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Table of Content

    20 May 2020 Volume 39 Issue 05
      
    The disenchanted aacceleration in analytical mechanics
    ZHANG Xiao-bing
    College Physics. 2020, 39(05):  1-3.  doi:10.16854 /j.cnki.1000-0712.190442
    Abstract ( 1396 )   PDF (167KB) ( 783 )  
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    By using the Lagrangian approach to classical mechanics,we investigate the condition of static equilibrium

    and the continuum dynamics,respectively. By using Hamiltonian approach,we introduce the distinct

    point of equilibrium as well as the stable ensemble distribution,which makes sense in the scope of statistical mechanics,

    in the phase space.The examples show that the concept of acceleration is disenchanted in the framework of

    analytical mechanics.Also,the so-called“equilibrium states”are found to be realized by the different ways from

    the case of Newtonian approach.

    Splittings of atomic energy levels caused by the magnetic hyperfine interaction and diagram drawing of the splitted energy levels
    SUN Zhen-dong, TIAN Yu-feng
    College Physics. 2020, 39(05):  4-9.  doi:10.16854 /j.cnki.1000-0712.190371
    Abstract ( 2763 )   PDF (627KB) ( 1927 )  
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    Hyperfine interaction is one of the important contents in the course of“Atomic Physics”. So far in

    domestic and foreign textbooks of atomic physics,authors just write down the expressions of splittings of atomic energy

    levels caused by the magnetic hyperfine interaction without and with an external magnetic field,and show some

    related research examples. Here,for the cases of without and with a weak or a strong external magnetic field,the

    derivation processes of these formulas and discussions about diagram drawing of these splitted energy levels are described

    in details. The contents in this paper will be helpful for teachers and students in understanding and truly

    mastering the related parts of knowledge in the course of“Atomic Physics”.

    Several“Pythagorean theorems”in special relativity
    ZHOU Guo-quan
    College Physics. 2020, 39(05):  10-13.  doi:10.16854 /j.cnki.1000-0712.190395
    Abstract ( 2573 )   PDF (214KB) ( 1027 )  
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    Some teaching experiences about electrodynamics and special relativity are summarized. Several relativistic

    invariants and“Pythagorean theorems”in special relativity are derived by means of the tensor theory in

    four - dimensional Minkowski space and the contraction operation rules of these tensors. Meanwhile, some

    application examples are given in illustration of these formulae.

    The Fourier-Bessel integral expansion of a function in semi-infinite space
    JIANG Xiang-qian, HOU Chun-feng, MENG Qing-xin, ZHANG Yu
    College Physics. 2020, 39(05):  14-15.  doi:10.16854 /j.cnki.1000-0712.190248
    Abstract ( 2670 )   PDF (147KB) ( 1267 )  
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    In cylindrical coordinates,the family of intrinsic Bessel function constitutes a complete orthogonal function series,which can be used as the bases of generalized Fourier expansion. In this paper,starting from the generalized Fourier expansion of a function defined on a finite interval and using the approximate formula of Bessel function and its zero point formula,we discuss the Fourier-Bessel integral expansion of a function defined in semiinfinite space,and get the approximate expression of module square of Bessel function. In the asymptotical situation, discontinuous parameter becomes continuous one,we obtain the Fourier-Bessel integral and coefficient formula of the function.
    Twin paradox and interstellar travel
    QIN Li, LIN Ran-xi, GAN Xiao-long, ZHU Hu
    College Physics. 2020, 39(05):  16-19.  doi:10.16854 /j.cnki.1000-0712.190225
    Abstract ( 1295 )   PDF (286KB) ( 722 )  
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    The time discrepancy associated with the“Twin Paradox”in two hypothetical interstellar travel programs, is calculated. This result reflects an absolute difference about the time experienced between inertial and noninertial reference frames,rather than a " relative" effect correlating the two references.
    Study of the critical density and stability of suspension in standing wave sound field
    JIN Shuo, YAN Qi-qi, LI Cheng-yi, ZHANG Zhao-hang, HUANG An-ping
    College Physics. 2020, 39(05):  20-26.  doi:10.16854 /j.cnki.1000-0712.190546
    Abstract ( 1305 )   PDF (1378KB) ( 1274 )  
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    In this paper,the object in the sound field is studied,and the acoustic radiation pressure equation

    is theoretically derived both in the travelling wave and the standing wave. The concept of the critical suspension

    density is introduced into the standing wave sound field,which should be used as a criterion for suspension in a

    nonlinear sound field. At the same time,the maximum range of Resonant cavity's movement speed is given. Furthermore,

    by the combination of numerical computations and experimental results,the influence of the density and the

    size of the sample in the standing wave sound field,the shape of the emitting surface and the reflecting surface,the

    distance between these two surface,and the size of the reflecting surface on the suspension stability are investigated.

    It is found that when the size and the density of the object are determined,adjusting the length of the resonant cavity

    and increasing the sound pressure at the antinode are effective means to improve the acoustic suspension stability.

    Teaching research on simulation experiment of electrostatic field
    LI Li, ZHANG Hao-jing, ZHANG Xiong, QIU Long-bin, WU Yang-feng
    College Physics. 2020, 39(05):  27-30.  doi:10.16854 /j.cnki.1000-0712.190545
    Abstract ( 2099 )   PDF (195KB) ( 823 )  
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    Simulation of electrostatic field with a steady current field is a very classic general physics experiment.

    In the traditional physics experiment,the experimental data was generally recorded by an equal arm recording method,

    and then the inner cylinder radius and the outer ring inner radius were obtained according to the linear relationship

    between the equipotential voltage and the logarithm of the equipotential circle radius. According to the characteristics

    of the experimental data,the exponential fitting method,the binary linear regression method and the A-type

    uncertainty method are simultaneously sued to process of the experimental data obtained by simulating the electrostatic

    field with the steady current field. The static current field is simulated and error analysis of field experiments is given.

    Through comparison,the application and analysis of data processing methods in experiments are carried out.

    Measuring the magnetic field of Helmholtz coil with the magnetic sensor of a smart phone
    LIU Wei, CHENG Min-xi
    College Physics. 2020, 39(05):  31-32.  doi:10.16854 /j.cnki.1000-0712.190402
    Abstract ( 1713 )   PDF (986KB) ( 1014 )  
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    The magnetic sensor in the smart phone is located by a pre-experiment. The magnetic field distribution throughout the axle wire of Helmholtz Coil is measured,Biot-Savart Law and magnetic field’s superposition principle are verified by a handy and precise new measurement method.
    An easy-to-understand teaching method about entropy
    DONG Zhan-hai
    College Physics. 2020, 39(05):  33-37.  doi:10.16854 /j.cnki.1000-0712.190409
    Abstract ( 1433 )   PDF (435KB) ( 869 )  
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    The entropy,like force,energy and momentum,is an important concept in physics. If a simple and

    understandable method could be designed,it is useful for teaching physics for liberal arts. In this paper,an easy-to

    -understand teaching method about the entropy is proposed. Therefore,the concept of entropy can be taught without

    the needing for students to learn the second law of thermodynamics. The corresponding teaching design is as follows: introducing the concept of entropy ( namely,Boltzmann entropy) through daily life examples,designing two examples for students to calculate the entropy,making students fully understand the meaning of entropy through discussion on specific problems,obtaining the Clausius entropy from Boltzmann entropy through an example,designing an entropy demonstration experiment to strengthen teaching effect,and connecting the entropy with environmental protection to make physics humanistic,and finally specifying the different levels of entropy calculation. Problem-based learning ( PBL) is adopted in the teaching design.

    Teaching reform and exploration of Poisson equation based on flipped classroom mode
    CHANG Jun-li, DONG Ning, ZHOU Chun-qiong, ZHANG Hua
    College Physics. 2020, 39(05):  38-43.  doi:10.16854 /j.cnki.1000-0712.190354
    Abstract ( 1128 )   PDF (592KB) ( 657 )  
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    During many years of teaching practice,it was found that some undergraduates were often faced

    with difficulties in learning Poisson equation,such as difficult knowledge points,fast teaching progress and no way

    to start self-study. In view of the situation,flipped classroom mode is introduced in the teaching of Poisson equation

    for teaching reform and the scheme of teaching design is primarily explored for achieving superior teaching effect.

    Quantitative detection of trace crude oil in the sand using reflected terahertz time-domain spectroscopy
    LI Xin-yu, ZHAN Hong-lei, ZHANG Yan, REN Ze-wei, ZHAO Kun, JIAO Yu-qiu
    College Physics. 2020, 39(05):  44-46.  doi:10.16854 /j.cnki.1000-0712. 190303
    Abstract ( 895 )   PDF (1066KB) ( 503 )  
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    The contamination of crude oil in the sea is a major threat to marine organism and the environment

    safely. The detection of crude oil in the sand near the sea is of significance to petroleum exploration and environmental

    protection. Reflected terahertz time-domain spectroscopy is used for the quantitative detection of the crude

    oil in the sand. A detailed analysis is performed about the delay time and wave velocity across the sample. The research

    indicates that the relationship between the crude oil concentration and the delay time shows linear decrement

    character,the reflected terahertz time-domain spectroscopy is a potential method for quantitative detection in the

    environmental protection.

    The colors in“A panorama of Rivers and Mountains” ———Teaching physics with an interdisciplinary approach
    WEI Ran
    College Physics. 2020, 39(05):  47-51.  doi:10.16854 /j.cnki.1000-0712.190493
    Abstract ( 2502 )   PDF (737KB) ( 868 )  
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    The famous painting“A Panorama of Rivers and Mountains”of the Northern Song Dynasty collected

    in the Palace Museum is well known to the public through CCTV's program: The Nation's Greatest Treasures. The

    painting was regarded as a giant masterpiece in the blue-green landscape painting. Although it has gone through

    nearly a thousand years,it is still brilliant as usual,the secret of which was that all the pigments were made of

    gemstone minerals. According to the principle of physical chemistry,the chromatic mechanism of these pigments is

    revealed one by one in this paper. This kind of crossover thinking could not only stimulate interest in learning,but

    also could realize the perfect combination of modern science education and traditional culture.

    Spring-mass oscillator confined to horizontal frictionless plain
    XU Shi-hao, ZHANG Xiong
    College Physics. 2020, 39(05):  52-57.  doi:10.16854 /j.cnki.1000-0712.190309
    Abstract ( 1980 )   PDF (980KB) ( 1716 )  
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    Among spring-mass oscillators with nonlinear motions and two degrees of freedom,the model confined

    to horizontal frictionless plane has features of simple dynamic differential equations and separable variables. In

    this study polar coordinates are used to construct the dynamic differential equations of the spring-mass oscillator

    confined to horizontal frictionless plain. Variables related to radial motion are separated to form an individual dynamic

    differential equation,which is researched by qualitative analysis and approximation theory due to its

    nonlinear characteristic. Software MATLAB is used as a numerical method to simulate paths of the oscillator,verify

    qualitative results and demonstrate the accuracy of approximate solutions in two specific situations.

    Influence of inhomogeneity of the dip angle and the friction coefficient on the core result of Galileo's inclined plane experiment
    ZHANG Run, ZHANGYANG Yu-ying, XIONG gang
    College Physics. 2020, 39(05):  58-61.  doi:10.16854 /j.cnki.1000-0712.190368
    Abstract ( 1447 )   PDF (624KB) ( 789 )  
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    The core result of Galileo's inclined plane experiment is the proportion relation between distance and

    the square of time,but the local inhomogeneity of the dip angle and friction coefficient leads to inhomogeneity of local

    acceleration. In this paper,a simplified model including inhomogeneity of the dip angle and friction coefficient

    is introduced. Numerical results show that this inhomogeneity not only induces random error but also leads to deviation

    of the square relation between the distance and the time. It is further found that if the dip angle keeps unchanged

    and the friction coefficient decreases,the ball should change from non-slip rolling to slip rolling,the deviation

    degree of the square relation between the distance and the time would increase rather than decrease. This result,

    although contrary to intuition,coincides with the result achieved in some corresponding researches on the history

    of physics. These theoretical results are confirmed by our experiments. In order to exclude the random factors in

    releasing the ball,an equipment is designed to release the ball with zero velocity. A more convenient method is also

    carried out to measure the friction coefficient.

    Effect of massive string and pulley on the motion of Atwood machine
    WANG Jie, HE Xi-ping
    College Physics. 2020, 39(05):  62-65.  doi:10.16854 /j.cnki.1000-0712.190258
    Abstract ( 1022 )   PDF (348KB) ( 833 )  
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    The string and pulley are often used as ideal models ( e.g.,Atwood machine with a massless pulley

    and a massless string) in textbooks to solve the dynamics problem of Atwood machine. The dynamical methods are

    used to describe the motion of Atwood machine with a massive string. The effects on the system motion caused by

    the mass of the pulley,the mass of the massive string and the initial position of the weight are analyzed. Furthermore,

    the difference between the ideal model described in the text book and the motion of the Atwood machine under

    the real conditions is discussed.

    An improvement to the verification of parallel axis theorem for moment of inertia
    YAN Min, DAI Yu-qin, YUAN Jun, WANG Xiao-xiong
    College Physics. 2020, 39(05):  66-69.  doi:10.16854 /j.cnki.1000-0712.190392
    Abstract ( 3630 )   PDF (733KB) ( 2560 )  
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    An improved experiment scheme about the verification of parallel axis theorem for moment of inertia

    is introduced. In the new scheme,the moment of inertia of the whole system is changed by changing the distance of

    the steel pillars to the instrument rotational axis symmetrically. The variation of moment of inertia is made in a large

    range and the symmetrical mass distribution is preserved. So that the relative error is significantly reduced and the

    reliability of the verification of the theorem is substantially improved.

    Design and Production of the liquid-resistivity measuring device
    WANG Shu-guang, SUN Li-yuan, BAI Jing-zhao, REN Bo, SONG Yang
    College Physics. 2020, 39(05):  70-73.  doi:10.16854 /j.cnki.1000-0712.190245
    Abstract ( 1346 )   PDF (667KB) ( 1355 )  
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    Aiming to the complex physical properties of liquid lead to the difficulty in measuring its resistivity,

    a new liquid-resistivity measuring device is designed in this paper. In order to collect the information of the object

    under test effectively,the container is designed skillfully. Graphite electrode is applied innovatively to realize the

    integration of the electrode and the container,which improves the measuring accuracy. The sensing technology is

    used to collect voltage and current signals and transmitted the data to the MCU. The value of resistivity is displayed

    on the LCD screen in real time after the operation of the MCU. With the advantages of quick and accurate measurement,

    it has certain practical value in teaching and research.

    Autocollimating Method Based on Lateral Moiré Fringe
    ZHU Chao-yi, LU Wei-xin, GAO Hong, WANG Mei
    College Physics. 2020, 39(05):  74-77.  doi:10.16854 /j.cnki.1000-0712.190264
    Abstract ( 1204 )   PDF (731KB) ( 864 )  
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    Combining with lateral displacement amplification of Moiré fringe and auto-collimation angle measuring

    principle,based on the lateral Moiré fringe of auto-collimation angle measurement method,is analyzed by using

    the shading principle of Moiré fringe displacement amplification effect. On the basis of the method to build the

    principle of the optical path,the Moiré fringe signal is stable and can satisfy the measurement requirements. On the

    basis of the system,data processing steps are simplified and dynamic measurement is realized. The quantitative calibration

    experiment results show that the system resolution up to 10″,applying this method to the autocollimator can

    significantly improve the resolution.