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The Concept of Potential Energy Theorem Should Not Be Introduced or Established in the Compilation of Physics Textbooks and Research on Physics Science
DOI: 10.12677/mp.2024.142007, PDF, HTML, XML, 下载: 79  浏览: 118

Abstract: Introduce the scientific nature of physical concepts, the expression of kinetic energy theorem, the introduction of potential energy, the relationship between work done by conservative forces and corresponding potential energy changes, as well as the introduction and inference process of so-called potential energy theorems published on some self media platforms. By analyzing the specificity of potential energy corresponding to various conservative forces, it is demonstrated that the superposition of potential energy or potential energy changes with different essential properties is meaningless, further demonstrating that the introduction of potential energy theorem does not have rigorous and serious scientific significance.

1. 引言

2. 物理概念的科学性

2.1. 物理概念的内涵

${c}_{\left(比热容\right)}=\frac{{Q}_{\left(热量\right)}}{{m}_{\left(质量\right)}\cdot \Delta {t}_{\left(温度变化\right)}}$ (1)

2.2. 物理概念的外延

2.3. 物理概念的特点

3. 动能定理的表述

$\Delta {E}_{\text{k}}=\frac{1}{2}m{v}_{2}^{2}-\frac{1}{2}m{v}_{1}^{2}={E}_{\text{k}2}-{E}_{\text{k}1}={W}_{合外力}={W}_{1}+{W}_{2}+{W}_{3}+\cdots +{W}_{n\text{\hspace{0.17em}}-1}+{W}_{n}$ (2)

Figure 1. Theorem of kinetic energy

4. 保守力及其做功的特点

4.1. 保守力和非保守力

4.2. 几种常见保守力做功的情况

1) 重力做功

${W}_{重力}=\int mg\cdot \text{d}\text{ }r=-mg\text{ }k\cdot \int \left(\text{d}\text{ }x\text{ }i+\text{d}\text{ }y\text{ }j+\text{d}\text{ }z\text{ }k\right)=-mg{\int }_{{z}_{1}}^{{z}_{2}}\text{d}\text{ }z=mg\left({z}_{1}-{z}_{2}\right)$ (3)

Figure 2. Gravity potential energy

2) 万有引力做功

${W}_{万有引力}={\int }_{A}^{B}-G\frac{{m}_{\text{ }1}{m}_{2}}{{r}^{3}}r\cdot \text{d}r={\int }_{A}^{B}-G\frac{{m}_{\text{ }1}{m}_{2}}{{r}^{2}}|\text{d}r|\mathrm{cos}\alpha =-G{m}_{\text{\hspace{0.17em}}1}{m}_{2}{\int }_{A}^{B}\frac{\text{d}r}{{r}^{2}}=G{m}_{\text{\hspace{0.17em}}1}{m}_{2}\left(\frac{1}{{r}_{B}}-\frac{1}{{r}_{A}}\right)$ (4)

Figure 3. Gravity doing work

3) 保守弹力做功

${W}_{保守弹力}={\int }_{A}^{B}-k\text{ }x\text{ }i\cdot \left(i\text{d}x\right)=-{\int }_{A}^{B}k\text{ }x\text{ }\text{d}x=\frac{1}{2}k\text{ }{x}_{1}^{2}-\frac{1}{2}k\text{ }{x}_{2}^{2}$ (5)

Figure 4. Conservative elastic force doing work

5. 势能及其变化

5.1. 势能的引入

${E}_{\text{P}Q}={W}_{Q\to O}={\int }_{Q}^{O}F\cdot \text{d}r$ (6)

${E}_{\text{p}\left(重力势能\right)}=m\text{ }g\text{ }z$ (7)

${E}_{\text{p}\left(引力势能\right)}=-G\frac{{m}_{\text{\hspace{0.17em}}1}{m}_{2}}{r}$ (8)

${E}_{\text{p}\left(弹性势能\right)}=\frac{1}{2}k\text{ }{x}^{2}$ (9)

${E}_{\text{p}\left(库仑力电势能\right)}=-k\frac{{q}_{1}{q}_{2}}{r}$ (10)

5.2. 势能的变化

${W}_{A\to B}={\int }_{A}^{B}F\cdot \text{d}r={E}_{\text{p}\text{\hspace{0.17em}}A}-{E}_{\text{p}\text{\hspace{0.17em}}B}$ (11)

$\Delta {E}_{\text{p}}={E}_{\text{P}B}-{E}_{\text{P}A}=-{\int }_{A}^{B}F\cdot \text{d}r$ (12)

6. 准势能定理的引入欠科学性

6.1. 准势能定理的表述摘录

${W}_{21}=\frac{1}{2}{m}_{1}{{v}^{\prime }}_{1}^{2}-\frac{1}{2}{m}_{1}{v}_{1}^{2}$ (13)

${W}_{12}=\frac{1}{2}{m}_{2}{{v}^{\prime }}_{2}^{2}-\frac{1}{2}{m}_{2}{v}_{2}^{2}$ (14)

${W}_{总}={W}_{21}+{W}_{12}=\left(\frac{1}{2}{m}_{1}{{v}^{\prime }}_{1}^{2}+\frac{1}{2}{m}_{2}{{v}^{\prime }}_{2}^{2}\right)-\left(\frac{1}{2}{m}_{1}{v}_{1}^{2}+\frac{1}{2}{m}_{2}{v}_{2}^{2}\right)$ (15)

$\Delta {E}_{\text{p}}=-\Delta {E}_{\text{k}}=\left(\frac{1}{2}{m}_{1}{v}_{1}^{2}+\frac{1}{2}{m}_{2}{v}_{2}^{2}\right)-\left(\frac{1}{2}{m}_{1}{{v}^{\prime }}_{1}^{2}+\frac{1}{2}{m}_{2}{{v}^{\prime }}_{2}^{2}\right)$ (16)

${W}_{总}={W}_{21}+{W}_{12}=-\Delta {E}_{\text{p}}$ (17)

Figure 5. Inference of the quasi potential energy theorem

6.2. 准势能定理欠科学性

[模型1] 三个物体组成的引力场系统

${W}_{总}={W}_{21}+{W}_{12}+{W}_{\text{31}}+{W}_{\text{13}}+{W}_{32}+{W}_{23}=\left(-\underset{1↔2}{\Delta {E}_{\text{p}}}\right)+\left(-\Delta \underset{1↔3}{{E}_{\text{p}}}\right)+\left(-\Delta \underset{2↔3}{{E}_{\text{p}}}\right)$ (18)

[模型2] 两个物体组成的引力场和库仑力场复合系统

${W}_{总}=\underset{12}{\overset{引力功}{W}}+\underset{21}{\overset{引力功}{W}}+\underset{12}{\overset{库仑力功}{W}}+\underset{21}{\overset{库仑力功}{W}}=\left(-\underset{1↔2}{\overset{引力势能变化}{\Delta {E}_{\text{p}}}}\right)+\left(-\underset{1↔2}{\overset{电势能变化}{\Delta {E}_{\text{p}}}}\right)$ (19)

7. 结论

NOTES

*第一作者。

#通讯作者。

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