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Optimal trajectories for symmetric turns
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| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 91 (No. 6) |
| Halaman | : | 425-431 |
| Abstrak | : | 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. |
Sarah Frances Whiting, pioneer of laboratory instruction in astronomy
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 91 (No. 6) |
| Halaman | : | 417-424 |
| Abstrak | : | 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. |
The game of life as a species model
| Pengarang | : | David A. Faux,Wong, Jing Syuan |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 91 (No. 7) |
| Halaman | : | 561-568 |
| Abstrak | : | Conway's classic game of life is a two-dimensional cellular automaton in which each cell is alive or dead and evolves according to simple rules that depend solely on the number of live cells in its immediate neighborhood. The emergence of complex multi-cellular objects provides a fascinating vehicle for exploration. A variant of the classic game of life is presented, the generalized semi-classical game of life, in which each cell contains a qubit that evolves by repeated application of birth, death, and survival operators. Species are characterized by just two parameters: a preferred neighborhood liveness representing the tendency to herd and a resilience parameter representing species' vulnerability to environmental changes. This generalized model provides the opportunity to model the fortune of species and to compare to available data. The model is shown to mimic environmental catastrophes and is illustrated by the model's prediction of a return to the pre-hunting level of the global whale population by 2140. A student-designed predator–prey model is shown to qualitatively describe the fate of strongly- and weakly coupled predator–prey systems (snowshoe hare/lynx and rabbit/fox, respectively) and sudden and slow predatory impact (dodo and diprotodon, respectively). |
Simple realization of the polytropic process with a finite-sized reservoir
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 91 (No. 7) |
| Halaman | : | 555-558 |
| Abstrak | : | In most thermodynamics textbooks, polytropic processes are introduced by defining the process equation rather than explaining their physical origin. In this paper, we propose a simple model to realize a polytropic process for an ideal gas. The ideal gas is compressed or expanded quasi-statically while in thermal contact with a finite reservoir with constant heat capacity, and the entire system is thermally isolated from the outside environment. We propose an experimental implementation of our model with realistic parameters. |
Wigner rotation and Euler angle parametrization Open Access
| Pengarang | : | Leehwa Yeh |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 91 (No. 7) |
| Halaman | : | 547-554 |
| Abstrak | : | Analogous to the famous Euler angle parametrization in three-dimensional Euclidean space, a reflection-free Lorentz transformation in (2 + 1)-dimensional Minkowski space can be decomposed into three simple parts. Applying this decomposition to the Wigner rotation problem, we are able to show that the related mathematics becomes much simpler and the physical meanings more comprehensible and enlightening. |
Analytical calculation of plasmonic resonances in metal nanoparticles: A simple guide
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 91 (No. 7) |
| Halaman | : | 538-546 |
| Abstrak | : | Localized surface plasmons (LSPs) in metal particles are used in medical, chemical, physical, and biological sensing applications. In this paper, we revisit the classical description of LSPs. We use the Drude model and the Quasi-Static approximation to describe the plasmon resonances in terms of the material and the size of the particles embedded in a dielectric host. We then incorporate the Clausius–Mossotti relation to include shape effects in the classical description. Finally, we incorporate surface damping and retardation effects to arrive at a unified, classical description providing an intuitive and realistic model of plasmonic resonances in metal particles. |
Oblique collision of a soft rubber disk with a rigid surface
| Pengarang | : | Nasution, M. Teguh Ariffaiz,Daneswara, Muhammad Rifqi |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 91 (No. 7) |
| Halaman | : | 532-537 |
| Abstrak | : | An oblique collision of an object with a rigid surface involves an initial sliding phase that persists throughout the collision at glancing angles of incidence but which involves a subsequent grip phase at higher angles of incidence. The grip phase itself terminates towards the end of the collision if the contact region starts to slide backwards. Experimental evidence of the three separate stages of the collision process is presented using a high speed video camera to film the impact of a rubber disk on a rigid horizontal surface. A simplified model of the process is presented, providing analytical solutions that are at least qualitatively consistent with the experimental observations. |
Analysis of ill-conditioned cases of a mass moving on a sphere with friction
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 91 (No. 7) |
| Halaman | : | 527-531 |
| Abstrak | : | Previous work treated the problem of a mass sliding over a rough spherical surface in broad generality, providing both analytic and numerical solutions. This paper examines special cases of 2D motion along a surface meridian when the initial speed is precisely chosen so that the sliding mass nearly stops before speeding up and subsequently leaving the surface. Carrying the solution for these critical cases into the time domain via both an analytical method and numerical integration adds richness that might otherwise be missed. The numerical method raises practical mathematical issues that must be handled carefully to obtain accurate results. Although conceptually simple, this classical mechanics problem is an excellent vehicle for students to gain proficiency with mathematical analysis tools and further their appreciation for how applied mathematics can bring new insight into situations where intuition may fall short. |
Using rotation matrices to calculate the locations of sunrise and sunset, the hours of daylight, observed path of the Sun, and its elevation angle for any latitude
| Pengarang | : | Margaret Stautberg Greenwood |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 91 (No. 7) |
| Halaman | : | 519-526 |
| Abstrak | : | During the course of one year, I photographed 95 sunrises along the east bank of the Columbia River from my home on the west bank in Richland, WA (46.3° N latitude). I then calculated the seasonal phenomena listed in the title with the intention of explaining the variation of the photographed sunrises. The calculations use a simplified model of the Sun-Earth system and employ rotation matrices to predict the path of the Sun, as observed at any location in the northern hemisphere, throughout the year. These predictions are in good agreement with those listed by NOAA and also with the photographic data. The analysis presented here provides a novel way to calculate and understand the seasonal variations of visible sunlight. |
Memories of a mid-20th century electrical measurements laboratory and its instrumentation
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 91 (No. 7) |
| Halaman | : | 510-518 |
| Abstrak | : | There was a time when undergraduate physics majors took a junior-level course in Electricity and Magnetism, accompanied by a semester of laboratory work, learning to make precision electrical measurements. This laboratory experience is long gone, replaced by coursework in digital and analog electronics. Even the latter has been downplayed in favor of a course in the use of digital computers to solve problems in physics. In this article, I will discuss the course that I took as an undergraduate at Amherst College in the late 1950s and then taught as a young faculty member at Kenyon College in the late sixties. I was a participant in the demise of the E&M laboratory and the rise of the ensuing vacuum tube and digital electronics course. I will concentrate on the precision apparatus, which is presently living out its life in the dusty back shelves of apparatus closets. This may help new faculty members to answer the perennial question: It is attractive, but what is it and how was it used? |