大学物理 ›› 2017, Vol. 36 ›› Issue (4): 12-16.doi: 10.16854 /j.cnki.1000-0712.2017.04.003

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质点自由下落和上抛运动的精确解及偏移量和能量的讨论

鲍四元,沈峰,陈留凤   

  1. 苏州科技大学土木学院工程力学系,江苏苏州215011
  • 收稿日期:2016-05-31 修回日期:2016-08-30 出版日期:2017-04-20 发布日期:2017-04-20
  • 作者简介: 鲍四元( 1980—) ,男,安徽六安人,副教授,博士,主要从事力学教学工作,研究方向: 分数阶问

Accurate solutions of free-falling and up-casting problems and discussion on drift and energy

BAO Si-yuan,SHEN Feng,CHEN Liu-feng   

  1. Department of Engineering Mechanics,School of Civil Engineering,Suzhou University of Science and Technology,Suzhou,Jiangsu 215011,China
  • Received:2016-05-31 Revised:2016-08-30 Online:2017-04-20 Published:2017-04-20

摘要: 基于质点自由下落和上抛在非惯性系下的动力学微分方程,得到质点坐标的精确解,然后获得两类问题的东西方 向偏移量.得到了动能和势能的表达式,验证了运动过程中机械能守恒的特点.算例讨论了不同初始高度和不同初始速度下的 偏移量值.

关键词: 自由下落质点, 上抛质点, 非惯性系, 偏移量, 机械能

Abstract:

Based on the dynamic differential equations of a free-falling particle and an upward casting particle in the non-inertial system,the accurate solutions of the particle’s coordinates are obtained.Then the eastward and westward drift for the two problems are obtained.Expressions of the kinetic energy and potential energy are also obtained. It is demonstrated that the mechanical energy conserves to a constant during the movement. In the numerical examples,we discuss the values of drift with different initial height or initial velocity.

Key words: free-falling particle, up-casting particle, the non-inertial system, drift value, mechanical energy