弹性势能的表达式的实验验证

教材上从理论上探究了弹性势能的表达式,结合该探究过程,利用弹性势能与重力势能和动能的转换关系设计了2个验证性实验.     

关于弹性势能的讨论

讨论了当势能零点任意选取时弹性势能的表达式及其取值情况，并对这些情况作了理论上的解释。     

弹性势能零点选择与弹性势能表达式问题讨论

弹性势能差值不会因为弹性势能的零点选择而改变,但当规定弹性势能的零点位置不同时,系统的弹性势能却有不同的表达式.当选择弹簧原长时为零势能点,弹性势能的表示形式最简单,Ep=1/2kx2.是不是通常情况都是以弹簧原长时为零势能点?在具体问题中,零势能点的选取有没有特定的要求?文中对上述问题作出了系统性的分析与回答.     

选择典型过程 治疗学生的恐簧症

对如何选择典型过程,让弹性势能为零或者弹性势能等量替代的方法作了一些分析与探讨,让学生了解了弹簧题的特点和解题技巧.     

势能零点位置选取的简便方法

力学问题中常见的势能是弹性势能和重力势能．由于势能的相对性，在选取不同的势能零点位置时，计算过程有简有繁．因而，确定合适的势能零点会给解决问题带来方便．     

高考对弹性势能的要求

笔者研究了近几年的高考试题，发现与弹性势能有关的试题考生的得分率总是很低。这是什么原因造成的呢？笔者从高考试题的知识要求、能力要求这两方面着手讨论：高考对弹性势能的要求。     

从弹性势能储能系数出发讨论两光滑小球的斜碰问题

给出了物体的弹性势能储存系数的定义．从弹性势能储存系数出发讨论两光滑小球的斜碰问题,并导出了碰撞前后系统动能之间的关系．     

用可变化的恢复系数讨论两个光滑小球的斜碰问题

将恢复系数看作与接触点位置相关的函数,利用函数关系计算斜碰过程的能量损失和弹性势能储能系数,发现可变化的恢复系数有简化斜碰问题的作用.     

弹性力学的插值型重构核粒子法

采用具有离散点插值特性的重构核粒子法形函数, 较精确地重构弹性体 变形的位移试函数, 再与弹性力学的最小势能原理相结合, 形成新的分析弹性力 学平面问题的插值型重构核粒子法. 由于插值型重构核粒子法形函数具有点插值特性和不低于核函数 的高阶光滑性, 因而既克服了多数无网格方法处理本质边界条件的困难, 也保证了较高的数值精度. 与早期的无网格方法相比, 本方法具有精度高、解题规模较小、可直接施加边界条件等优点. 通过对典型弹性力学问题数值模拟, 验证了所提方法的有效性和正确性.     

浅析探究性学习能力培养

通过对高考北京卷物理第2 3题的分析, 梳理了高中阶段“ 势能”概念的理解, 并进一步来讨论探究性学 习能力的培养     

控能发射装置

现行的碰撞实验多在气垫导轨上进行,并利用橡皮筋发射滑块,由于橡皮筋容易老化问题难于解决,所以设计了可调节、可显示弹射能量的弹簧枪,用弹簧枪代替橡皮筋,从而可以实现多种被弹射物体的定速发射和同速发射.     

Lattice Dynamics of Some Fcc F-Shell Metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is used to study the binding energy, equation of state, ion-ion interaction, phonon dispersion curves (q-space and r-space analysis), phonon density of states, Debye temperature, mode Grüneisen parameters, dynamical elastic constants, Debye-Waller factor, mean-square displacement, Debye-Waller temperature parameter and propagation velocities of elastic waves of some fcc f-shell metals La, Yb, Ce, and Th. The contribution of the s-like electrons is calculated in the second-order perturbation theory for the model potential while d- and f-like electron is taken into account by introduction of repulsive short-range Born-Mayer term. Very recently proposed screening function due to Sarkar et al. has been used to obtain the screened form factor. The parameter of the potential is evaluated by zero pressure condition. Which is independent of any fitting procedure. An excellent agreement between theoretical investigations and experimental findings prove the ability of the potential for d- and f-shell metals exclusively.     

Elastic constitutive laws for incompatible crystalline media: the contributions of dislocations,disclinations and G-disclinations

Linear higher-grade higher-order elastic constitutive laws for compatible (defect-free) and incompatible (containing crystal line defects) media are presented. In the proposed model, the free energy density of a body subjected to elastic deformation under the action of surface tractions, moments or hyper-traction tensors (second-order tensors whose anti-symmetric part corresponds to moments) has contributions coming from the first two gradients of displacements. Thermodynamic considerations reveal that only the symmetric component of the gradient of elastic displacement, i.e., compatible elastic strain tensor, and the anti-symmetric component of the second gradient of elastic displacement, i.e., compatible third-order elastic curvature tensor, contribute to the free energy density during compatible deformation of the body. The line crystal defect contributions are accounted for by incorporating the incompatible components of elastic strains, curvatures and symmetric 2-distortions as state variables of the free energy density. In particular, the presence of generalized disclinations (G-disclinations) is acknowledged when the medium is subjected to surface hyper-traction tensors having a non-zero symmetric component along with surface-tractions on its boundary. Mechanical dissipation analysis provides for the coupling between the Cauchy stresses and third-order symmetric hyper-stresses. The free energy density and elastic laws for a defect-free and line crystal defected medium are proposed in a linear setting. In the special case of isotropy, the cross terms between elastic strains and curvatures contribute to the free energy density through a single elastic constant. More interestingly, the Cauchy and couple stresses are found to have contributions coming from both, elastic strains and curvatures.     

Anchoring properties of substrate with a grating surface

The anchoring properties of substrate with a grating surface are investigated analytically. The alignment of nematic liquid crystal (NLC) in a grating surface originates from two mechanisms, thus the anchoring energy consists of two parts. One originates from the interaction potential between NLC molecules and the molecules on the substrate surface, and the other stems from the increased elastic strain energy. Based on the two mechanisms, the expression of anchoring energy per unit area of a projected plane of this grating surface is deduced and called the equivalent anchoring energy formula. Both the strength and the easy direction of equivalent anchoring energy are a function of the geometrical parameters (amplitude and pitch) of a grating surface. By using this formula, the grating surface can be replaced by its projected plane and its anchoring properties can be described by the equivalent anchoring energy formula.     

A Study of Intermediate Energy Proton-^16O Elastic Scattering Based on the α-Particle Model

In the framework of KMT multiple scattering theory, an optical potential for the intermediate energy proton-160 elastic scattering is presented based on the α particle model of 160. The differential cross sections, the analyzing powers, and the total cross sections of the intermediate energy proton-160 scattering have been calculated by using the obtained optical potential. The main features of the measured angular distributions of the cross section and the analyzing power can be well described. The calculated total cross sections are in good agreement with the experimental data at energies below 0.7 GeV and underestimate the data about 8% at higher energies.     

Theoretical study of structural energy, phonon spectra, and elastic constants of Rh and Ir

The transition metal pair potential (TMPP) is used to study band structure energy of Rh and Ir. Both metals are found to be most stable in fcc structure down to atomic volume 0.5V ₀. The pressure at 0.5V ₀ is found to be 5.235 Mbar and 9.216 Mbar in Rh and Ir, respectively. The TMPP is also used to study other properties of these metals like cohesive energy, phonon frequencies at observed volume. The bulk moduli and elastic constants of these metals at observed volume are calculated by including the volume contribution.     

Lower Energy α Elastic Scattering on ^20Ne and Anomaly of α＋^20Ne Scattering System

The α+²⁰Ne elastic scattering angular distributions at lower incident energies of Eα= 12.7--31.1 MeV have been analyzed by using the α-folding potential based on the α+¹⁶O structure model of the ²⁰Ne nucleus. The α-folding potential with a standard Woods-Saxon type imaginary part, can reasonably describe experimental cross sections and the anomalous large angle scattering (ALAS) features. The anomaly of the α+²⁰Ne scattering system is further confirmed in the lower incident energy region.