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某兴趣小组设计了一种实验装置,用来研究碰撞问题,其模型如图所示。用完全相同的轻绳将N个大小相同、质量不等的小球并列悬挂于一水平杆、球间有微小间隔,从左到右,球的编号依次为1、2、3……N,球的质量依次递减,每球质量与其相邻左球质量之比为k(k<1)。将1号球向左拉起,然后由静止释放,使其与2号球碰撞,2号球再与3号球碰撞……所有碰撞皆为无机械能损失的正碰。(不计空气阻力,忽略绳的伸长,g取10 m/s2) (1)设与n+1号球碰撞前,n号球的速度为vn,求n+1号球碰撞后的速度。(2)若N=5,在1号球向左拉高h的情况下,要使5号球碰撞后升高16h(16 h小于绳长),问k值为多少?
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