力学分析中的正号与负号  

ON THE PLUS AND MINUS SIGNS IN MECHANICS ANALYSIS

作　　者：陈奎孚[1] 何坤娜[1] Chen Kuifu He Kunna(College of Sciences #74, China Agricultural University, Beijing 100083)

机构地区：[1]中国农业大学理学院,北京100083

出　　处：《物理与工程》2017年第2期15-21,共7页Physics and Engineering

摘　　要：力学关系的矢量形式整齐简明,但手工计算往往倾向于投影的标量式。不少学生在标量分析过程中有正负号的纠结。笔者对如下学习情境中的正负号纠结进行了剖析:物理关系、运动量、功、力矩、力偶和力矢量图示。指出消除正负号纠结的关键在于是否画矢量形式的分析图。基于矢量关系的演绎不需要图示信息,但手工计算总是喜欢用图形。有图形情形下,方向相反的矢量关系会由图形显示,标量关系就无负号。理解上述原则有助于提升力学分析的教学效率。The vector form of mechanics relationship is concise and tidy whereas the projected scalar form is preferred to in manual computation. Plenty of students are frustrated with choosing plus or minus signs in scalar form computation. The frustration with plus or minus signs are investigated in the following contexts, physics relationship, kinematic quantities, work, force moment, force couple and force vector graphing. It is pointed that a key factor is wheth- er the vector diagram is drawn or not. The vector form of relationship does not necessitate a vector diagram; as a result, there is no need to consider the plus or minus sign. On the other hand, a vector diagram is preferred, especially in the case of planar problems. Concerning this case, the opposite directions of two vectors are delineated in the diagram; as a result, the minus sign should not appear in the scalar relationship. Apprehending above rules benefits the educational efficacy of force analysis.

关 键 词：力学教学 力矢量 力偶 惯性力主矢 惯性力主矩 功 运动量 阻尼振子 隔离体图 

分 类 号：O316[理学—一般力学与力学基础]