简介:一、正碰撞的动能损失设发生正碰撞的两个物体的质量分别为m1、m2,碰撞前的速度分别为v1、v2,碰撞后的速度分别为v′1、v′2。正碰前,由这两个物体组成的系统的动能为E1=1/2m1v12+1/2m2v22=(m12v12+m1m2v12)/(2(m1+m2))+(m1m2v22+m22v22)/(2(m1+m2))=(m1m2(v12+v22)+(m1v1+m2v2)2-2m1m2v1v2)/(2(m1+m2))=(m1m2(v1-v2)2+(m1v1+m2v2)2)/(2(m1+m2))。参照上式,可得正碰后系统的动能为E2=1/2m1v′12+1/2m2v′22=(m1m2(v′1-v′2)2+(m1v′1+m2v′2)2)/(2(m1+m2))。于是,正碰撞过程中损失的动能可用下式表示:
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