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质点在均为时间的单值函数主动力作用下的两个力学规律OA

Two mechanical laws for a particle under the action of various active forces of single-valued functions of time

中文摘要英文摘要

推理出当作用在质点上的力均为时间t的单值函数主动力(彼此独立)时,力的独立作用原理的具体内涵为各单力单独作用时所产生的加速度的矢量和、速度增量的矢量和、位移增量的矢量和分别等于合力所产生的加速度、速度增量、位移增量;并指出该内涵的本质是这些矢量的独立性.在同样的前提下,又推理出所谓的"功的独立作用原理"的成立条件为各单力的冲量彼此间的标积之和为零;并给出两种典型的情况.最后指出做功的路径不一致、力的含义不一致是"功的独立作用原理"一般不能成立的两个原因.推理出的两个力学规律或可为基础力学教学提供一些参考.

Deduces that when the forces acting on a particle are all single-valued functions of time t and are independent of each other,the specific connotation of the principle of independent action of forces is as follows,the vector sum of the accelerations,velocity increments,and displacement increments produced by each single force acting alone is equal to the acceleration,velocity increment,and displacement increment produced by the resultant force,respectively.It also points out that the essence of this connotation lies in the independence of these vectors.Under the same premise,further deduces that the condition for the so-called"principle of independent action of work"to hold is that the sum of the scalar products between the impulses of each single force is zero;and it presents two typical scenarios.Finally,it is pointed out that inconsistent paths of doing work and inconsistent meanings of force are two reasons why the"principle of independent action of work"generally does not hold.The two mechanical laws deduced in the article may provide some reference for basic mechanics teaching.

邵云;丁宗妍;王芷琪

南京晓庄学院 电子工程学院,江苏 南京 211171南京晓庄学院 电子工程学院,江苏 南京 211171南京晓庄学院 电子工程学院,江苏 南京 211171

数理科学

力的独立作用原理"功的独立作用原理"合力单力t的单值函数

principle of independent action of force"principle of independent action of work"resultant forcesingle forcesingle valued function of t

《高师理科学刊》 2026 (5)

106-110,5

10.3969/j.issn.1007-9831.2026.05.018

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