When two flat surfaces approach each other, the fluid in between is accelerated and ejected from the sides at large speeds. This situation occurs often in everyday life, such as when you step in a puddle and create splashes of water, or when you clap your hands or close a book and create jets of air. For these systems, the inertia of the fluid resists the acceleration, creating large nonlinear forces on the flat surfaces. In this work, we study the case of a closing book. The fluid motion in this case is relatively easy to model, using the conservation of mechanical energy, and to measure using a MEMS gyroscopic sensor. This study reveals the unusual forces that occur when two plates collide in an experiment that can be performed by students at home.
{"title":"How the air slows a closing book","authors":"J. Pantaleone","doi":"10.1119/5.0106926","DOIUrl":"https://doi.org/10.1119/5.0106926","url":null,"abstract":"When two flat surfaces approach each other, the fluid in between is accelerated and ejected from the sides at large speeds. This situation occurs often in everyday life, such as when you step in a puddle and create splashes of water, or when you clap your hands or close a book and create jets of air. For these systems, the inertia of the fluid resists the acceleration, creating large nonlinear forces on the flat surfaces. In this work, we study the case of a closing book. The fluid motion in this case is relatively easy to model, using the conservation of mechanical energy, and to measure using a MEMS gyroscopic sensor. This study reveals the unusual forces that occur when two plates collide in an experiment that can be performed by students at home.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":"34 5","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139127842","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}
J. Essick, Harvey Gould, C. Marrache-Kikuchi, Raina Olsen, B. Parks, B. C. Reed, Donald Salisbury, J. Tobochnik
{"title":"In this issue: January 2024","authors":"J. Essick, Harvey Gould, C. Marrache-Kikuchi, Raina Olsen, B. Parks, B. C. Reed, Donald Salisbury, J. Tobochnik","doi":"10.1119/5.0189551","DOIUrl":"https://doi.org/10.1119/5.0189551","url":null,"abstract":"","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":"98 5","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139127552","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}
Among the several methods to compute the perihelion precession for bounded orbits in Schwarzschild spacetime, the simplest is to ignore a term in the equations of motion. This is currently justified under the assumption that the eccentricity of the orbit is small. For cases such as Mercury in our solar system, whose eccentricity is not small, this method seems not to be applicable. Yet it gives the right result, the reason being that the term that has been excluded, although responsible for first order—in the ratio of the Schwarzschild radius over the radial coordinate—corrections of the orbit, only produces completely negligible higher order corrections for the perihelion precession. We show this result by two different procedures. We claim, therefore, that as long as the aim of the computation is the perihelion precession, one can safely drop that term regardless of the magnitude of the eccentricity.
{"title":"Expanding the range of validity of the simplest computation of the perihelion precession in Schwarzschild spacetime","authors":"Josep M. Pons","doi":"10.1119/5.0136332","DOIUrl":"https://doi.org/10.1119/5.0136332","url":null,"abstract":"Among the several methods to compute the perihelion precession for bounded orbits in Schwarzschild spacetime, the simplest is to ignore a term in the equations of motion. This is currently justified under the assumption that the eccentricity of the orbit is small. For cases such as Mercury in our solar system, whose eccentricity is not small, this method seems not to be applicable. Yet it gives the right result, the reason being that the term that has been excluded, although responsible for first order—in the ratio of the Schwarzschild radius over the radial coordinate—corrections of the orbit, only produces completely negligible higher order corrections for the perihelion precession. We show this result by two different procedures. We claim, therefore, that as long as the aim of the computation is the perihelion precession, one can safely drop that term regardless of the magnitude of the eccentricity.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":"54 42","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139126863","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}
P. Chen, Z. Q. Yang, Z. Z. Shi, Q. Y. Hou, G. R. Jin
The bound states of a particle confined in a one-dimensional finite square well cannot be solved analytically, since the eigen-energies are determined by transcendental equations. Here, we numerically calculate the bound states and show their non-classical properties, using Wigner's quasi-probability distribution (also called the Wigner functions) in the phase space (x, p). In contrast to the infinite-well case, we find that the Wigner functions spread over the space dimension x, get squeezed along the momentum dimension p, and show negativity outside the well. Negativity in a Wigner function indicates non-classical properties of the bound states.
束缚在一维有限方井中的粒子的束缚态无法用解析法求解，因为其特征能是由超越方程决定的。在这里，我们利用相空间（x, p）中的维格纳准概率分布（又称维格纳函数）对束缚态进行数值计算，并展示了它们的非经典特性。与无限井的情况相反，我们发现维格纳函数在空间维度 x 上扩散，在动量维度 p 上受到挤压，并在井外显示出负性。维格纳函数的负性表明束缚态具有非经典特性。
{"title":"Wigner functions of the finite square-well bound states","authors":"P. Chen, Z. Q. Yang, Z. Z. Shi, Q. Y. Hou, G. R. Jin","doi":"10.1119/5.0071891","DOIUrl":"https://doi.org/10.1119/5.0071891","url":null,"abstract":"The bound states of a particle confined in a one-dimensional finite square well cannot be solved analytically, since the eigen-energies are determined by transcendental equations. Here, we numerically calculate the bound states and show their non-classical properties, using Wigner's quasi-probability distribution (also called the Wigner functions) in the phase space (x, p). In contrast to the infinite-well case, we find that the Wigner functions spread over the space dimension x, get squeezed along the momentum dimension p, and show negativity outside the well. Negativity in a Wigner function indicates non-classical properties of the bound states.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":"9 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139124955","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 mean relative speed and relative speed distribution function of molecules play important roles in kinetics and related topics. College textbooks frequently present a simplified derivation of these quantities that, while yielding the correct result, are not well justified. This paper presents a detailed physical picture of collision-related processes based on the microscopic kinetic theory. Formulas for the mean relative speed and mean collision rate along with the relative speed distribution function and the distribution function of relative speed of the paired particles in collisions (collision possible distribution function) are derived for molecules from two different systems that are each at thermal equilibrium.
{"title":"Microscopic derivation of the collision properties of molecules in two systems at thermal equilibrium","authors":"Tongli Wei, Xiansheng Cao","doi":"10.1119/5.0128644","DOIUrl":"https://doi.org/10.1119/5.0128644","url":null,"abstract":"The mean relative speed and relative speed distribution function of molecules play important roles in kinetics and related topics. College textbooks frequently present a simplified derivation of these quantities that, while yielding the correct result, are not well justified. This paper presents a detailed physical picture of collision-related processes based on the microscopic kinetic theory. Formulas for the mean relative speed and mean collision rate along with the relative speed distribution function and the distribution function of relative speed of the paired particles in collisions (collision possible distribution function) are derived for molecules from two different systems that are each at thermal equilibrium.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":"26 16","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139129276","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}
Andrea Boskovic, Kate M. Jones, Alejandra Velasquez, Isabel P. Hardy, Maya L. Bulos, Ashley R. Carter, Martin Wiklund
Acoustic trapping is used in modern biophysics laboratories to study cell adhesion or aggregation, to sort particles, or to build model tissues. Here, we create an acoustic trapping setup in liquid for an undergraduate instructional laboratory that is low-cost, easy to build, and produces results in a 1-hour laboratory period. In this setup, we use a glass slide, cover slip, and double-sided tape to make the sample chamber. A piezo-electric transducer connected to a function generator serves as the acoustic source. We use this setup to measure the node spacing (millimeters) and the acoustic trap force (picoNewtons). We anticipate that the simplicity of the experimental setup, the tractability of the theoretical equations, and the richness of the research topics on the subject will lead to an undergraduate laboratory with many interesting student projects.
{"title":"Acoustic trapping in the undergraduate laboratory","authors":"Andrea Boskovic, Kate M. Jones, Alejandra Velasquez, Isabel P. Hardy, Maya L. Bulos, Ashley R. Carter, Martin Wiklund","doi":"10.1119/5.0167269","DOIUrl":"https://doi.org/10.1119/5.0167269","url":null,"abstract":"Acoustic trapping is used in modern biophysics laboratories to study cell adhesion or aggregation, to sort particles, or to build model tissues. Here, we create an acoustic trapping setup in liquid for an undergraduate instructional laboratory that is low-cost, easy to build, and produces results in a 1-hour laboratory period. In this setup, we use a glass slide, cover slip, and double-sided tape to make the sample chamber. A piezo-electric transducer connected to a function generator serves as the acoustic source. We use this setup to measure the node spacing (millimeters) and the acoustic trap force (picoNewtons). We anticipate that the simplicity of the experimental setup, the tractability of the theoretical equations, and the richness of the research topics on the subject will lead to an undergraduate laboratory with many interesting student projects.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":"12 7","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139127756","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}
J. Essick, Harvey Gould, C. Marrache-Kikuchi, B. Parks, Todd Springer, J. Tobochnik, Keith Zengel
{"title":"In this issue: December 2023","authors":"J. Essick, Harvey Gould, C. Marrache-Kikuchi, B. Parks, Todd Springer, J. Tobochnik, Keith Zengel","doi":"10.1119/5.0184717","DOIUrl":"https://doi.org/10.1119/5.0184717","url":null,"abstract":"","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":" 10","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138618174","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}
A mirage or fatamorgana is typically an upside-down “mirror” image of a scenery in deserts, over sun-heated roads, or above bodies of water. When the temperature gradient of air is large, as can happen near a surface, it results in a large gradient of the density and the refractive index as a function of height. Mirages appear when light travels through a medium with a gradient in its refractive index and, therefore, get bent towards the higher values, generating reflected images. A computer program that simulates mirages above water using the method of ray tracing has been developed and is presented here in detail for educational purposes. Results on the effect are shown by simulated images for various water-air temperature-difference cases with values ranging from 5 to 0 °C. Comparison of the simulations to a real-life scenario at Lake Balaton, Hungary has also been provided.
{"title":"Numerical simulation of mirages above water bodies","authors":"Anna Horváth, Balázs Bámer, G. G. Barnaföldi","doi":"10.1119/5.0111635","DOIUrl":"https://doi.org/10.1119/5.0111635","url":null,"abstract":"A mirage or fatamorgana is typically an upside-down “mirror” image of a scenery in deserts, over sun-heated roads, or above bodies of water. When the temperature gradient of air is large, as can happen near a surface, it results in a large gradient of the density and the refractive index as a function of height. Mirages appear when light travels through a medium with a gradient in its refractive index and, therefore, get bent towards the higher values, generating reflected images. A computer program that simulates mirages above water using the method of ray tracing has been developed and is presented here in detail for educational purposes. Results on the effect are shown by simulated images for various water-air temperature-difference cases with values ranging from 5 to 0 °C. Comparison of the simulations to a real-life scenario at Lake Balaton, Hungary has also been provided.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":" 33","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138618306","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}
F. Eggermont, Moniek A. M. Munneke, Vera Adriaens, Cornelia R. M. G. Fluit, Jan G. M. Kooloos, Esther Tanck
A daily quiz on Newtonian biomechanics has previously been shown to improve student self-confidence, enthusiasm, and test results in biomechanics courses. This study investigated whether such a quiz could also improve retention of knowledge over a longer term. Our study found that students who participated very actively in daily quizzes scored significantly better on a retention test compared to those who participated less actively or not at all. From these results, we can conclude that very active participation in a daily quiz resulted in a slight gain in the long-term retention of biomechanics knowledge.
{"title":"Does active participation in a daily quiz (TOPday) improve long-term retention in biomechanics?","authors":"F. Eggermont, Moniek A. M. Munneke, Vera Adriaens, Cornelia R. M. G. Fluit, Jan G. M. Kooloos, Esther Tanck","doi":"10.1119/5.0101494","DOIUrl":"https://doi.org/10.1119/5.0101494","url":null,"abstract":"A daily quiz on Newtonian biomechanics has previously been shown to improve student self-confidence, enthusiasm, and test results in biomechanics courses. This study investigated whether such a quiz could also improve retention of knowledge over a longer term. Our study found that students who participated very actively in daily quizzes scored significantly better on a retention test compared to those who participated less actively or not at all. From these results, we can conclude that very active participation in a daily quiz resulted in a slight gain in the long-term retention of biomechanics knowledge.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":" 19","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138611911","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 central forces follow a power law, Cameron Reed [Am. J. Phys. 90(5), 394–396 (2022)] showed that the resulting force on a test particle located outside an object with spherical symmetry is the same as if the source were located at the center of the sphere, if and only if the potential is either Newtonian, F ∝ r−2, or Hookean, F ∝ r. This Note shares another simple proof of this result and comments on the result in the light of the so-called transmutation law of central forces.
{"title":"Comment on the article “A note on Newton's shell-point equivalency theorem” [Am. J. Phys. 90, 394 (2022)]","authors":"Christian Carimalo","doi":"10.1119/5.0153897","DOIUrl":"https://doi.org/10.1119/5.0153897","url":null,"abstract":"When central forces follow a power law, Cameron Reed [Am. J. Phys. 90(5), 394–396 (2022)] showed that the resulting force on a test particle located outside an object with spherical symmetry is the same as if the source were located at the center of the sphere, if and only if the potential is either Newtonian, F ∝ r−2, or Hookean, F ∝ r. This Note shares another simple proof of this result and comments on the result in the light of the so-called transmutation law of central forces.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":" 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138618945","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：