摘要:

Rolling with slipping of a uniform rigid body of revolution on a rough horizontal or inclined plane in two‐dimensional motion is a standard problem in elementary dynamics; in such motion each cross section of the body of revolution remains parallel to a fixed vertical plane that is taken to contain the line of greatest slope in the case of motion on an inclined plane. Consider similar two‐dimensional motion inside a fixed cylinder with general, rather than circular, cross‐sectional curve C. This much more difficult problem is considerably simplified if there is no gravity force. The translational and rotational velocities of the body are then found to depend only on the change in direction of the tangent to the curve C up to the current point of contact during the motion and not on the curve itself.

ISSN:0002-9505    

DOI:10.1119/1.14950

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

摘要:

A classical hydrogen atom will polarize in a direction perpendicular to a uniform electric field in its orbital plane. While some features of this unexpected behavior can be reconciled with physical reality, it illustrates representative difficulties of classical mechanics applied to atomic physics. The exceedingly unintuitive results have instructional value for students.

ISSN:0002-9505    

DOI:10.1119/1.14951

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

摘要:

In the collision of a particle (A) with a system of bonded particles (B–C), only the energy in the center of mass reference frame is available for breaking the bond. This is because some of the initial energy must be used in conserving the momentum of the system. This article describes a simple air‐track experiment illustrating this well‐known fact. Two carts on a horizontal air track are bonded together by small magnets; a sudden impulse is provided to one of the carts by a falling weight. A feature of the experiment is the direct determination of magnetic bond energy by numerical integration ofFdx. For cases where the energy in the center of mass is sufficient to break the magnetic bond, the ensuing motion of the system can be described in terms of an effective mass.

ISSN:0002-9505    

DOI:10.1119/1.14952

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

摘要:

The radial form of Hylleraas’ equation for the hydrogen atom, Λl‖El〉=4ℏ4a−2‖El〉 (a=Bohr radius), is considered and it is shown that the operator Λlcan be factorized. Hence ladder operatorsP±lare derived that are linear in the position operatorrand are nonlinear functions of the momentum operatorp. It is proven thatP±l‖El〉 =2ℏ2a−1[1+(l+ (1)/(2) ± (1)/(2) )2×(2Mℏ−2a2E)]1/2‖E,l±1〉. In the momentum representation of wave mechanics the solutions to these equations are the radial momentum‐space wavefunctions for the hydrogen atom. Thus a simple method of calculating these wavefunctions is obtained. The results complement the familiar operator solution for the hydrogen atom that is based on factorization of the radial Hamiltonian and yields operators that are linear inpand are nonlinear functions ofr.

ISSN:0002-9505    

DOI:10.1119/1.14953

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

摘要:

Although Fabry–Perot interferometers have found widest application in the visible portion of the spectrum, their properties are conveniently observed in the microwave region, where high‐quality spherical mirrors are easily fabricated on a lathe, and partially transmitting (high reflectance) flat mesh is commercially available at modest cost. The scaling properties of paraxial beams of such interferometers, as the frequency is varied from optical to microwave for a fixed resonator geometry, are well known. This allows studies that are relevant to contemporary optics research to be carried out in an upper division undergraduate laboratory without the need for sophisticated equipment.

ISSN:0002-9505    

DOI:10.1119/1.14954

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

摘要:

It is shown how the Runge–Lenz vectorAcan be used to give the orbit equation and the Rutherford cross section without the necessity of solving differential equations. After that, the Greenberg’s method is applied to obtain the perihelion shift of Mercury using the vectorA. Some suggestions are given in the conclusions.

ISSN:0002-9505    

DOI:10.1119/1.14955

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

摘要:

The problems of a square well in quantum mechanics, a slab reactor in neutron diffusion theory, and a planar dielectric waveguide imply solving the same second‐order differential equation but with different boundary conditions. In order to study the influence of different boundary conditions on the accuracy of first‐ and second‐order perturbation theory, the above problems are solved both exactly and by perturbation methods for the case of three slabs. A numerical comparison shows that the simpler the boundary conditions are, the more accurate the results of perturbation theory become.

ISSN:0002-9505    

DOI:10.1119/1.14906

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

摘要:

The use of a noncalculus technique (imposing the condition that physically meaningful roots of a quadratic equation must be real) to obtain the maximum or minimum value of some variable of interest is found appropriate for a class of mechanics problems. Three examples are illustrated. An overall review of other possible cases is listed.

ISSN:0002-9505    

DOI:10.1119/1.14907

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

摘要:

Atomic or nuclear collisions can be modeled using the ‘‘Welch’’ scattering apparatus. The student obtains and analyzes ‘‘macroscopic’’ data from a scattering experiment in order to ascertain ‘‘microscopic’’ properties (orientation and shape) of a hidden target. The procedure described emphasizes the analysis of data that are analogous to the data obtained in atomic or nuclear collision studies. The student finds that the position of a cluster of scattered projectiles indicates the orientation of the scattering surface while the density of the cluster indicates the shape (radius of curvature) of the scattering surface.

ISSN:0002-9505    

DOI:10.1119/1.14908

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

摘要:

An improved apparatus has been developed for demonstrating the hysteresis loops of ferromagnetic materials. Using a Hall probe, a storage oscilloscope, and specially designed circuitry one can in effect plot the initial magnetization curve and the hysteresis loop of a sample point by point, either manually or automatically. Under manual control, the apparatus can also be used to demonstrate minor hysteresis loops of the sample. These minor loops are related to the concepts of permeability μ, incremental permeability μΔand reversible permeability μr.

ISSN:0002-9505    

DOI:10.1119/1.14909

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP