牛顿第三定律的疑惑与修正

牛顿第三定律:相互作用的两个物体之间的作用力和反作用力总是大小相等,方向相反,作用在同一条直线上。

Feynman 说:

“Newton told us only two things about the nature of forces. In the case of gravitation, he gave us the complete law of the force. In the case of the very complicated forces between atoms, he was not aware of the right laws for the forces; however, he discovered one rule, one general property of forces, which is expressed in his Third Law, and that is the total knowledge that Newton had about the nature of forces—the law of gravitation and this principle, but no other details.

This principle is that action equals reaction.

What is meant is something of this kind: Suppose we have two small bodies, say particles, and suppose that the first one exerts a force on the second one, pushing it with a certain force. Then, simultaneously, according to Newton’s Third Law, the second particle wnill push on the first with an equal force, in the opposite direction; furthermore, these forces effectively act in the same line. This is the hypothesis, or law, that Newton proposed, and it seems to be quite accurate, though not exact (we shall discuss the errors later). ”
你也可看https://www.wired.com/ 的A Closer Look at Newton’s Third Law

“————–Let me make something clear. Isaac Newton had it tough. Here he is trying to make a model that describes what forces do to objects. However, he just doesn’t have all the words we have – like momentum, acceleration, velocity.Fortunately, there is an online translation of the original works of Newton. Here is an older translation into English of Newton’s The Mathematical Principles of Natural Philosophy (volume 1).The part about the Third Law says:To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.He also writes:
If you press a stone with your finger, the finger is also pressed by the stone.This above example could indicate that he did not mean the stone and the finger have to move. I would suggest that perhaps Newton meant the word “action” to really mean “force”. However, he later uses the word force so I’m not exactly sure of his intentions. Perhaps by “action” he means a force that actually does something. I don’t know.Oh, and it seems Newton does use the words momentum and velocity (if you read more of the passage). Maybe he was just trying to be poetic with his use of the words “action” and “reaction”.”

此”第三定律“更确切是一个力传送原理———应用于接触并相对静止的物体。在大一的statics(静力学)里的刚体的平衡系统里,”第三定理“就用来创建模型。但是在相对运动的物体呢?

以上图的物体与地上是相对静止的,你的手指对物体施加的力的大小=于你的手指的反作用力(指力)的。基于对此”力传送原理”的认识,促成我完成《行星齿轮的动力学》并发表在《知识创新与应用》2020 年 第12 期。*

以上图的物体与地上是相对运动的,你的手指对物体施加的力的大小若是等于于你的手指的反作用力(指力),那你的手指对物体施加的力只是用来抵抗摩檫力,物体会以等速运动。
你的手指对物体施加的力的大小若是大于动摩擦力,那物体会有一个加速度,而于你的手指的反作用力(指力)等同于动摩擦力。

以上两个图在Y轴方向,物体与地上是相对静止的,所以作用于物体的重力的大小等于于物体的反作用力(重力)的大小。

再来看两个相对接触的转动圆柱的力传送模型,也就是齿轮的力传送机制。以上图取自我的《行星齿轮的动力学》

圆柱 A 与圆柱 B在接触点是相对静止的。圆柱 A 在接触点施加力, Ftr 在圆柱B 身上 ,而同时会有一个同样大小的反作用力在圆柱 A身上。

切线力,Ft 促成圆柱B 旋转,我们可以把Ftr =Ft 因为Ѳ 很小。而圆柱 A半径是rA,圆柱 B半径是rB

扭矩比= Ftr . rB / Ftr . rA = rB /rA

而角速度比是扭矩比的倒数

以上的推导是以我对第三定律修正后推导出来的——”第三定律更确切是一个力传送原理———应用于接触并相对静止的物体,相互作用的两个物体之间的作用力和反作用力总是大小相等,方向相反,作用在同一条直线上。”

*为何写《行星齿轮的动力学》?
就如newgnay在网站:知乎    《行星齿轮原理的详细图文介绍(含超详细的公式推导)》的开场白:  

这几天我对行星齿轮的原理很感兴趣,但看了知乎上(以及百度到的)很多关于行星轮原理的介绍后,发现它们不是太过简略就是太过专业(不加推导地使用了太多专业公式),以至于连我这个凝聚态理论专业的研究人员也看不懂。无奈,我只得根据网上找到的行星齿轮结构,自已推导了行星齿轮的工作原理,在此给大家分享一下。

而若要看我的论文《行星齿轮的动力学》全文按以下link
https://limsaukong.com/%e8%a1%8c%e6%98%9f%e9%bd%bf%e8%bd%ae%e7%bb%84%e7%9a%84%e5%8a%a8%e5%8a%9b%e5%ad%a6-dynamics-of-planetary-gear-set/

Published by limsaukong

Mechanical engineer,amateur photographer,poetry written by me (chinese) is the another method to express emotion found in photo taken by me.

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