细绳牵引条件下二体弹性碰撞的分析与讨论

ANALYSIS AND DISCUSSION ON ELASTIC COLLISION WITH ROPE TRACTION

针对物理竞赛中出现的细绳牵引条件下小球碰撞问题,引入能量耗散,建立相应的谐振子模型,求解得到其运动学方程。结合数值计算进一步探索完全与非完全弹性牵引碰撞的动力学演化和规律,得到弹性牵引碰撞后两物体运动呈现非线性特征,并随着时间演化两物体速度趋于一致的结论;同时对质心系和其他非惯性系中分析该牵引碰撞过程也作了讨论。本文对牵引过程的动力学方程和物体运动状态随时间的演化给出了具体的定量分析,为深入研究牵引碰撞的本质规律提供一定参考价值。

The problem of the collision between two small balls with rope traction which appeared in the 1991 college students’physics contest is discussed.Considering two cases of complete elastic and incomplete elastic respectively,a harmonic oscillator model is established by introducing the energy dissipation to obtain the kinematic equation of the system.The nature of the complete and incomplete elastic traction collision is further explored by numerical simulation.It is found that the motion of the two objects exhibits nonlinear characteristics after the elastic traction collision and the velocity of the two objects tends to be consistent with the time evolution.In addition,the analysis of the traction expansion process in the mass center system and other non-inertial systems is also discussed.In this paper,the dynamic equation of the traction process and the evolution of motion state of the object with time are analyzed quantitatively,which provides a certain reference value for the in-depth study of the essential law of traction collision.