质点在球体隧道中运动的研究  

Research on the Movement of Particle in the Tunnel of Sphere

作　　者：赵春然[1] 朱孟正[1] 

机构地区：[1]淮北师范大学物理与电子信息学院,安徽淮北235000

出　　处：《吉林师范大学学报（自然科学版）》2017年第4期91-95,共5页Journal of Jilin Normal University:Natural Science Edition

基　　金：安徽省高等学校质量工程项目(2011248);淮北师范大学教研项目(jy15130)

摘　　要：质点在一个匀质的大球体的隧道中的运动呈现何种规律性,需要利用万有引力定律来分析该质点的受力情况,从而判知其运动规律并研究运动特点.万有引力定律是经典力学中一个重要的知识点,通过对质点在该球体隧道中的受力情况分析,是对该知识点综合有效的应用.运用已有的知识分析隧道中质点的受力,阐明质点所在球面以外的整个外层球壳中的物质对该质点的引力为零;而质点受到的引力作用仅是其所在位置到大球体球心为半径的球内物质的引起的.文中通过3种方法分析了处于匀质大球体内部的质点受力情况,进而研究了该质点的运动规律.研究发现:质点在大球体的沿直径或沿任意弦隧道中运动规律均是作简谐振动,振动的周期仅取决于匀质大球体的密度.It is necessary to use the law of universal gravitation to analyze the force of the particle in the homogeneous sphere in order to determine its movement law and study the characteristics of the movement. The law of universal gravitation is an important point of knowledge in classical mechanics. It is an effective application of the law about the force analysis of the particle. Using the existing knowledge to analyze the force of the particle in the tunnel,we clarify that the gravitational action of the material in the outer spherical shell outside the sphere where the particle is located is zero; and the gravitational effect between the particle and the sphere is caused only by the material within the particle＇s position to the spherical center as a radius of the ball. In this paper,three methods are used to analyze the particle force in the homogeneous sphere. And the motion law of the particle is studied. It is found that the particle in the large sphere along the diameter or along any string of tunnels are simple harmonic vibration and the vibration period only depends on the density of the large sphere.

关 键 词：质点 万有引力定律 简谐振动 

分 类 号：O313[理学—一般力学与力学基础]