手推车上坡的数学模型  

The Mathematical Model on Handcart Being Pulled to Upslope

作　　者：王有文[1] 

机构地区：[1]太原理工大学阳泉学院,山西阳泉045044

出　　处：《忻州师范学院学报》2014年第2期1-3,13,共4页Journal of Xinzhou Teachers University

摘　　要：当推着载有重物的手推车上坡时,人们习惯于走直道,实践证明,走弯道上坡往往更省劲,没有人从理论上对此进行过探讨。为此,文章首先建立了人推车直接上坡的简单数学模型,求出了人克服重力所做的功和功率的表达式;其次建立了人推车走"之"字型路线上坡的数学模型,由物理学和高等数学知识求出功、功率和路程的表达式,依据高等数学知识求出一个最佳路线对应的角度;最后分析了不同范围的推力对应的最佳上坡路线。A person is habit to pull a handcart to upslope directly when the handcart is loading heavy stuff,but it is easier when a handcart is pulling to upslope directly than indirectly,none has explored it in theory. In this paper,a simple mathematical model on the handcart being pulled to upslope directly is firstly established,expressions on the work and power which are produced by the person are obtained; secondly,such mathematical model,when the handcart is being pulled to upslope by the way like Chinese word Zhi,is established,expressions on the work and power and distance are given in the light of theory on physics and advanced mathematics,an angle about best way to upslope is worked out; at last,every kind of best way to upslope is analyzed in terms of different scope of pulling forces.

关 键 词：手推车 坡面 摩擦力 功 功率 数学模型 

分 类 号：O151.21[理学—数学]