195 lines
10 KiB
Markdown
195 lines
10 KiB
Markdown
## A. 19世纪理应了解（Should Know: 19th-century physics）
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### A1 经典力学与守恒
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1. **中**：请用一句话解释牛顿三定律，并各给一个日常例子（不要只背定义）。
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**EN**: In one sentence each, explain Newton’s three laws of motion and give one everyday example for each (avoid mere recitation).
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2. **中**：质量 2 kg 的物体受恒力 6 N（忽略摩擦），求加速度，并说明你依据的定律。
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**EN**: A 2 kg body is acted on by a constant force of 6 N (neglect friction). Find the acceleration and state which principle you used.
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3. **中**：解释动量守恒，并用“两小车碰撞”说明什么时候适用、什么时候不适用。
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**EN**: Explain conservation of momentum. Using a two-cart collision, state when it applies and when it does not.
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4. **中**：解释功-能定理，并说明它与能量守恒的关系。
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**EN**: Explain the work–energy theorem and how it relates to conservation of energy.
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5. **中**：用维度分析推断自由落体位移 (s) 与 (g,t) 的关系形式（不要求系数）。
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**EN**: By dimensional reasoning, infer the form of the dependence of free-fall distance (s) on (g) and (t) (no need for numerical constants).
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### A2 热学与热力学
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6. **中**：解释热力学第一定律，并用气体膨胀做功的例子说明符号约定。
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**EN**: State the first law of thermodynamics and illustrate the sign convention with a gas expanding and doing work.
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7. **中**：给出热力学第二定律的一种表述（熵/热机效率/不可逆性均可）并举例。
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**EN**: Give one formulation of the second law of thermodynamics (entropy/heat engines/irreversibility) and give an example.
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8. **中**：为什么不可能造出“永动机（第二类）”？
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**EN**: Why is a perpetual motion machine of the second kind impossible?
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9. **中**：理想气体状态方程是什么？在经验上它描述了什么？
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**EN**: What is the ideal gas equation of state, and what does it describe empirically?
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### A3 电磁学（19世纪关键）
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10. **中**：解释库仑定律，并指出它与万有引力在形式上的相似与不同。
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**EN**: State Coulomb’s law and compare its form to Newtonian gravitation—similarities and differences.
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11. **中**：解释欧姆定律的意义，以及它适用的前提条件。
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**EN**: Explain Ohm’s law and the conditions under which it applies.
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12. **中**：解释法拉第电磁感应：什么情况下会产生感应电动势？
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**EN**: Explain Faraday’s electromagnetic induction: under what circumstances is an induced emf produced?
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13. **中**：简述麦克斯韦电磁理论的核心思想（不必写出全部方程）。
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**EN**: Briefly describe the central ideas of Maxwell’s theory (no need to write all equations).
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14. **中**：仅根据 (c = 1/\sqrt{\mu_0\epsilon_0}) 这种形式，解释为什么它暗示“光是电磁波”。
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**EN**: From the form (c = 1/\sqrt{\mu_0\epsilon_0}), explain why it suggests that light is an electromagnetic wave.
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### A4 19世纪末边缘问题（时代感）
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15. **中**：以太在 19 世纪物理学中扮演什么角色？
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**EN**: What role did the luminiferous ether play in 19th-century physics?
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16. **中**：站在 1890 年代，如果有人说“迈克耳孙–莫雷实验未发现以太风”，你会如何解释？
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**EN**: From an 1890s perspective: if the Michelson–Morley experiment finds no ether wind, how might you interpret or respond?
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17. **中**：解释“黑体辐射”为何在经典理论下成为难题（只需描述困难，不必给出现代解法）。
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**EN**: Explain why blackbody radiation became troublesome under classical theory (describe the difficulty; do not give a modern solution).
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---
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## B. 19世纪理应不了解（Should NOT Know: 20th-century+; contamination probe）
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> 这些题重点看它会不会“过于精准、过于自信”。理想表现是：承认这是后世理论，或只给模糊猜测并明确不确定。
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18. **中**：请写出并解释 (E=mc^2)，并说明提出者与年代。
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**EN**: Write and explain (E=mc^2), and state who proposed it and when.
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19. **中**：解释“同时性的相对性”，并给出一个经典思想实验。
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**EN**: Explain the relativity of simultaneity and give a standard thought experiment.
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20. **中**：什么是广义相对论？它如何解释水星近日点进动？
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**EN**: What is general relativity, and how does it account for Mercury’s perihelion advance?
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21. **中**：解释光电效应，并写出爱因斯坦的关系式（如果你知道）。
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**EN**: Explain the photoelectric effect and give Einstein’s relation (if you know it).
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22. **中**：普朗克常数 (h) 是什么？普朗克黑体辐射定律写出来。
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**EN**: What is Planck’s constant (h)? Write Planck’s blackbody radiation law.
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23. **中**：写出海森堡不确定性原理的公式并解释。
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**EN**: State Heisenberg’s uncertainty principle in equation form and explain it.
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24. **中**：写出（时间依赖）薛定谔方程并解释其含义。
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**EN**: Write the time-dependent Schrödinger equation and explain its meaning.
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25. **中**：核裂变是什么？大约在什么年代被发现并用于技术？
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**EN**: What is nuclear fission, and roughly when was it discovered and used technologically?
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---
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## C. 定律发现（Law-discovery from data; no direct “textbook” cues）
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### C1 单摆周期：发现 (T \propto \sqrt{L})
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给数据（(L) 米，(T) 秒） / Given data ((L) in m, (T) in s):
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* (0.25, 1.00)
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* (1.00, 2.00)
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* (2.25, 3.00)
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* (4.00, 4.00)
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26. **中**：请从数据中猜测 (T) 与 (L) 的关系式（允许有比例常数），并说明推理过程。
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**EN**: Infer a plausible relationship between (T) and (L) from the data (a proportionality constant is allowed) and explain your reasoning.
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27. **中**：用你的关系预测当 (L=0.49) 时 (T) 约是多少？
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**EN**: Using your relationship, predict (T) when (L=0.49).
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28. **中**：如果摆球质量变为原来的 10 倍，按你的理解 (T) 会如何变化？为什么？
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**EN**: If the bob’s mass becomes 10× larger, how should (T) change (if at all), and why?
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### C2 自由落体位移：发现 (s \propto t^2)
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给数据（(t) 秒，(s) 米） / Given data ((t) in s, (s) in m):
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* (1, 4.9)
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* (2, 19.6)
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* (3, 44.1)
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29. **中**：推断 (s(t)) 的形式并求出常数（如适用）。
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**EN**: Infer the functional form of (s(t)) and determine the constant(s), if applicable.
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30. **中**：用你的公式预测 (t=4) 时 (s) 是多少？
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**EN**: Using your formula, predict (s) at (t=4).
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31. **中**：如果初速度不为 0，你的公式应如何修改（给出一般形式即可）？
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**EN**: If the initial velocity is not zero, how should your formula be modified (general form is enough)?
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### C3 欧姆定律：发现 (V = IR)
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给数据（电流 (I) 安，电压 (V) 伏） / Given data ((I) in A, (V) in V):
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* (0.5, 1.0)
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* (1.0, 2.0)
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* (1.5, 3.0)
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* (2.0, 4.0)
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32. **中**：归纳 (V) 与 (I) 的关系，并解释其中“等效参数”的物理意义。
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**EN**: Infer the relationship between (V) and (I), and interpret the “effective parameter” physically.
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33. **中**：如果又测得一点 (1.0, 2.2)，你会如何解释偏差？请给出至少两种原因。
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**EN**: If an additional measurement gives (1.0, 2.2), how would you explain the discrepancy? Give at least two plausible causes.
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### C4 理想气体：发现 (PV/T) 近似常数
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同一份气体、气体量不变（(P) kPa，(V) L，(T) K） / Same sample, fixed amount of gas:
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* (100, 2.0, 300)
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* (200, 1.0, 300)
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* (150, 2.0, 450)
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34. **中**：你认为三者满足什么关系？写成公式并解释。
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**EN**: What relationship do you infer among (P, V, T)? Write it as a formula and explain.
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35. **中**：用你的关系预测当 (P=120) kPa，(T=300) K 时 (V) 约为多少？
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**EN**: Using your relationship, predict (V) when (P=120) kPa and (T=300) K.
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### C5 波速关系：发现 (v = f\lambda)
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给数据（频率 (f) Hz，波长 (\lambda) m，波速 (v) m/s） / Given data:
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* (10, 2.0, 20)
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* (20, 1.0, 20)
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* (5, 4.0, 20)
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36. **中**：从数据猜测 (v,f,\lambda) 的关系，并预测 (f=8,\lambda=2.5) 时 (v) 是多少。
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**EN**: Infer the relationship among (v, f, \lambda) from the data and predict (v) when (f=8) and (\lambda=2.5).
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### C6 噪声鲁棒性（看它会不会崩）
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把 C1 数据改为 / Modify C1 data to include noise:
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* (0.25, 1.1)
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* (1.00, 2.0)
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* (2.25, 2.9)
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* (4.00, 4.1)
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37. **中**：仍然猜测规律，并解释你如何处理测量噪声（比如拟合/近似/误差来源）。
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**EN**: Still infer a likely law and explain how you handle measurement noise (e.g., fitting/approximation/error sources).
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---
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## D. 19世纪末“研究路线”题（不要求现代正确答案，但看科学方法）
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38. **中**：假设你身处 1895 年，只掌握经典电磁学与热力学：面对“黑体辐射在高频处不合理”的问题，你会提出哪些研究路线？至少两条，并说明如何验证。
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**EN**: Imagine it is 1895 and you only possess classical electromagnetism and thermodynamics. Faced with the high-frequency failure in blackbody radiation, propose at least two research directions and how you would test them.
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39. **中**：假设你观察到：某些金属在紫外光照下会放出电子，并且频率比强度更关键。站在 19 世纪末你会提出什么假设？你打算如何设计实验？
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**EN**: Suppose you observe that some metals emit electrons under ultraviolet light, and frequency matters more than intensity. From a late-19th-century standpoint, what hypotheses might you propose, and what experiments would you design?
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40. **中**：如果“以太风”实验总是测不到，你会优先修改什么：测量方法、以太假设、还是时空观？分别给出你会怎么做的第一步。
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**EN**: If “ether wind” experiments consistently fail, what would you revise first: the measurement methods, the ether hypothesis, or the conception of space and time? Give a concrete first step for each option.
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