摘要:

The effect of rolling friction on the motion of a ball rolling on a uniformly spinning horizontal turntable is evaluated by a first‐order perturbation approach, in which the unperturbed trajectories are the circular gyrations of the rolling ball in the absence of rolling friction. The analysis provides qualitative and quantitative understanding of the effect of rolling friction by itself and in combination with other ‘‘perturbations,’’ such as a tilt of the turntable.

ISSN:0002-9505    

DOI:10.1119/1.18333

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

Stroboscopic holographic interferometry has been developed at an advanced undergraduate level allowing real‐time imaging of standing sound waves in gas filled, closed tube resonators. A heterodyne Mach–Zehnder interferometer was first built by students to show the feasibility of interferometric detection of sound waves in a small cell. In the subsequent holographic study, the laser irradiance is modulated by an acousto‐optic cell at frequencies near that of the standing wave, and a video camera records the fringe motion due to sound pressure changes. Fractional fringe shifts are observed for an air filled cell, and multiple fringe shifts are imaged for the case of freon. Sound reflections from the cell ends are easily observed, with nonsinusoidal waveforms dominating at high intensities due to superposition of resonator harmonics.

ISSN:0002-9505    

DOI:10.1119/1.18358

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

The Schmidt decomposition theorem allows us to express an entangled wave function of two quantum systems in a particularly simple form. The purpose of this paper is to describe a geometrical method of performing the Schmidt decomposition that complements the usual algebraic method. This geometrical method is worked out in detail for a pair of spin‐1/2 particles and its utility is illustrated by giving a simple discussion of several aspects of Hardy’s version of Bell’s theorem.

ISSN:0002-9505    

DOI:10.1119/1.18334

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

A truncated cone, made of material of uniform resistivity, is given in many introductory physics texts as a nontrivial problem in the computation of resistance. The intended method and answer are incorrect and the problem cannot be solved by elementary means. In this paper, we (i) discuss the physics of current flow in a nonconstant cross‐section conductor, (ii) examine the flaws in the ‘‘standard’’ solution for the truncated cone, (iii) present a computed resistance found from a numerically generated solution for the electrical potential in the truncated cone, and (iv) consider whether any problem exists to which the standard solution applies.

ISSN:0002-9505    

DOI:10.1119/1.18335

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

We discuss the implications of Poincaré invariance within the context of Lagrangian field theories. It is shown that the correct implementation of this invariance leads in a straightforward manner to a conserved energy‐momentum tensor which is both symmetric and gauge invariant.

ISSN:0002-9505    

DOI:10.1119/1.18336

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

The conditions governing the existence of conformally dual scalar fields in both classical and quantum theories are derived. The transformation properties of the Hamilton–Jacobi and Klein–Gordon equations under conformal mappings are established and utilized as the basis for the analysis. The existence of self‐dual fields is demonstrated and examples are presented. Previously known results applicable to the Schrödinger equation and to Newtonian mechanics are shown to follow in the nonrelativistic limit as special cases of the present study.

ISSN:0002-9505    

DOI:10.1119/1.18337

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

Real lenses do not behave according to the laws of Gaussian optics to which the teaching of lens theory is often confined; Hamilton and Maxwell showed already that this would contradict Fermat’s principle. This paper shows that the rudiments of a correct treatment can be easily incorporated in an undergraduate course. This will help students to develop a clearer notion of what they can expect from the various lenses they will encounter in the laboratory. In addition, it will give them some insight into the value of variational principles.

ISSN:0002-9505    

DOI:10.1119/1.18359

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

In the present paper we propose a simple and easy method to determine the latent heat of vaporization of pure water, using the Clausius–Clapeyron equation. The vapor pressure of water was calculated from measurements of temperature and volume, assuming an ideal gas behavior for the vapor. The calculated heat of phase change is in a good agreement with the latent heat of vaporization, obtained from the empirical Antoine equation and from the literature.

ISSN:0002-9505    

DOI:10.1119/1.18338

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

The theoretical description of interacting fermions in one spatial dimension is simplified by the fact that the low‐energy excitations can be described in terms of bosonic degrees of freedom. This fermion–boson transmutation (FBT) which lies at the heart of the Luttinger liquid concept is presented in a way which does not require a knowledge of quantum field theoretical methods. As the basic facts can already be introduced for noninteracting fermions they are mainly discussed. As an application we use the FBT to present exact results for the low‐temperature thermodynamics and the occupation numbers in the microcanonical and the canonical ensemble. They are compared with the standard grand canonical results.

ISSN:0002-9505    

DOI:10.1119/1.18339

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

The Hamilton least action principle, a reformulated Maupertuis least action principle, and their reciprocals, are shown to be useful as direct methods for approximate solutions of dynamics problems. We discuss applications to trajectories of all types, i.e., periodic, quasiperiodic, chaotic, scattering, and arbitrary segments of arbitrary trajectories. The analogy with the standard technique used in quantum mechanics is very striking, especially in one of the reformulations (extremization of the mean energy), and in the calculational procedure (Rayleigh–Ritz type).

ISSN:0002-9505    

DOI:10.1119/1.18340

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP