关于落链问题的解的分析

Analyse the answer to the question of falling chain

在部分理论力学论著中，对落链这个典型的变质量问题解答欠妥，主要是在分析变质量系统受的外力Ｆ时，没有包括分离链元受到的地板的冲击力；错误地分析了分离链元的速度ｕ及运动过程中落链的质量ｍ（ｔ）本文在分析以上问题的基础上，从变质量物体的动力学方程出发，根据链条质量变化的规律及落地链元的受力特点，得出了落链问题的正确解答，分析了变质量问题与不变质量问题的根本区别。

In some book of theoretical mechanics,the solution to the question of falling chain which is a typical variable- mass material was not entirely proper. The main reason was that theimpulse force from the floor that the separating ele-ment chain received was not included when thev analvsed the external forces that the variable- mass system received,so that the speed u of separating ele-ment chain and the m(t) of falling chain in the course of movement were anal-ysed mistakenly. In this article , after analyzing the above mentioned question,in the light of the kinetic equation of variable-mass material , according to the law of the variation of the mass of chain and the peculiarity of floor-element-chain in receiviing the force, the proper solution to the question offalling chain is vielded and in addition the essential difference between the problem of vari-able-mass and that of unvariable-mass is analyzed.