European Journal of Physics最新文献

{"title":"A horizontally driven inverted pendulum","authors":"Rod Cross","doi":"10.1088/1361-6404/ad2cf5","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2cf5","url":null,"abstract":"An inverted pendulum can be stabilised by hand or by a high frequency sinusoidal vertical oscillation of the bottom end or by feedback control if a horizontal force is applied at the bottom end. The pendulum is unstable if a sinusoidal force is applied in a horizontal direction at the bottom end. It is shown in the present paper that an inverted pendulum can be stabilised if a low frequency horizontal force is applied at the bottom end to right the pendulum after it falls through a small angle. The technique requires a measurement of the fall angle but is not sensitive to the actual fall angle. The technique represents a simple example of feedback control and is more easily understood than vertical oscillation of the bottom end.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"131 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311905","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":"Trajectory of a golf ball on a sloping green","authors":"Rod Cross","doi":"10.1088/1361-6404/ad2c2d","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2c2d","url":null,"abstract":"Calculations are presented on the trajectory of a golf ball that rolls across the inclined surface of a golf green. The ball follows a curved path and comes to a stop at a point displaced at an angle to the initial launch direction. It is shown that the displaced angle is independent of the launch speed but depends on the launch angle and the ratio of the incline angle to the coefficient of rolling friction. The stopping distance is proportional to the launch speed squared. A simple experiment is described to check the calculations.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"14 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311721","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":"Derivation of the Schrödinger equation from QED","authors":"Spyros Efthimiades","doi":"10.1088/1361-6404/ad2c2f","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2c2f","url":null,"abstract":"The Schrödinger equation relates the emergent quantities of wavefunction and electric potential and is postulated as a principle of quantum physics or obtained heuristically. However, physical consistency requires that the Schrödinger equation is a low-energy dynamical condition we can derive from the foundations of quantum electrodynamics. Due to the small value of the electromagnetic coupling constant, we show that the electric potential accurately represents the contributions of intermediate low-energy photon exchanges. Then, from the total nonrelativistic energy relation, we see that the dominant term of the electron wavefunction is a superposition of plane waves that satisfies the Schrödinger equation. Our derivation shows that the Schrödinger equation is not an energy conservation relation because its middle term does not represent the electron kinetic energy as assumed. We analyze the physical content of the Schrödinger equation and verify our assessments by calculating and evaluating the physical quantities in the ground state of the hydrogen atom. Furthermore, we explain why nonrelativistic quantum dynamics differs from classical dynamics. Undergraduate students can follow the derivation because it involves fundamental physical concepts and mathematical expressions, and we explain every step.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"32 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311718","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":"The initial trajectory of a ball released from uniform circular motion","authors":"Milan Batista","doi":"10.1088/1361-6404/ad2c2e","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2c2e","url":null,"abstract":"This short paper presents a simple analytical model for the abrupt termination of circular motion, as discussed in the ‘<italic toggle=\"yes\">The Most Mind-Blowing Aspect of Circular Motion’</italic>. The model confirms that when a string is released, a ball at the far end of the string continues to move in a near-circular motion for a short time.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"68 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311841","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":"Maximal submergence in dense granular suspensions","authors":"Hollis Williams","doi":"10.1088/1361-6404/ad2aa2","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2aa2","url":null,"abstract":"How far can a person sink downwards in quicksand? Experience would seem to suggest that there is low risk of submerging completely, but it is not easy to demonstrate this because of the complex rheology of granular suspensions. We study several mathematical models for the sinking of a vertical cylinder downwards into quicksand, finding that an approach with a buoyancy equation modified by drag force gives an unphysical answer. We instead argue that our proposed conclusion is supported by considering the dynamics of vibration-induced compactification of liquid-saturated granular suspensions. We compare quicksand with other non-Newtonian fluids, emphasising that in this case the same model does not apply and that the risk of drowning could be much more significant. We finish by suggesting some relevant experiments that can be performed in a classroom setting.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"23 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140316982","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":"Two-point resistances in symmetric bracelet resistor networks: accurate estimates and exact expressions","authors":"Frédéric Perrier, Frédéric Girault","doi":"10.1088/1361-6404/ad242a","DOIUrl":"https://doi.org/10.1088/1361-6404/ad242a","url":null,"abstract":"Resistor networks, used to model new types of natural or artificial matter, also provide generic examples for practising the methods of physics for obtaining estimates, revealing the main properties of a system and deriving exact expressions. Symmetric bracelet resistor networks are constructed by connecting <italic toggle=\"yes\">n</italic> identical resistors in a circle, and then connecting two such circles by another set of <italic toggle=\"yes\">n</italic> identical resistors. First, using van Steenwijk’s method, we establish that the equivalent resistance or two-point resistance (TPR) between any two nodes is derived when the layer-to-layer resistance <italic toggle=\"yes\">R</italic>\u0000_{0<italic toggle=\"yes\">n</italic>\u0000} is known. We then determine <italic toggle=\"yes\">R</italic>\u0000_{0<italic toggle=\"yes\">n</italic>\u0000} by an elementary recurrence relation which converges rapidly to its large <italic toggle=\"yes\">n</italic> limit. Using this reference value of <italic toggle=\"yes\">R</italic>\u0000_{0<italic toggle=\"yes\">n</italic>\u0000}, accurate estimates of other TPRs follow for all values of <italic toggle=\"yes\">n</italic>, characterised by a leading 1/<italic toggle=\"yes\">n</italic> variation. In addition, exact explicit expressions of the TPRs can be calculated for any value of <italic toggle=\"yes\">n</italic>. These networks, prototypes of three-dimensional networks considered in research, can be used to illustrate the diversity of the physical approach, the power of elementary methods, and to learn to be comfortable with approximations. Easy to make and use for experimental tests, they can support hands-on activities and conceptual changes.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"43 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311842","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":"Student understanding of the Bloch sphere","authors":"Peter Hu, Yangqiuting Li, Roger S K Mong, Chandralekha Singh","doi":"10.1088/1361-6404/ad2393","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2393","url":null,"abstract":"Quantum information science is a rapidly growing interdisciplinary field that is attracting the attention of academics and industry experts alike. It requires talent from a wide variety of traditional fields, including physics, engineering, chemistry, and computer science, to name a few. To prepare students for such opportunities, it is important to give them a strong foundation in the basics of quantum information science, in which quantum computing plays a central role. In this study, we discuss the development, validation, and evaluation of a tutorial on the Bloch sphere, a useful visual tool for developing intuition about single quantum bits (qubits), which are the basic building block of any quantum computer. Students’ understanding was evaluated after they received traditional lecture-based instruction on the requisite topics, and again after engaging with the tutorial. We observe, analyze, and discuss their improvement in performance on concepts covered in the tutorial.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"463 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140007988","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":"Wilks’s theorem, global fits, and neutrino oscillations","authors":"J M Hardin","doi":"10.1088/1361-6404/ad261d","DOIUrl":"https://doi.org/10.1088/1361-6404/ad261d","url":null,"abstract":"Tests of models for new physics appearing in neutrino experiments often involve global fits to a quantum mechanical effect called neutrino oscillations. This paper introduces students to methods commonly used in these global fits starting from an understanding of more conventional fitting methods using log-likelihood and <italic toggle=\"yes\">χ</italic>\u0000² minimization. Specifically, we discuss how the Δ<italic toggle=\"yes\">χ</italic>\u0000², which compares the <italic toggle=\"yes\">χ</italic>\u0000² of the fit with the new physics to the <italic toggle=\"yes\">χ</italic>\u0000² of the Standard Model prediction, is often interpreted using Wilks’s theorem. This paper uses toy models to explore the properties of Δ<italic toggle=\"yes\">χ</italic>\u0000² as a test statistic for oscillating functions. The statistics of such models are shown to deviate from Wilks’s theorem. Tests for new physics also often examine data subsets for ‘tension’ called the ‘parameter goodness of fit’. In this paper, we explain this approach and use toy models to examine the validity of the probabilities from this test also. Although we have chosen a specific scenario—neutrino oscillations—to illustrate important points, students should keep in mind that these points are widely applicable when fitting multiple data sets to complex functions.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"4 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140008094","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":"A research-informed graphical tool to visually approach Gauss’ and Stokes’ theorems in vector calculus","authors":"L Hahn, S A Blaue, P Klein","doi":"10.1088/1361-6404/ad2390","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2390","url":null,"abstract":"Gauss’ and Stokes’ theorems are fundamental results in vector calculus and important tools in physics and engineering. When students are asked to describe the meaning of Gauss’ divergence theorem, they often use statements like this: ‘The sum of all sources of a vector field in a region gives the net flux out of the region’. In order to raise this description to a mathematically sound level of understanding, we present an educational approach based on the visual interpretation of the vector differential operators, i.e. divergence and curl. As a starting point, we use simple vector field diagrams for a qualitative approach to connect both sides of the integral theorems, and present an interactive graphical tool to support this connection. The tool allows to visualise two-dimensional vector fields, to specify vector decomposition, to evaluate divergence and curl point wise, and to draw rectangles to determine surface and line integrals. From a meta-perspective, we situate this educational approach into learning with (multiple) representations. Based on prior research, the graphical tool addresses various learning difficulties of vector fields that are connected to divergence and curl. The tool was incorporated into the weekly lecture-based recitations of Physics II (electromagnetism) in 2022 and 2023, and we assessed various educational outcome measures. The students overall reported the tool to be intuitive and user-friendly (level of agreement 76%, <inline-formula>\u0000<tex-math>\u0000<?CDATA $N=125$?>\u0000</tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>125</mml:mn></mml:math>\u0000<inline-graphic xlink:href=\"ejpad2390ieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>), considered it helpful for understanding and recommended its use for introductory physics courses (level of agreement 65%, <inline-formula>\u0000<tex-math>\u0000<?CDATA $N=65$?>\u0000</tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>65</mml:mn></mml:math>\u0000<inline-graphic xlink:href=\"ejpad2390ieqn2.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>).","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"79 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140007860","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":"How can the global temperature increase be explained to students?","authors":"R De Luca, V Lamberti","doi":"10.1088/1361-6404/ad2429","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2429","url":null,"abstract":"The temperature increase of the system Earth-atmosphere can be described by means of a parallelism between the leaking bucket’s dynamics and the energy balance between the incoming radiant power from the Sun and the outcoming net heat flow rate to outer space. The analogy is interesting from a didactical point of view, since the stable fixed point of the temperature can be related to the height of the water inside the leaking bucket in the presence of a fixed fluid flow rate. Qualitative predictions of global temperature increase for increasing concentration of greenhouse gases in the atmosphere can be obtained by reducing the outcoming net heat flow rate, using buckets with smaller orifices.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"24 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140011480","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}