ISSN:0002-9505    

DOI:10.1119/1.17566

出版商:American Association of Physics Teachers    

年代:1994

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.17568

出版商:American Association of Physics Teachers    

年代:1994

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.17569

出版商:American Association of Physics Teachers    

年代:1994

数据来源: AIP

摘要:

A model is presented which predicts the path along which ordinary machine‐made paper will tear. Based on the idea of minimum work being done as the paper tears, this model leads to curve‐generating equations which are solved numerically via a simplebasicprogram. A key feature making this a pedagogically attractive activity is that immediate experimental feedback is possible by printing out the theoretical curves and comparing them to the actual tearing curves produced when the printouts are torn. Typical results obtained when this is done are included.

ISSN:0002-9505    

DOI:10.1119/1.17570

出版商:American Association of Physics Teachers    

年代:1994

数据来源: AIP

摘要:

Electrostatic vacuum fields having straight flux lines—so that flux lines are possible orbits for charged test particles—are shown to be restricted to those cases which come to mind immediately: the fields of a point charge, an infinite straight charged wire, and the homogeneous fields. The length of the argument is surprising.

ISSN:0002-9505    

DOI:10.1119/1.17571

出版商:American Association of Physics Teachers    

年代:1994

数据来源: AIP

摘要:

The motion of bodies in power‐law potentials of the formV(r)=λrαhas been of interest ever since the time of Newton and Hooke. Aspects of the relation between powers α and ᾱ, where (α+2)(ᾱ+2)=4, are derived for classical motion and the relation to the quantum‐mechanical problem is given. An improvement on a previous expression for the WKB quantization condition for nonzero orbital angular momenta is obtained. Relations with previous treatments, such as those of Newton, Bertrand, Bohlin, Fauré, and Arnold, are noted, and a brief survey of the literature on the problem over more than three centuries is given.

ISSN:0002-9505    

DOI:10.1119/1.17572

出版商:American Association of Physics Teachers    

年代:1994

数据来源: AIP

摘要:

In a novel set of acoustic resonators, alterations of the nonuniformity in cross‐sectional area are utilized to change the resonance frequency. Each resonator is designed to yield two, three, or four frequencies whose differences correspond to musical intervals. The apparatus have a simple piecewise‐uniform geometry that can easily be changed, and are useful as educational demonstrations of an effect of nonuniformity on waves. The shifts in frequency can be accurately calculated by imposing boundary conditions on solutions of the wave equation in the uniform regions. The phenomenon can be physically understood with the energy method of Rayleigh, or more generally with the method of adiabatic invariance. The latter methods yield the shift in resonance frequency for arbitrary but small nonuniformity.

ISSN:0002-9505    

DOI:10.1119/1.17573

出版商:American Association of Physics Teachers    

年代:1994

数据来源: AIP

摘要:

The dependence of time’s arrow on initial conditions is illustrated by a numerical example in which plane waves produced by an initial pressure pulse are followed as they are multiply reflected at internal interfaces of a layered medium. Wave interactions at interfaces are shown to be analogous to the retarded and advanced waves of point sources. The model is linear and the calculation is exact and demonstrably time reversible; nevertheless the results show most of the features expected of a macroscopically irreversible system, including the approach to the Maxwell–Boltzmann distribution, ergodicity, and concomitant entropy increase.

ISSN:0002-9505    

DOI:10.1119/1.17574

出版商:American Association of Physics Teachers    

年代:1994

数据来源: AIP

摘要:

Symmetry considerations are used to simplify the derivation of time‐invariant vectors for the Kepler motion, the harmonic motion, and the motion of an electric charge in a magnetic field.  

ISSN:0002-9505    

DOI:10.1119/1.17575

出版商:American Association of Physics Teachers    

年代:1994

数据来源: AIP

摘要:

A detailed analysis is given of a 1685 graphical construction by Robert Hooke for the polygonal path of a body moving in a periodically pulsed radial field of force. In this example the force varies linearly with the distance from the center. Hooke’s method is based directly on his original idea from the mid‐1660s that the orbital motion of a planet is determined bycompoundingits tangential velocity with a radial velocityimpressedby the gravitational attraction of the sun at the center. This hypothesis corresponds to the second law of motion, as formulated two decades later by Newton, and itsgeometricalimplementation constitutes the cornerstone of Newton’sPrincipia. Hooke’s diagram represents the first known accurate graphical evaluation of an orbit in a central field of force, and it gives evidence that he demonstrated that his resulting discrete orbit is an approximate ellipse centered at the origin of the field of force. A comparable calculation to obtain orbits for an inverse square force, which Hooke had conjectured to be the gravitational force, has not been found among his unpublished papers. Such a calculation is carried out here numerically with the Newton–Hooke geometrical construction. It is shown that for orbits of comparable or larger eccentricity than Hooke’s example, a graphical approach runs into convergence difficulties due to the singularity of the gravitational force at the origin. This may help resolve the long‐standing mystery why Hooke never published his controversial claim that he had demonstrated that an attractive force, which is ‘‘...in a duplicate proportion to the Distance from the Center Reciprocall...’’ implies elliptic orbits.

ISSN:0002-9505    

DOI:10.1119/1.17576

出版商:American Association of Physics Teachers    

年代:1994

数据来源: AIP