Showing papers in "American Journal of Physics in 2009"
TL;DR: The Legendre transform is a powerful tool in theoretical physics and plays an important role in classical mechanics, statistical mechanics, and thermodynamics as mentioned in this paper. But the motivation and elegance of the method are often missing, unlike the treatments frequently enjoyed by Fourier transforms.
Abstract: The Legendre transform is a powerful tool in theoretical physics and plays an important role in classical mechanics, statistical mechanics, and thermodynamics. In typical undergraduate and graduate courses the motivation and elegance of the method are often missing, unlike the treatments frequently enjoyed by Fourier transforms. We review and modify the presentation of Legendre transforms in a way that explicates the formal mathematics, resulting in manifestly symmetric equations, thereby clarifying the structure of the transform. We then discuss examples to motivate the transform as a way of choosing independent variables that are more easily controlled. We demonstrate how the Legendre transform arises naturally from statistical mechanics and show how the use of dimensionless thermodynamic potentials leads to more natural and symmetric relations.
153 citations
TL;DR: The University of Maryland Physics Education Research Group has done a five-year project to rethink, observe, and reform introductory algebra-based (college) physics, which primarily serves life science majors as mentioned in this paper.
Abstract: The University of Maryland Physics Education Research Group has done a five-year project to rethink, observe, and reform introductory algebra-based (college) physics, which primarily serves life-science majors. We refocused the class on helping the students learn to think scientifically—to build coherence, think in terms of mechanisms, and to follow the implications of assumptions. We designed the course to tap into students’ productive conceptual and epistemological resources, based on a theoretical framework from research on learning. The reformed class retains its traditional structure in terms of time and instructional personnel, but we modified existing best-practices curricular materials. We provided class-controlled spaces for student collaboration, which allowed us to observe and record students learning directly. We also scanned all written homework and examinations and administered pre-post conceptual and epistemological surveys. The reformed class enhanced the strong gains on pre-post conceptual tests produced by the best-practices materials while obtaining unprecedented pre-post gains on epistemological surveys instead of the traditional losses.
135 citations
TL;DR: The authors compared the efficacy of multimedia learning modules with traditional textbooks for the first few topics of a calculus-based introductory electricity and magnetism course and found that the students receiving the multimedia learning module performed significantly better on both tests than the students experiencing the text-based presentations.
Abstract: We compared the efficacy of multimedia learning modules with traditional textbooks for the first few topics of a calculus-based introductory electricity and magnetism course. Students were randomly assigned to three groups. One group received the multimedia learning module presentations, and the other two received the presentations via written text. All students were then tested on their learning immediately following the presentations as well as 2weeks later. The students receiving the multimedia learning modules performed significantly better on both tests than the students experiencing the text-based presentations.
119 citations
TL;DR: In this paper, the authors describe the use of inexpensive hobbyist-grade accelerometers and spreadsheet software to explore inertial navigation via numerical integration of the measured acceleration, which is not so simple.
Abstract: In most introductory physics courses, the first equations encountered are the kinematic equations. Though the emphasis at this level tends to be on cases of constant acceleration, many real-world examples of motion are not so simple. We describe the use of inexpensive hobbyist-grade accelerometers and spreadsheet software to explore inertial navigation via numerical integration of the measured acceleration.
108 citations
TL;DR: The authors found that before instruction, no more than 6% of all students could give completely correct responses to relevant questions posed in both general and concrete contexts, and nearly two-thirds of the students showed clear evidence of conservation-type reasoning regarding entropy.
Abstract: We report on students’ thinking regarding entropy in an introductory calculus-based physics course. We analyzed students’ responses to a variety of questions on entropy changes of an arbitrarily defined system and its surroundings. In four offerings of the same course we found that before instruction, no more than 6% of all students could give completely correct responses to relevant questions posed in both general and concrete contexts. Nearly two-thirds of the students showed clear evidence of conservation-type reasoning regarding entropy. These outcomes were little changed even after instruction. Targeted instruction that guided students to recognize that entropy is not a conserved quantity appears to yield improved performance on qualitative questions related to this concept.
100 citations
TL;DR: This paper developed a curriculum on the photoelectric effect including an interactive computer simulation, interactive lectures with peer instruction, and conceptual and mathematical homework problems, which led to better student mastery of the first goal than either traditional instruction or previous reformed instruction.
Abstract: We have developed a curriculum on the photoelectric effect including an interactive computer simulation, interactive lectures with peer instruction, and conceptual and mathematical homework problems. Our curriculum addresses established student difficulties and is designed so that students will be able to (1) correctly predict the results of experiments on the photoelectric effect and (2) describe how these results lead to the photon model of light. Our instruction leads to better student mastery of the first goal than either traditional instruction or previous reformed instruction, with approximately 85% of students correctly predicting the results of changes to the experimental conditions. Most students are able to correctly state the observations made in the photoelectric effect experiment and the inferences that can be made from these observations, but are less successful drawing a clear logical connection between the observations and the inferences.
85 citations
TL;DR: In this article, the authors apply a few simple first-principles equations to identify the parameter space in which controlled fusion might be possible and introduce magnetized target fusion as one possible way of accessing a density regime that is intermediate between the two extremes of inertial confinement fusion and magnetic confinement fusion, and is potentially lower cost than either of these two.
Abstract: We apply a few simple first-principles equations to identify the parameter space in which controlled fusion might be possible. Fundamental physical parameters such as minimum size, energy, and power as well as cost are estimated. We explain why the fusion fuel density in inertial confinement fusion is more than 1011 times larger than the fuel density in magnetic confinement fusion. We introduce magnetized target fusion as one possible way of accessing a density regime that is intermediate between the two extremes of inertial confinement fusion and magnetic confinement fusion and is potentially lower cost than either of these two.
84 citations
TL;DR: In this paper, a soccer ball was launched from a machine while two cameras recorded portions of its trajectory, and the authors obtained two values of the lift coefficient for spin parameters that had not been obtained previously.
Abstract: We performed experiments in which a soccer ball was launched from a machine while two cameras recorded portions of its trajectory. Drag coefficients were obtained from range measurements for no-spin trajectories, for which the drag coefficient does not vary appreciably during the ball’s flight. Lift coefficients were obtained from the trajectories immediately following the ball’s launch, in which Reynolds number and spin parameter do not vary much. We obtain two values of the lift coefficient for spin parameters that had not been obtained previously. Our codes for analyzing the trajectories are freely available to educators and students.
75 citations
TL;DR: In this paper, the authors show that an observed frequency shift in any spacetime can be interpreted either as a kinematic (Doppler) shift or a gravitational shift by imagining a suitable family of observers along the photon's path.
Abstract: A common belief about big-bang cosmology is that the cosmological redshift cannot be properly viewed as a Doppler shift (that is, as evidence for a recession velocity) but must be viewed in terms of the stretching of space. We argue that, contrary to this view, the most natural interpretation of the redshift is as a Doppler shift, or rather as the accumulation of many infinitesimal Doppler shifts. The stretching-of-space interpretation obscures a central idea of relativity, namely that it is always valid to choose a coordinate system that is locally Minkowskian. We show that an observed frequency shift in any spacetime can be interpreted either as a kinematic (Doppler) shift or a gravitational shift by imagining a suitable family of observers along the photon’s path. In the context of the expanding universe, the kinematic interpretation corresponds to a family of comoving observers and hence is more natural.
74 citations
TL;DR: In this paper, the authors present a simple theoretical analysis for Doppler-broadened spectroscopy of alkali metals on the D2 line that emphasizes the importance of the transient nature of the population dynamics, and the crucial role of the distribution of the times of flight of atoms through the probe beam.
Abstract: Laser spectroscopy experiments are often conducted with a probe that does not significantly alter the medium’s properties. For a two-level atom a clear measure of the strength of a probe beam in terms of the saturation intensity is known. We show that for a multilevel atom the situation is very different, and the effects of optical pumping are crucial to understanding the opacity of the medium. We present a simple theoretical analysis for Doppler-broadened spectroscopy of alkali metals on the D2 line that emphasizes the importance of the transient nature of the population dynamics, and the crucial role of the distribution of the times of flight of atoms through the probe beam. Experimental results are obtained with room temperature rubidium vapor probed by an extended-cavity diode laser and confirm our theoretical prediction.
72 citations
TL;DR: In this article, it was shown that even static fields can carry momentum, and this would appear to contradict a general theorem that the total momentum of a closed system is zero if its center of energy is at rest.
Abstract: Electromagnetic fields carry energy, momentum, and angular momentum. The momentum density, ϵ0(E×B), accounts (among other things) for the pressure of light. But even static fields can carry momentum, and this would appear to contradict a general theorem that the total momentum of a closed system is zero if its center of energy is at rest. In such cases, there must be some other (nonelectromagnetic) momenta that cancel the field momentum. What is the nature of this “hidden momentum” and what happens to it when the electromagnetic fields are turned off?
TL;DR: In this paper, a computer generated holography technique is employed to generate a custom defined wavefront, realized in the + 1 diffraction order when a collimated laser beam is diffracted by a binary transmission hologram.
Abstract: This article describes a graduate level optics laboratory experiment on the manipulation of the wavefront of a laser beam using a spatial light modulator. A computer generated holography technique is employed to generate a custom defined wavefront, realized in the +1 diffraction order when a collimated laser beam is diffracted by a binary transmission hologram. The hologram is written on a liquid crystal spatial light modulator and can be updated at a video rate using a personal computer interface.
TL;DR: In this paper, a simple analysis of the dynamics of a charged particle beam in a solenoid and emphasize an intuitive understanding of some of the interesting features. But it is generally understood that a uniform magnetic field can only guide charged particles.
Abstract: The focusing of a charged particle beam in a solenoid is typically explained by invoking the concept of a Larmour frame and using Busch’s theorem. Often, there is some confusion about how a uniform magnetic field of a long solenoid focuses the electron beam because it is generally understood that a uniform magnetic field can only guide charged particles. We perform a simple analysis of the dynamics of a charged particle beam in a solenoid and emphasize an intuitive understanding of some of the interesting features.
TL;DR: The authors suggest that the origin of the Mpemba effect is due to freezing-point depression by solutes, either gaseous or solid, whose solubility decreases with increasing temperature so that they are removed when water is heated.
Abstract: I suggest that the origin of the Mpemba effect (the freezing of hot water before cold) is due to freezing-point depression by solutes, either gaseous or solid, whose solubility decreases with increasing temperature so that they are removed when water is heated. The solutes are concentrated ahead of the freezing front by zone refining in water that has not been heated, reducing the temperature of the freezing front, and thereby reducing the temperature gradient and heat flux, slowing the progress of the freezing front. I present a simple calculation of this effect, and suggest experiments to test this hypothesis.
TL;DR: In this article, the authors describe how graduate students categorize introductory mechanics problems based on the similarity of their solutions and compare their categorizations with the categorizations by introductory physics students and physics faculty who categorized the same problems.
Abstract: We describe how graduate students categorize introductory mechanics problems based on the similarity of their solutions. Graduate students were asked at the end of a teaching assistant training class to categorize problems from their own perspective and from the perspective of typical introductory physics students whom they were teaching. We compare their categorizations with the categorizations by introductory physics students and physics faculty who categorized the same problems. The utility of categorization as a tool for teaching assistant training and faculty development workshops is discussed.
TL;DR: In this article, the authors present the results of a national study on the teaching and learning of astronomy as taught in general education, non-science-major, introductory astronomy courses.
Abstract: We present the results of a national study on the teaching and learning of astronomy as taught in general education, non-science-major, introductory astronomy courses. Nearly 4000 students enrolled in 69 sections of courses taught by 36 different instructors at 31 institutions completed (pre- and post-instruction) the Light and Spectroscopy Concept Inventory (LSCI) from Fall 2006 to Fall 2007. The classes varied in size and were from all types of institutions, including 2- and 4-year colleges and universities. Normalized gain scores for each class were calculated. Pre-instruction LSCI scores were clustered around ∼25%, independent of class size and institution type, and normalized gain scores varied from about −0.07 to 0.50. To estimate the fraction of classroom time spent on learner-centered, active-engagement instruction we developed and administered an Interactivity Assessment Instrument (IAI). Our results suggest that the differences in gains were due to instruction in the classroom, not the type of class or institution. We also found that higher interactivity classes had the highest gains, confirming that interactive learning strategies are capable of increasing student conceptual understanding. However, the wide range of gain scores seen for both lower and higher interactivity classes suggests that the use of interactive learning strategies is not sufficient by itself to achieve high student gain.
TL;DR: The concept of relativistic mass, which increases with velocity, is not compatible with the standard language of relativity theory and impedes the understanding and learning of the theory by beginners.
Abstract: The concept of relativistic mass, which increases with velocity, is not compatible with the standard language of relativity theory and impedes the understanding and learning of the theory by beginners. The same difficulty occurs with the term rest mass. To get rid of relativistic mass and rest mass it is appropriate to replace the equation E=mc2 by the true Einstein’s equation E0=mc2, where E0 is the rest energy and m is the mass.
TL;DR: In this article, a simple electromagnetic model is developed for the structural scattering from Morpho butterfly scales, and the blue color and iridescence normally seen for these butterflies are predicted by this model.
Abstract: Structural color is caused by wavelength-selective scattering of light by microscopic features, such as those on the scales of some insects. The brilliant blue displayed by some male Morpho butterflies is a classic example of this phenomenon. In this paper, experiments used to distinguish structural color from color due to pigmentation are reviewed. A simple electromagnetic model is developed for the structural scattering from Morpho butterfly scales, and the blue color and iridescence normally seen for these butterflies are predicted by this model. The analysis is based on topics usually discussed in courses on electromagnetism and optics and can be used as an example to supplement classroom discussions of these topics.
TL;DR: In this article, the authors present a design of a coincidence counting module that replaces the traditional method based on time-to-amplitude conversion and pulse-height analysis for quantum optics experiments at the undergraduate level, but cost has created an entry barrier for many schools.
Abstract: Coincidence counting is a necessary ingredient for quantum optics experiments at the undergraduate level, but cost has created an entry barrier for many schools. We present a design of a coincidence-counting module that replaces the traditional method based on time-to-amplitude conversion and pulse-height analysis. Our module accepts inputs from up to four detectors, has a coincidence-time window of less than 10 ns, and has a throughput of more than triple that of the traditional method. The cost of our coincidence-counting module is less than 5% of the cost of the traditional method. © 2009 American Association of Physics Teachers.
TL;DR: The authors report results from an investigation of student ability to apply the concepts of work and energy to situations in which the internal structure of a system cannot be ignored, i.e., the system is not treated as a particle.
Abstract: We report results from an investigation of student ability to apply the concepts of work and energy to situations in which the internal structure of a system cannot be ignored, that is, the system cannot be treated as a particle. Students in introductory calculus-based physics courses were asked written and online questions after relevant instruction by lectures, textbook, and laboratory. Several difficulties were identified. Some related to student ability to calculate the work done on a system. Failure to associate work with the change in energy of a system was also widespread. The results have implications for instruction that aims for a rigorous treatment of energy concepts that is consistent with the first law of thermodynamics. The findings are guiding the development of two tutorials to supplement instruction.
TL;DR: In this article, the authors report on a three-year longitudinal study at the Colorado School of Mines using innovations in course content, textbook, teaching methods, and assessment tools, and find that graduate students respond well to research-based techniques.
Abstract: We address four main areas in which graduate quantum mechanics education can be improved: course content, textbook, teaching methods, and assessment tools. We report on a three year longitudinal study at the Colorado School of Mines using innovations in all these areas. In particular, we have modified the content of the course to reflect progress in the field of quantum mechanics over the last 50years, used textbooks that include such content, incorporated a variety of teaching techniques based on physics education research, and used a variety of assessment tools to study the effectiveness of these reforms. We present a new assessment tool, the Graduate Quantum Mechanics Conceptual Survey, and further testing of a previously developed assessment tool, the Quantum Mechanics Conceptual Survey. We find that graduate students respond well to research-based techniques that have been tested mainly in introductory courses, and that they learn much of the new content introduced in each version of the course. We a...
TL;DR: In this article, a new instructor (Famiano) co-taught an introductory calculus-based physics course with an instructor experienced in PER-based reforms (Henderson), the pair taught within the course structure typically used by Henderson and met regularly to discuss instructional decisions.
Abstract: Physics Education Research (PER) has made significant progress in developing effective instructional strategies, but disseminating the background knowledge and strategies to other faculty has proven difficult. Co-teaching is a promising and cost-effective alternative to traditional professional development which may be applicable in particular situations. We discuss the theoretical background of co-teaching and describe our initial experience with it. A new instructor (Famiano) co-taught an introductory calculus-based physics course with an instructor experienced in PER-based reforms (Henderson). The pair taught within the course structure typically used by Henderson and met regularly to discuss instructional decisions. An outsider (Beach) conducted separate interviews with each instructor and observed several class sessions. Classroom observations show an immediate use of PER-based instructional practices by the new instructor. Interviews show a significant shift in the new instructor’s beliefs about teaching and intentions of future use of PER-based instructional approaches.
TL;DR: In this article, the authors introduce symmetry and chaos in the context of planar lattices and icon mappings, and introduce the concept of symmetry icons and symmetry fractals as well.
Abstract: 1. Introduction to symmetry and chaos 2. Planar symmetries 3. Patterns everywhere 4. Chaos and symmetry creation 5. Symmetric icons 6. Quilts 7. Symmetric fractals Appendix A. Picture parameters Appendix B. Icon mappings Appendix C. Planar lattices Bibliography Index.
TL;DR: In this paper, Euclidean three-space and Minkowski four-space identities and uniqueness theorems are reviewed and extended, and a time-dependent extension of the Helmholtz identity is also derived.
Abstract: Euclidean three-space and Minkowski four-space identities and uniqueness theorems are reviewed and extended. A Helmholtz identity is used to prove two three-vector uniqueness theorems in Euclidean three-space. The first theorem specifies the divergence and curl of the vector, and the second is a Helmholtz type theorem that sums the irrotational and solenoidal parts of the vector. The second theorem is shown to be valid for three-vector fields that are time dependent. A time-dependent extension of the Helmholtz identity is also derived. However, only the three-vector and scalar components of a Minkowski space four-vector identity are shown to yield two identities that lead to a uniqueness theorem of the first or source type. Also, the field equations of this latter theorem appear to be sufficiently general such that the field equations naturally divide into two distinct classes, a four-solenoidal electromagnetic type class in a relativistic transverse gauge and a four-irrotational class in a relativistic longitudinal gauge.
TL;DR: In this paper, two sections of an introductory astronomy class were given different grading incentives for clicker participation for two consecutive semesters, in the high stakes classroom points were awarded only for correct answers, in contrast to the low stakes classroom in which points were not awarded simply for participating.
Abstract: Two sections of an introductory astronomy class were given different grading incentives for clicker participation for two consecutive semesters. In the high stakes classroom points were awarded only for correct answers, in contrast to the low stakes classroom in which points were awarded simply for participating. Self-formed groups of four students each were recorded in both sections several times during the spring 2007 semester and their conversations were transcribed and categorized into nine topics to analyze the variations between the sections. Performance on clicker questions and tendency to block vote were correlated with class grades and gains for the pre- and post-test scores on the Astronomy Diagnostic Test.
TL;DR: In this article, the magnetic pickup of an electric guitar uses electromagnetic induction to convert the motion of a ferromagnetic guitar string to an electrical signal, and a model that accurately predicts the output of a magnetic guitar pickup is presented.
Abstract: The magnetic pickup of an electric guitar uses electromagnetic induction to convert the motion of a ferromagnetic guitar string to an electrical signal. Although the magnetic pickup is often cited as an everyday application of Faraday’s law, few sources mention the distortion that the pickup generates when converting the motion of a string to an electric signal, and fewer analyze and explain this distortion. We model the magnet and ferromagnetic wire as surfaces with magnetic charge and construct an intuitive model that accurately predicts the output of a magnetic guitar pickup. This model can be understood by undergraduate students and provides an excellent learning tool due to its straightforward mathematics and intuitive algorithm. Experiments show that it predicts the change in a magnetic field due to the presence of a ferromagnetic wire with a high degree of accuracy.
TL;DR: In this article, an apparatus for generating rotating sound waves in free space by superimposing two orthogonal standing modes with a quarter wave phase lag is described, and the creation of a standing wave from the superposition of two counter-rotating waves is also possible with the same apparatus.
Abstract: We describe an apparatus for generating rotating sound waves in free space by superimposing two orthogonal standing modes with a quarter wave phase lag. The creation of a standing wave from the superposition of two counter-rotating waves is also possible with the same apparatus. The experiment permits direct measurement of both the amplitude and phase structure of the sound waves. A demonstration of angular momentum transfer from rotating acoustic waves to matter in free field is also described.
TL;DR: In this paper, a model of AC-driven Brownian motors consisting of a classical particle which is placed in a potential that is periodic in space and time and which is coupled to a heat bath is studied by a time-dependent Fokker-Planck equation.
Abstract: We consider a model of AC-driven Brownian motors consisting of a classical particle which is placed in a potential that is periodic in space and time and which is coupled to a heat bath. The effects of fluctuations and dissipation are studied by a time-dependent Fokker-Planck equation. The approach lets us map the original stochastic problem onto a system of ordinary linear algebraic equations. The solution of the equations provides complete information about ratchet transport, avoiding the disadvantages of direct stochastic calculations such as long transients and large statistical fluctuations. The Fokker-Planck approach to dynamical ratchets opens the possibility for further generalizations.
TL;DR: In this paper, ladder-type electromagnetically induced transparency (EIT) in rubidium gas was investigated and the theoretical absorption profile of a weak probe laser beam at 780.2nm (5S1∕2→5P3∕ 2 ) was modeled in the presence of a strong coupling laser beam (776.0nm) and the absorption transparency window was characterized.
Abstract: We investigate ladder-type electromagnetically induced transparency (EIT) in rubidium gas. The theoretical absorption profile of a weak probe laser beam at 780.2nm (5S1∕2→5P3∕2) is modeled in the presence of a strong coupling laser beam at 776.0nm (5P3∕2→5D5∕2) and the absorption transparency window is characterized. We use two grating-feedback diode lasers and observe EIT experimentally in rubidium and compare the results to the theory. This experiment brings quantum optics into the advanced undergraduate laboratory and utilizes equipment and expertise commonly available in laboratories equipped to perform diode-laser-based absorption spectroscopy of rubidium.
TL;DR: In this paper, the authors introduce some of the same one-dimensional examples as matrix diagonalization problems, with a basis that consists of the infinite set of square well eigenfunctions.
Abstract: Courses on undergraduate quantum mechanics usually focus on solutions of the Schrodinger equation for several simple one-dimensional examples. When the notion of a Hilbert space is introduced, only academic examples are used, such as the matrix representation of Dirac’s raising and lowering operators or the angular momentum operators. We introduce some of the same one-dimensional examples as matrix diagonalization problems, with a basis that consists of the infinite set of square well eigenfunctions. Undergraduate students are well equipped to handle such problems in familiar contexts. We pay special attention to the one-dimensional harmonic oscillator. This paper should equip students to obtain the low lying bound states of any one-dimensional short range potential.