堆沙成锥体作功的微元解

针对计算物体在某一过程中的作功问题,首先对以小圆柱薄片作为求体积的微元给予肯定,然后指出了该方法的不当之处,并用计算结果说明小圆柱簿片这种堆沙方式不符合实际意义。堆沙过程中,沙堆是从小圆锥到大圆锥逐渐堆起来的,小圆锥高度在一直不断增高的同时小圆锥的厚度也增加了,进而介绍了另一种体积微元,并对以上2种方式选取的体积微元进行求积验证。在此基础上,根据变力作功的意义,进一步明确按不同方式选取的体积微元求积的结果可能相同,但由体积微元形成作功微元之后,所提出方法的积分结果更加符合实际。

Infinitesimal elements solution of work done by piling sand into cone

In order to get the work done by objects in a certain process,this paper gives the affirmation to the selection of small cylindrical volume of micro-flakes as the infinitesimal,and points out the method is inappropriate.Moreover,calculation results are given so as to show that this approach of piling is impractical and unrealistic.In the process of piling sand,the sand is piled up gradually from small cone to large one,during which the height of small cone,as well as the thickness,is increased.Therefore,ano...