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    20 November 2019 Volume 38 Issue 11
      
    Matrix relationship of the basic vectors between direct and reciprocal lattices
    XUE De-sheng, CHANG Peng, FAN Xiao-long
    College Physics. 2019, 38(11):  1.  doi:10.16854 / j.cnki.1000- 0712.180665
    Abstract ( 3617 )   PDF (146KB) ( 616 )  
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    Based on the coordinates of crystal axis,a reciprocal vector b*j ( j = 1,2,3 ) of a vector ai i = 1,2,3 ( ) is presented. By introducing the relatioanship bj = 2π b*j ,it is proved that bj is the basic vector of the reciprocal lattice,which is related to the direct lattice with basic vector ai . The matrix relationship of the basic vectors between the direct and the reciprocal lattices is equivalent to that definedin the textbook. This result indicates that the reciprocity of the basic vectors bj and ai embody in the duality property between the direct and the reciprocal lattices.
    Strict mathematical theory of tangential boundary value relationship of electromagnetic field
    LUO Ling-xiao
    College Physics. 2019, 38(11):  3.  doi:10.16854 / j.cnki.1000- 0712.180704
    Abstract ( 1062 )   PDF (313KB) ( 369 )  
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    This paper expounds though the line integral that the vector field along the first-order infinitesimal line is also the first-order dimensionless,but in particular cases demand the computational accuracy must achieve the second-order dimensionless. For this purpose,we need to divide the first-order infinitesimal line segment into infinitely many second-order infinitesimal line element to calculate the line integral,and give the law that followed by the result that obtained through such calculation: the theorem of vector field along first-order infinitesimal line segment’s line integral under second-order infinitesimal accuracy. We introduce application of this theorem in curl theory and in the theory of electromagnetic field tangential boundary value relations.
    An analysis and solution of a relativistic problem from the physics competition
    JU Guo-xing
    College Physics. 2019, 38(11):  9.  doi:10.16854 / j.cnki.1000- 0712.180555
    Abstract ( 1300 )   PDF (397KB) ( 658 )  
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    Several questions involved in the solution of a relativistic problem from the physics competition are analyzed in detail,and they are clarified through a complete solution to the problem.
    A note on the proof of the property of crystal space group
    RAO Xiang, LU Gui-wu
    College Physics. 2019, 38(11):  15.  doi:10.16854 / j.cnki.1000-0712.190018
    Abstract ( 907 )   PDF (124KB) ( 224 )  
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    This paper pointes out a mistake in the proof of the properties of crystal space group in the textbook “Group Theory and Its Application in Solid State Physics”,and gives a strict proof.
    Deriving mass-velocity relation without dependence on conservation laws
    DAI You-shan
    College Physics. 2019, 38(11):  17.  doi:10.16854 / j.cnki.1000-0712.180317
    Abstract ( 1184 )   PDF (192KB) ( 450 )  
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    The principle of relativity requires that the expressions for particle’s momentum and energy take the same functions of the particle’s velocity in all inertial frames.The mass-velocity relation of relativity is derived independent of conservation laws. It direct proves that neither conservation laws nor the Lorentz transformation is a necessary condition for mass-velocity relation.From the mass-velocity relation,the generalized Lorentz transformation formula of inertial frames can be obtained. The proof implies that the mass-energy equivalence and the massvelocity relation of relativity are more fundamental than the Lorentz transformation formula in relativity.
    The reform in measuring objects’processional moment by torsion pendulum method
    WANG Wei-guang
    College Physics. 2019, 38(11):  21.  doi:10.16854 / j.cnki.1000-0712.190008
    Abstract ( 1628 )   PDF (573KB) ( 567 )  
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    In the current college physics experiment teaching,the experiment of measuring objects’processional moment by torsion pendulum method has some logical confusion because of the intertwining with the geometric method. This paper proposes that the definition method rather than the geometric method is directly used to calculate the torsion coefficient K. Then,this paper rearranges the experimental content and makes the process more clearly.
    Simulation and application of multiple rectangular flow loop combined magnetic field
    LI Qing-fang, HU Xin-yu, MA Xiao-fei, ZHANG Ya-nan
    College Physics. 2019, 38(11):  25.  doi:10.16854 / j.cnki.1000-0712.180506
    Abstract ( 1327 )   PDF (898KB) ( 278 )  
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    The formula for the production of magnetic field in space by rectangular carrier coil is derived according to Safaer's law. The formula is used to calculate the distribution of magnetic field when two and four rectangular flow line rings have opposite magnetic poles of the same name. According to the calculation results,a magnetic field energy conversion demo instrument is designed to analyze the movement characteristics of the projectile in the magnetic field and the source of kinetic energy.
    Discussions on the biprism interference experiment teaching
    DUAN Xiu-ming, YI Zhi-jun, YU Jian-yong, QU Li-cheng
    College Physics. 2019, 38(11):  29.  doi:10.16854 / j.cnki.1000-0712. 180635
    Abstract ( 1296 )   PDF (1726KB) ( 280 )  
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    The adjustment of light path of biprism interference is complicated,and there are many details for operating to notice,it is difficult for students to understand these details about experiment if teacher does not introduce and explain these details,and students often obtain abnormal experimental phenomena. Teacher presents the experimental principles through macro view,consciously heuristic students establish optical set-up,and finds out the origin of the abnormal experimental phenomena. Finally,teacher explains the abnormal experiment images. As a result,students can take the experiment process as a whole,and achieve experimental expectations.
    Research on the air resistance and the motion trajectory of badminton based on Tracker software
    WANG Xi-yan, DING Yi-min, YAN Yan, SHI Zhen-yu
    College Physics. 2019, 38(11):  33.  doi:10.16854 / j.cnki.1000-0712.190028
    Abstract ( 1624 )   PDF (755KB) ( 486 )  
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    Air resistance has a great influence on the track of badminton,but the coefficient of the air resistance is difficult to get. In this paper,by using the automatic tracking function of Tracker software,the dynamics model of badminton is established,and the air resistance coefficient of the badminton is calculated. The badminton trajectory model is also improved.
    Construction of awater immersion objective-darkfield condenser combination optical system and its initial application in cell image
    HUANG Shan, GAO Ji-min
    College Physics. 2019, 38(11):  36.  doi:10.16854 / j.cnki.1000-0712.190128
    Abstract ( 1160 )   PDF (978KB) ( 158 )  
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    The traditional method of cell imaging is too much operation on the cells in the preparation work.It is not suitable for real-time observation of living cells.This experiment introduces a method of combining a large numerical aperture oil immersed dark-field condenser and a coverslip-less water immersion objective to high resolution real-time cell imaging.To minimize cell operation in the preparations for the real-time imaging,this experiment by using water immersion lens inserted directly into the Petri dish in PBS ( phosphate Physiological Buffered Saline ) or culture medium to replace the traditional cell smear and cell drop operation,to obtain adherent and suspension cultured cells real- time dark field image culture. Observation of adherent cells in PBS can get better effect in this dark field imaging system; observation of suspension cell in culture medium can be obtained, but the dark field effect.This optical system is simple and inexpensive,and can be widely used in the research work related to cells.
    Simulation of abnormal football movement and its practical application with MATLAB
    JIANG Xin-yi, LV Jian-feng
    College Physics. 2019, 38(11):  41.  doi:10.16854 / j.cnki.1000-0712.190037
    Abstract ( 1688 )   PDF (1448KB) ( 1608 )  
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    The influence of Magnus effect on football trajectory and goal probability is studied.Firstly,the dynamical equation of the mass-center of football is established by analyzing the force exerted on it,and through the simulation by MATLAB,its motion characteristics are presented,namely,its trajectory is not coplanar either symmetric compared with the ideal parabolic ones.Then,by using Monte Carlo simulation,the initial velocity distribution for scoring the goal is also obtained.Furthermore,we get the goal probability distribution and the difference distribution between the two cases whether there is Magnus effect in the region considered,it is found that the relative magnitude of the goal probability of these two cases presents the alternate radiation bands which centered on the goal.
    Study of bursting of soap bubble and its residue droplets
    DUAN Xiang-pan, WU Hai-juan, WANG Xu, GUO Rong, LI Kai-lu, MA Chun-wang
    College Physics. 2019, 38(11):  48.  doi:10.16854 / j.cnki.1000-0712. 190116
    Abstract ( 1500 )   PDF (863KB) ( 580 )  
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    The size and number of residue droplets are affected by the soap bubble bursting process. A study is performed to understand how the size and height of soap bubble influence the residue droplets and their distributions after the soap bubble bursting. It is seen in the experiment that the distributions of the residue droplets have a phenomenon of radioactive linear distribution when the bursting height is low. But the radioactive linear distribution will disappear with the increasing height. With the change of soap bubble volume,the rules of both droplets numbers and soap film thickness are analyzed. A power function dependence of the soap bubble volume on the droplets numbers is found. In the ideal condition,a power function dependence of the thickness of the soap film on the number of fragments is found. The results show that the residue droplets can be roughly divided into three types,i.e.,the small fragments,medium fragments and large fragments,according to the fitting result,which can be explained according to the three different stages of the soap bubble bursting process.
    A measurement of the liquid surface tension coefficient based on PASCO experimental platform
    ZHANG Zhen-lei, ZHOU Wei, WANG Dian-sheng, WANG Hui, LI Jing, LIU Xue-feng
    College Physics. 2019, 38(11):  54.  doi:10.16854 / j.cnki.1000-0712.190175
    Abstract ( 1233 )   PDF (640KB) ( 214 )  
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    Currently,in the experiment of measuring the surface tension coefficient of liquid with pull-off method, when the liquid film breaks,the judge of the moment could cause artificial error. In this paper,a set of experimental equipment which can measure the tension in high frequency is built by using the PASCO experimental platform. With this equipment,the tension acting on the metal ring is measured systematically. The process of the metal ring getting out of water is studied. The change of the interracial tension and the buoyancy in this process are also analyzed. The surface tension coefficient of water in air is extract through fitting the data measured. The coefficient achieved in this paper is 0.0705 N /m which had about 2.7% difference from the standard value.
    An interesting thermodynamic question: when does a coin“dance”?
    TAO Feng-yi, ZHUANG Yang, HUANG Min, ZHAO Yun-he, MA Yu-han
    College Physics. 2019, 38(11):  58.  doi:10.16854 / j.cnki.1000-0712.190042
    Abstract ( 1784 )   PDF (640KB) ( 443 )  
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    From the perspective of thermodynamics,this paper conducts a theoretical analysis of the phenomenon of dancing coin,the third question of 2018 IYPT. This phenomenon is closely related to daily life,describes the motion of a coin on the neck of a very cold bottle,and such a thermodynamic system can serve as a good teaching model,enabling students to have an intuitive and in-depth understanding of thermodynamic processes such as gas heating and adiabatic expansion. In this study,the relationship between the bouncing time of the coin with the thermodynamic quantity of the system is obtained. It is found that the time interval of the coin dancing is negatively correlated with the temperature difference between the system and the environment,that is,the time interval of coin dancing will be longer and longer as a system is heated by the environment,until it could not jump. Further research shows that,the greater the difference between the initial temperature of the gas in the bottle and the ambient temperature,the greater the maximum bouncing time,and the closer the critical pressure is to the atmospheric pressure,the greater the maximum bouncing time. This paper further verifies the reasonability of theoretical hypothesis and the results deduced from theoretical analysis through experiments.
    Investigation on the radial wave function and energy level of hydrogen atom by the variational method
    LU Xin, ZHENG Hua
    College Physics. 2019, 38(11):  62.  doi:10.16854 / j.cnki.1000-0712.190086
    Abstract ( 1854 )   PDF (329KB) ( 532 )  
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    We investigate the hydrogen atom model in quantum mechanics by using the variational method and present the corresponding deduction. The software Mathematica is utilized to calculate the optimal trial wave functions and the corresponding energy levels. We also compare our results with the exact ones given by the confluence hypergeometric function ( Kummer function) .