密立根油滴实验中的布朗运动

在进行密立根油滴实验时,如果选择的油滴过小,油滴会有明显的布朗运动,造成测得的下落时间与理想下落时间存在偏差.本文对密立根油滴实验中油滴的下落问题进行了实验观察和理论研究,并基于朗之万理论,求解了描述油滴运动的随机微分方程.通过引入单次下落时间偏差和多次下落时间偏差分别考察了油滴布朗运动的剧烈程度以及布朗运动对油滴下落时间的影响.结果表明,实验中由于实验次数有限,当油滴比较小时油滴的布朗运动对于实验的影响仍然需要考虑.     

初始角度对平板自由下落运动的影响

平板的自由下落是一个经典的流体力学-动力学耦合问题,且具有明显的非线性特性.针对二维平板自由下落的非线性特性,文章通过耦合求解N-S方程和运动方程,以期认识其非线性特征.从不同初始角度对平板自由下落状态和轨迹的影响出发,分析了运动状态的相轨线和频谱特性,以及其中的非线性系统特征.研究发现,在平板自由下落初期,不同初始角度下平板呈现不同的运动状态和轨迹,常为非周期性摆动或小幅翻滚运动.在自由下落后期,平板自由下落最终呈现周期性摆动或翻滚运动,运动模态归为一致,初始角度对该模态没有影响.      

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.     

又一个形式的趋稳运动

在有关教材中讨论过物体下落这类运动.如图1所示,物体受到动力F和阻力f,F不变(在下落运动中F=mg),f与速度v成正比,f=kv是变力.     

走向统一的自然力天上力与地上力的统一(Ⅱ)

 地上运动,主要是物体的运动,例如,人抛物、马拉车、石下落、弦振动等.现在我们知道,人抛物的力、马拉车的力、绳子和弦的张力等,都是分子间力,也就是有效电磁力,只有导致物体垂直下落的地心吸引力才是我们所要讨论的与天上力对应的地上力,因此,本节主要讨论与物体垂直下落有关的自由落体运动和平抛运动.     

马格努斯效应与空竹的下落运动

简单介绍马格努斯效应,研究绕水平轴旋转的空竹的下落运动轨迹,并与赤道附近的自由落体、水平磁场中带电球的下落运动对比.     

堆积链条下落过程中的机械能分析

利用动量定理可计算出链条堆在下落过程中的速度,结果表明在这个下落过程中链条的机械能不守恒。链条堆下落的一个重要特点就是下落部分会带动静止部分一起运动。本文认为正是这个特点,链条堆在下落过程中会有机械能损失,机械能不守恒。并利用运动物体带动静止物体一起运动的牵引模型,分析了在此下落过程中机械能损失的机制。利用这种损失机制,计算得到链条在整个下落过程中的能量损失。计算结果与利用动量定理算得的能量损失一致。     

落球法测液体黏度的深入研究

利用流体力学的知识对小球下落计时起点的确定进行理论推导, 并给出了达到终极速度之前小球运动 的距离与速度之间的函数关系, 以及不同半径的小球达到终极速度时其半径与下落距离的关系     

折叠链条下落过程的动力学分析

本文从理论分析和实验模拟两方面对三种不同情况下的折叠链条下落运动进行研究。假设下落链条的机械能不变,建立动力学模型分析链条下落的问题。得出自由端的运动方程后,利用Mathematica模拟出三种初始条件下折叠链条自由端下落距离随时间变化的曲线图。将理论与实验对比分析,两者曲线基本吻合。理论和实验都表明,折叠链自由端的下落并不是自由落体运动。     

雨滴下落收尾速度的一般讨论

运用流体力学的相关知识,分析了雨滴下落所受的粘性阻力和压差阻力,考虑雨滴在空气中下落半径增加对雨滴速度的影响,得出了雨滴下落速度和雨滴半径的关系,对雨滴下落收尾速度进行了一般讨论.     

The Shell of Incoherent Charged Matter Falling onto a Charged Rotating Black Hole

The motion of the shell of charged testparticles falling radially from rest at infinity withzero total angular momentum onto a Kerr–Newmanblack hole is studied. The shell, initially spherical,becomes prolate along the axis of symmetry of the holeduring the fall. The shape of the shell from theviewpoint of distant observers is characterized by meansof the photons moving along geodesics of the outgoing principal null congruence. The motion of theshell is examined analytically for large distances andnear the horizon. In the special case, when at largedistances of the hole the attractive Newtongravitational force is compensated by the repulsive Coulombforce, the complete motion is given explicitly in termsof elementary functions.     

Relativity,thermodynamics and entropic forces

A recent assertion that inertial and gravitational forces are entropic forces is discussed. A more conventional approach is stressed herein, whereby entropy is treated as a result of relative motion between observers in different frames of reference. It is demonstrated that the entropy associated with inertial and gravitational forces is dependent upon the well known lapse function of general relativity. An interpretation of the temperature and entropy of an accelerating body is then developed, and used to relate the entropic force to Newton's second law of motion. The entropic force is also derived in general coordinates. An expression of the gravitational entropy of in‐falling matter is then derived by way of Schwarzschild coordinates. As a final consideration, the entropy of a weakly gravitating matter distribution is shown to be proportional to the self‐energy and the stress‐energy‐momentum content of the matter distribution.     

The falling cat as a port-controlled Hamiltonian system

In this article, the falling cat is modeled as two jointed axial symmetric cylinders with arbitrary twist under the constraint of the vanishing total angular momentum. As a control system with the constraint taken into account, this model is formulated as a port-controlled Hamiltonian system defined on the cotangent bundle of the shape space for the jointed cylinders. A control is then designed as a function on the cotangent bundle, according to a standard procedure. Thus, the equations of motion are determined on the cotangent bundle together with the control. The whole motion as a vibrational motion of the falling cat is obtained after integrating the constraint equation of the vanishing total angular momentum. An example of the falling cat is given in which the model turns a somersault to approach a target state in equilibrium with an expected rotation after finishing a vibrational motion.     

Concurrence of mass and energy density for conservative and dissipative systems

The falling body velocity is 00000 when mass and energy are interdependent. The overestimated 00000 prevails when mass and energy are separately independent. The falling time is found to be greater by a factor of 00000. A consistent account of the laws of motion from Galileo to Newton is made possible by using E = mv ² for conservative and dissipative systems. By the same token, the equivalence of energy and mass can be used for the mathematical assessment of gravitational waves at any velocities and not just at the speed of light. The personalized units should be replaced by the “energy density unit” to avoid ambiguities. The key step is the application of the Hookean “force” in conjunction with the work done as energy. The equivalence of mass and energy at any velocity were derived by using Ideomechanics, which is a mathematized verion of I-Ching. Gravitational waves are intimately related to the entanglement of multi-atom space-time.     

Transport in a ratchet with spatial disorder and time-delayed feedback

A Brownian motor with Gaussian short-range correlated spatial disorder and time-delayed feedback is investigated. The effects of disorder intensity, correlation strength and delay time on the transport properties of an overdamped periodic ratchet are discussed for different driving force. For small driving force, the disorder intensity can induce a peak in the drift motion and a linear increasing function in diffusion motion. For large driving force, the disorder intensity can suppress the drift motion but enhance the diffusion motion. For both small and large driving forces, the correlation strength of the spatial disorder can enhance the drift motion but suppress the diffusion motion. While the delay time can reduce the drift motion to a small value and enhance the diffusion motion to a large value. The drift motion increases as the driving force increases. However, the diffusion motion is either decreases or only increases slightly when the driving force increases.     

电磁阻尼落体运动实验仪研究

设计了电磁阻尼落体实验仪,可以定量研究受电磁阻尼的落体运动过程,在不同的阻尼条件下验证速度和路程公式,并计算出阻尼系数.     

利用Tracker视频分析软件测量液体黏度

在落球法测量液体黏度中利用Tracker视频分析软件捕捉分析小球下落轨迹,减小了实验中诸多不确定因素带来的测量误差,使数据处理更为直观、准确.结果表明此方法能准确测量小球的收尾速度,而且可以对现有实验内容进行扩展.     

气温和颗粒密度对声场中颗粒动力学影响的数值模拟

综合考虑黏性夹带力、Basset力、虚拟质量力和压力梯度力,建立颗粒在声场中的动力学模型,利用变步长四阶RungeKutta算法和二阶隐式Adams插值算法对颗粒的受力和运动进行数值模拟。将模拟和实验得到的颗粒运动特性进行对比,验证数值模拟的正确性。在此基础上,研究气温和颗粒密度对颗粒动力学的影响规律。结果表明,黏性夹带力对颗粒运动起主导作用;气温升高,压力梯度力与黏性夹带力之间的相位差减小,Basset力、虚拟质量力与黏性夹带力之间的相位差增大。研究还发现,气温较低时,颗粒密度对颗粒运动有重要影响,夹带系数随着密度的增加而迅速下降;气温较高时,颗粒密度对颗粒运动的影响较小,颗粒位移振幅和夹带系数相对低温时明显增加。