利用取帧技术在气轨上验证变力做功

在气垫导轨上研究了滑块在变力作用下的运动规律.利用质量较为均匀的细铁链的下落改变作用在滑块上的力,利用摄像机记录随铁链下落滑块的运动过程,通过取帧技术获得滑块运动的位移、速度和时间关系.     

对变质量问题的实验研究

对变质量问题的实验研究王晓耕，郝利（承德石油高等专科学校，０６７０００）在大学物理教学和习题中常遇到变质量问题，我们在气垫导轨的滑块上增加了载沙槽装置，在导轨上端悬挂一沙漏斗，当载沙槽、滑块组成的系统在外力作用下沿导轨运动时，漏斗中的沙子匀速地落在运...     

对变加速系统力学规律的实验研究

在普物实验中,气轨上通常研究的是恒力作用下的匀加速运动,学生对变力情况下的力学规律的研究一般仅限于理论探讨的范畴。笔者通过在气垫导轨上增加一个支板作为附件,利用它达到改变作用于滑块上力的方向的目的,使对恒力作用下的匀加速系统力学规律的研究转化为变力作用下的变加速系统力学规律的研究.     

气垫导轨上物体受变力作用运动规律的研究

主要研究物体在气垫导轨上受变力作用下的运动规律。用粗细均匀的刚性尼龙绳来改 变物体的受力大小,使其在变力作用下运动,并且通过实验获得数据来验证实验原理是 否一致。     

处理变力做功问题的几种方法

做功的一般表达式为W=Fscosθ,F是恒力.如果力是变力,就不能套用这个公式.笔者根据自己的教学实践,针对不同的题设条件,总结出以下几种求变力做功的方法.1 用平均力代替变力求变力的功 当变力与质点位移大小成线性关系时,平均力F=(F1+F2)/2,变力对质点所做的功,在数值上等于平均力做的功.     

落链实验研究

在物理习题中,人们通常把落链作为一个变力或变质量的问题进行研究,可否把金属链的落下问题通过实验进行研究呢?笔者用一均匀的金属链与气垫导轨组成的变质量系统,对变质量问题进行了研究。 一,实验装置及原理 图1为实验原理图。在图中,气垫导轨一端的底部垫有高h的垫块,滑块上的系线越过定滑轮与金属链相连,初始金属链全部落在地上,当滑块在重力作用下,沿导轨向下运动时,金属链被细线拉起,从而使系统质量发生变化。     

变质量完整力学系统的高阶运动微分方程

从Мещерский方程出发,建立变质量力学系统的高阶D'Alembert-Lagrange原理,导出变质量完整力学系统的各类高阶运动微分方程.结果表明,它们扩充和优化了完整力学的相关理论. 关键词： 变质量完整力学系统 高阶力变率 高阶D'Alembert-Lagrange原理 高阶运动微分方程     

在气轨上有关变力问题的实验

本文陈述了如何在气垫导轨上借助于柔软的金属细链来验证变力情况下的动能定理、动量定理及物体的运动方程等力学规律．并详细地叙述了实验原理，介绍了实验装置及实验方法，分析概括了产生实验误差的原因． 在普通物理学实验中，对变力问题的研究一直是一个非常棘手的问题．我们曾借助于柔软的金属细链与气垫导轨结合起来，来研究变力问题，很好地验证了变力情况下的力学规律．     

用EXCEL模拟变加速运动的尝试

利用"微元"思想借助Excel软件的计算功能推演出在变力作用下的运动规律,并可以描绘出各物理量之间的关系图像.列举了三个实例,简谐运动、洛伦兹力作用下的圆周运动、带电小球在复合场中的运动.     

一类变力 两种表现——关于"F=kV"类变力的讨论

在解决物理习题中,经常涉及两类变力:带电粒子垂直于匀强磁场方向运动时受到的洛伦兹力和闭合电路的部分导体在垂直切割磁感线时受到的安培力.这两种变力除了都是磁场力这一性质上的联系外,还具有一个重要的共同点,即力的大小都与速率成正比.     

Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system

Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system are investigated. Appell equations and differential equations of motion for a variable mass holonomic system are established. A new expression of the total first derivative of the function with respect of time t along the systematic motional track curve, and the definition and the criterion of Mei symmetry for Appell equations under the infinitesimal transformations of groups are given. The expressions of the structural equation and Mei conserved quantity for Mei symmetry in Appell are obtained. An example is given to illustrate the application of the results.     

Noether‘s theorem of a rotational relativistic variable mass system

Noether‘s theory of a rotational relativistic variable mass system is studied.Firstly,Jourdain‘s principle of the rotational relativistic variable mass system is given.Secondly,on the basis of the invariance of the Jourdain‘s principle under the infinitesimal transformations of groups,Noether‘s theorem and its inverse theorem of the rotational relativistic variable mass system are presented.Finally,an example is given to illustrate the application of the result.     

相对运动变质量完整系统的共形不变性与守恒量

研究了相对运动变质量完整系统的共形不变性与守恒量,提出了该系统共形不变性的概念,推导出了相对运动变质量完整系统的运动微分方程具有共形不变性并且是 Lie 对称性的充要条件,借助规范函数满足的结构方程导出系统相应的守恒量,并给出应用算例. 关键词： 变质量 相对运动 共形不变性 守恒量     

Effects of variable properties on MHD heat and mass transfer flow near a stagnation point towards a stretching sheet in a porous medium with thermal radiation

The effect of variable viscosity and thermal conductivity on steady magnetohydrodynamic(MHD) heat and mass transfer flow of viscous and incompressible fluid near a stagnation point towards a permeable stretching sheet embedded in a porous medium are presented,taking into account thermal radiation and internal heat genberation/absorbtion.The stretching velocity and the ambient fluid velocity are assumed to vary linearly with the distance from the stagnation point.The Rosseland approximation is used to describe the radiative heat flux in the energy equation.The governing fundamental equations are first transformed into a system of ordinary differential equations using a scaling group of transformations and are solved numerically by using the fourth-order Rung-Kutta method with the shooting technique.A comparison with previously published work has been carried out and the results are found to be in good agreement.The results are analyzed for the effect of different physical parameters,such as the variable viscosity and thermal conductivity,the ratio of free stream velocity to stretching velocity,the magnetic field,the porosity,the radiation and suction/injection on the flow,and the heat and mass transfer characteristics.The results indicate that the inclusion of variable viscosity and thermal conductivity into the fluids of light and medium molecular weight is able to change the boundary-layer behavior for all values of the velocity ratio parameter λ except for λ = 1.In addition,the imposition of fluid suction increases both the rate of heat and mass transfer,whereas fluid injection shows the opposite effect.     

变质量非完整系统的Lagrange对称性与守恒量

本文研究变质量非完整系统的Lagrange对称性, 给出变质量非完整系统Lagrange对称性的判据, 得到变质量非完整系统Lagrange对称性导致的守恒量及其存在的条件, 并举例说明结果的应用.     

Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion

Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion are studied.The definition and criterion of the Mei symmetry of Appell equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups are given.The structural equation of Mei symmetry of Appell equations and the expression of Mei conserved quantity deduced directly from Mei symmetry for a variable mass holonomic system of relative motion are gained.Finally,an example is given to illustrate the application of the results.     

Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion

Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from Lie symmetry for a variable mass holonomic system of relative motion is obtained. An example is given to illustrate the application of the results.     

相对运动变质量力学系统Appell方程的广义Lie对称性导致的广义Hojman守恒量

研究相对运动变质量完整系统Appell方程的广义Lie对称性及其直接导致的广义Hojman守恒量.在群的无限小变换下,给出相对运动变质量完整系统Appell方程广义Lie对称性的确定方程;得到相对运动变质量完整系统Appell方程广义Lie对称性直接导致的广义Hojman守恒量的表达式.最后,利用本文结果研究相对运动变质量完整约束的三自由度力学系统问题.     

黏弹性问题的改进的复变量无单元Galerkin方法

基于改进的复变量移动最小二乘法,提出了二维黏弹性问题的改进的复变量无单元Galerkin方法.采用改进的复变量移动最小二乘法建立形函数,根据Galerkin积分弱形式建立求解方程,并用罚函数法施加本质边界条件,推导了二维黏弹性问题的改进的复变量无单元Galerkin方法的计算公式.最后,通过实际算例,将计算结果与复变量无单元Galerkin方法及有限元法的结果进行了对比,说明了本文方法具有更高的计算精度和计算效率.     

Unified symmetry of nonholonomic mechanical systems with variable mass

Based on the total time derivative along the trajectory of the system the definition and the criterion for a unified symmetry of nonholonomic mechanical system with variable mass are presented in this paper. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, are also obtained. An example is given to illustrate the application of the results.