion of a particle in one dimension characterized by an “analogous potential energy” function UE(x), which generally depends on the total energy of the system (and thus on the initial conditions). We derive a general expression for UE(x) in terms of z(x) and the total energy and show that the equilibrium points of the actual potential energy U(x)=mgz(x) are also static equilibrium points for UE(x) with the same stability. However, UE(x) may have additional dynamic equilibrium points that are not present for U(x). As an example, we derive UE(x) for a double well track and determine the period of oscillations on that track. The results show that in general a single track corresponds to many different analogous potential energy functions, each with a different value for the total energy.
{"title":"The one-dimensional potential energy function that is analogous to a two-dimensional track","authors":"T. Timberlake, Robert Valentin Mbenoun Mahend","doi":"10.1119/5.0100950","DOIUrl":"https://doi.org/10.1119/5.0100950","url":null,"abstract":"When learning about potential energy functions, students are sometimes told that the potential energy function is analogous to that of a particle sliding along a frictionless roller coaster track or wire confined to a vertical plane with peaks and valleys of the track corresponding to unstable and stable equilibrium points. However, motion along a track with height z(x) is a constrained two-dimensional motion, not a one-dimensional motion, so the exact nature of this analogy may be unclear. We show that the horizontal motion of a point mass sliding along a frictionless track z(x) and subject to a uniform gravitational field is equivalent to the motion of a particle in one dimension characterized by an “analogous potential energy” function UE(x), which generally depends on the total energy of the system (and thus on the initial conditions). We derive a general expression for UE(x) in terms of z(x) and the total energy and show that the equilibrium points of the actual potential energy U(x)=mgz(x) are also static equilibrium points for UE(x) with the same stability. However, UE(x) may have additional dynamic equilibrium points that are not present for U(x). As an example, we derive UE(x) for a double well track and determine the period of oscillations on that track. The results show that in general a single track corresponds to many different analogous potential energy functions, each with a different value for the total energy.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45743172","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}
Objects that slide or roll along curved tracks in a vertical plane are investigated in two separate experiments. One concerns a smooth metal nut that slides along a semicircular track made from coat hanger wire. The other concerns a billiard ball that slides and rolls along a curved track. A simple theoretical model is provided to account for the results and to extend the discussion to consider shortest descent times down circular tracks.
{"title":"Sliding and rolling along circular tracks in a vertical plane","authors":"R. Cross","doi":"10.1119/5.0107553","DOIUrl":"https://doi.org/10.1119/5.0107553","url":null,"abstract":"Objects that slide or roll along curved tracks in a vertical plane are investigated in two separate experiments. One concerns a smooth metal nut that slides along a semicircular track made from coat hanger wire. The other concerns a billiard ball that slides and rolls along a curved track. A simple theoretical model is provided to account for the results and to extend the discussion to consider shortest descent times down circular tracks.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44960921","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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