流动沙漏视重变化的定量研究

Quantitative study of the changing weight of flowing hourglass

研究沙漏在流动过程中视重随时间变化的问题.理论方面,从动量角度入手分析,得出视重变化量正比于动量柱(颗粒流动的区域)纵向长度的变化率,比例系数为质量流量,所得物理图像清晰,并且给出了视重随时间变化的解析式.实验方面,利用PASCO系统搭建了称量平台,巧妙地实现了视重的精密数字化测量(采样率250 Hz).实验还采用了烧断引线的方式来启动沙漏以减小误差.理论与实验较好符合,并在不同的颗粒装填量下体现出普适性.

The changing weight of the flowing hourglass is researched.The theory,from the perspective of momentum,reveals that the weight variation is proportional to the rate of change of the length of the momentum column(the region that granules flow)and the proportionality coefficient is mass flow rate.The physical image is clear,and it gives the analytic expression of changing weight.Digital measurement of weight is realized by making use of PASCO system to build a weighing platform.Burning out the rope is adopted to decrease experimental error when starting the hourglass.The theory is in good agreement with the experimental results and it shows universality under different loading quantities.