关于Kane难题的一种解决方案  

A Solution Scheme to Kane Difficult Question

作　　者：张九铸 Zhang Jiuzhu(Longmen School of Jinchang City,Jinchang,Gansu 737100)

机构地区：[1]金昌市龙门学校,甘肃金昌737100

出　　处：《物理通报》2021年第10期86-89,共4页Physics Bulletin

摘　　要：两个刚体的摩擦碰撞,存在所谓Kane难题,即有时算出的系统动能损失为负.文章指出,这是由于问题给出的运动学条件、几何条件、动摩擦因数和恢复系数,往往不足以确定刚体在碰撞过程各阶段的受力或各力关系,甚至库仑摩擦定律不再适用.鉴于此,引入了“切向恢复系数k”概念,即二碰撞点的最终切向相对速度与初始切向相对速度之比,导出了针对两个做平面平行运动的刚球在碰撞过程中的动能损失计算式,据此及能量守恒定律给出了k值的范围及物理意义,避免了动能损失小于零的结果.For the collision of two rigid bodies with friction between them,there is the so called Kane problem,i.e.,sometimes the kinetic energy loss of the system calculated is negative.This paper points out that it is because the kinematic conditions,geometric conditions,dynamic friction coefficient and restitution coefficient given in the problem are often not enough to determine the force or the relationship between the forces in each stage of the collision process,and even Coulomb's law of friction sometimes doesn't apply at all.In view of this,this paper introduces the concept of"tangential coefficient of restitution k",which is the ratio of the final tangential relative velocity to the initial tangential relative velocity of the two collision points,and derives the formula of the kinetic energy loss in the collision process for two spheres moving in parallel.Based on this and the energy conservation law,the value range of k is given to avoid the result where the kinetic energy loss is less than zero.

关 键 词：Kane难题 碰撞 动能损失 切向恢复系数 

分 类 号：O313.4[理学—一般力学与力学基础]