摘要:

We present some applications of the Runge–Lenz invariants for the Kepler and harmonic oscillator problems. The precession rate of the elliptic orbits is calculated for various perturbations of the Kepler and harmonic potentials.

ISSN:0002-9505    

DOI:10.1119/1.13792

出版商:American Association of Physics Teachers    

年代:1984

数据来源: AIP

摘要:

A simple electro‐optical experiment is described that allows advanced undergraduates to measure the critical exponent γ. The experiment investigates the electric‐field‐induced birefringence as a function of temperature at the nematic‐isotropic phase transition in liquid crystals. The classical mean‐field result that γ=1 is verified.

ISSN:0002-9505    

DOI:10.1119/1.13793

出版商:American Association of Physics Teachers    

年代:1984

数据来源: AIP

摘要:

A simplified notation is introduced for dealing with systems of indistinguishable fermions and bosons. The second‐quantized form of system operators is obtained in a simpler manner than is offered ordinarily in textbooks. Details of the calculation of the nonrelativistic M≂ller cross section for scattering of two electrons are given as an example.

ISSN:0002-9505    

DOI:10.1119/1.13794

出版商:American Association of Physics Teachers    

年代:1984

数据来源: AIP

摘要:

We present a simple general proof that the spreading velocity of a relativistic free wave packet of de Broglie waves is limited. For a wide class of packets we confirm that the limit is the velocity of light, and we show how this limit is approached when the width Δpof the wave packet in momentum space tends to infinity and the minimum width σ(t=0) in ordinary space tends to zero.

ISSN:0002-9505    

DOI:10.1119/1.13795

出版商:American Association of Physics Teachers    

年代:1984

数据来源: AIP

摘要:

A vertically oscillating spring of massmand spring constantksuspended from its upper end and with a massMattached to its lower end is a system often used for demonstrations and experiments in introductory physics courses. We discuss the motion of this system for arbitrary values of ε=m/M, 0≤ε<∞ and show explicitly why theory predicts that the amplitude of the lowest normal‐mode frequency makes the major contribution to the motion ofM(or of the lower end of the spring) forallvalues of ε. Although a complete understanding of this fact involves detailed mathematical analysis, the results themselves are simply stated and readily verified even by students in an introductory calculus‐based physics course. The various predictions of the theory are easily demonstrated with simple equipment and lend themselves nicely to an introductory physics laboratory. These applications are discussed in some detail, and an analog electric circuit is given which exhibits similar behavior.

ISSN:0002-9505    

DOI:10.1119/1.13796

出版商:American Association of Physics Teachers    

年代:1984

数据来源: AIP

摘要:

The method of characteristic curves applied to the wave equation is employed to obtain explicit solutions to the problem of a spring of massmoscillating with a massMattached to one end. For the case of the free spring (M=0), the method produces simple solutions expressible in terms of functions which are linear in the displacement and in the time.

ISSN:0002-9505    

DOI:10.1119/1.13797

出版商:American Association of Physics Teachers    

年代:1984

数据来源: AIP

摘要:

The pendular motion of a giant censer (O Botafumeiro) that hangs in the transept of the cathedral of Santiago de Compostela, and is cyclically pumped by men who pull at the supporting rope, is analyzed. Maximum angular amplitude attainable, and number of cycles and time needed to attain it, are calculated; the results agree with observed values (∼82°, ∼17 cycles, ∼80 seconds) to the few percent accuracy of both the analysis and the observations and parameter measurements. The energy gain in a pumping cycle is obtained for an arbitrary pumping procedure to two orders in the small fractional change of pendular length; the relevance of the ratio (characteristic radial acceleration during pumping)/gto the gain is discussed. Effects due to rope mass, air drag on both Censer and rope, and the fact that the Censer is not a point mass, are considered. If the pumping cycle is inverted once the maximum amplitude has been attained, the Censer could be swiftly brought to rest, avoiding the usual violent stop. Historically recorded accidents, rope shape, and the influence of relevant parameters on the motion are discussed.

ISSN:0002-9505    

DOI:10.1119/1.13798

出版商:American Association of Physics Teachers    

年代:1984

数据来源: AIP

摘要:

An experiment with a spring is described to illustrate the fact that the irreversibility involved in a physical process in transforming the system from an initial state to a terminal state bears an inverse relationship to the number of discrete steps in which it is carried out, leading to the conclusion that the process becomes reversible as the number of steps tends to infinity. A similar relationship is shown to hold for processes like charging of a capacitor and compression of a perfect gas.

ISSN:0002-9505    

DOI:10.1119/1.13799

出版商:American Association of Physics Teachers    

年代:1984

数据来源: AIP

摘要:

Helmholtz’ theorem is a profound mathematical theorem which provides the definitive relationship between a vector field and mathematically defined source functions. The usual presentations of electromagnetic theory establish the principle sources of the electromagnetic field vectors, but leave the question of completeness unanswered, that is, whether all sources are included. Helmholtz’ theorem provides the basis for investigating the existence of other possible sources, and in at least one case shows a possible source not normally considered. Helmholtz’ theorem also provides a significant result pertaining to the meaning of the inverse square radial field, of which the Newtonian gravitational and Coulombic electrostatic fields are the classical examples. It can be established that the inverse square relation is determined by more elementary properties of the field and of the source function to which it relates.

ISSN:0002-9505    

DOI:10.1119/1.13800

出版商:American Association of Physics Teachers    

年代:1984

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.13944

出版商:American Association of Physics Teachers    

年代:1984

数据来源: AIP