摘要
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。
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,another volume infinitesimal is introduced and quadrate verification on the volume infinitesimals selected in above two methods is conducted in this paper.On that basis,this paper further clarifies that quadrate results of volume infinitesimals selected in different methods maybe the same according to the significance of work done of variable force.However,the integration results of the proposed method might be more realistic after force infinitesimal is formed by volume infinitesimal.
出处
《沈阳师范大学学报（自然科学版）》
CAS
2011年第4期478-481,共4页
Journal of Shenyang Normal University:Natural Science Edition
基金
辽宁省教育厅科学研究资助项目(20060842)
关键词
变力作功
体积
定积分
微元素
work done of variable force
volume
definite integration
infinitesimal elements
