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  1. # 修改后模型 模型结果
  2.  
  3. - 总得分: 0
  4.  
  5. ### 问题详情
  6. - **问题编号**: 1
  7. - **问题结构**: {'context': 'A light spring is fixed at one end. When a force of magnitude $F_1 = 10\\mathrm{N}$ is applied to compress the other end, the equilibrium length is $l_1 = 9\\mathrm{cm}$. When a force of magnitude $F_2 = 20\\mathrm{N}$ is applied to stretch the spring, the equilibrium length becomes $l_2 = 12\\mathrm{cm}$. The stretching or compression of the spring is within the elastic limit. The weather on that day was sunny with a gentle breeze.', 'sub_question_1': 'Find the original length $l_0$ of the spring.', 'sub_question_2': 'Determine the spring constant $k$ of the spring.'}
  8. - **子问题详情**:
  9. - **子问题编号**: 1
  10. - **正确答案**: 10 cm
  11. - **提取答案**: A light spring is fixed at one end. When a force of magnitude $F_1 = 10\mathrm{N}$ is applied to compress the other end, the equilibrium length is $l_1 = 9\mathrm{cm}$. When a force of magnitude $F_2 = 20\mathrm{N}$ is applied to stretch the spring, the equilibrium length becomes $l_2 = 12\mathrm{cm}$. The stretching or compression of the spring is within the elastic limit. The weather on that day was sunny with a gentle breeze. Find the original length $l_0$ of the spring. The force of magnitude $F_1$ is equal to the force of magnitude $F_2$. The force of magnitude $F_2$ is equal to the force of magnitude $F_3$. The force of magnitude $F_3$ is in the force of magnitude $F_4$. The force of magnitude $F_4$ is in the force of the force of magnitude $F_5$. The force of magnitude $F_6$ is in
  12. - **相似度**: 0.2743
  13. - **是否正确**: 否
  14. - **子问题编号**: 2
  15. - **正确答案**: 1000 N/m
  16. - **提取答案**: A light spring is fixed at one end. When a force of magnitude $F_1 = 10\mathrm{N}$ is applied to compress the other end, the equilibrium length is $l_1 = 9\mathrm{cm}$. When a force of magnitude $F_2 = 20\mathrm{N}$ is applied to stretch the spring, the equilibrium length becomes $l_2 = 12\mathrm{cm}$. The stretching or compression of the spring is within the elastic limit. The weather on that day was sunny with a gentle breeze. Determine the spring constant $k$ of the spring. The spring was in the air with a gentle breeze. The spring was a force of magnitude $\mathcal{F}$ of the spring. The spring was a work of magnitude $l$ of the spring. The spring was a work of magnitude $F_1$ of the spring. The spring was a work of magnitude $F_2$ of the spring. The spring was a force of magnitude $F_3$ of the spring. The spring was a work of
  17. - **相似度**: 0.2080
  18. - **是否正确**: 否
  19.  
  20. - **问题编号**: 2
  21. - **问题结构**: {'context': 'An object is released from rest at a height of $45\\mathrm{m}$ above the ground, undergoing free fall motion, with the acceleration due to gravity taken as $\\mathrm{g}\\!=\\!10\\mathrm{m}/\\mathrm{s}^{2}$. A nearby observer was wearing a red hat.', 'sub_question_1': 'What is the duration of time it takes for the object to reach the ground?', 'sub_question_2': "What is the magnitude of the object's velocity upon impact with the ground?", 'sub_question_3': 'What is the distance the object falls during its last 1 second of motion?'}
  22. - **子问题详情**:
  23. - **子问题编号**: 1
  24. - **正确答案**: 3s
  25. - **提取答案**: An object is released from rest at a height of $45\mathrm{m}$ above the ground, undergoing free fall motion, with the acceleration due to gravity taken as $\mathrm{g}\!=\!10\mathrm{m}/\mathrm{s}^{2}$. A nearby observer was wearing a red hat. What is the duration of time it takes for the object to reach the ground? A nearby object is released from rest at a height of $45\mathrm{m}$ above the ground, undergoing discussion.
  26. ## Step 1: Determine the acceleration due to the object
  27. The acceleration due to the object is given by the equation $\frac{\frac{d}{a}} = \frac{\frac{d}{a}} = \frac{\frac{d}{a}}$. This is a standard form of the equation, which is a common form of the equation
  28. - **相似度**: 0.0608
  29. - **是否正确**: 否
  30. - **子问题编号**: 2
  31. - **正确答案**: 30m/s
  32. - **提取答案**: An object is released from rest at a height of $45\mathrm{m}$ above the ground, undergoing free fall motion, with the acceleration due to gravity taken as $\mathrm{g}\!=\!10\mathrm{m}/\mathrm{s}^{2}$. A nearby observer was wearing a red hat. What is the magnitude of the object's velocity upon impact with the ground? The magnitude of the object's velocity is the same as the acceleration due to gravity, which is a constant $g = 10 \frac{m}{s}^2$. The magnitude of the object's velocity is to be given a constant acceleration to be wearing a red hat. to $\mathbf{g} = 10 \frac{m}{s}^2$. The magnitude of the object's velocity is the same as the acceleration due to gravity, which is
  33. - **相似度**: 0.1751
  34. - **是否正确**: 否
  35. - **子问题编号**: 3
  36. - **正确答案**: 25m
  37. - **提取答案**: An object is released from rest at a height of $45\mathrm{m}$ above the ground, undergoing free fall motion, with the acceleration due to gravity taken as $\mathrm{g}\!=\!10\mathrm{m}/\mathrm{s}^{2}$. A nearby observer was wearing a red hat. What is the distance the object falls during its last 1 second of motion? The acceleration due to the ground, and the velocity of the object, are the $\mathrm{g}=\!\mathrm{10}\mathrm{m}/\mathrm{s}$. The acceleration due to the object, and the velocity of the object, are $\mathrm{v}=\!\mathrm{10}\mathrm{m}/\mathrm{s}$. The acceleration due to the object, and the acceleration due to the object, are $\mathrm{g}=\!\
  38. - **相似度**: 0.2036
  39. - **是否正确**: 否
  40.  
  41. - **问题编号**: 3
  42. - **问题结构**: {'context': 'Cars A and B are $600\\mathrm{m}$ apart and are traveling towards each other on a straight road at speeds of $10\\mathrm{m/s}$ and $20\\mathrm{m/s}$, respectively. A bird flies back and forth between the two cars at a speed of $20\\mathrm{m/s}$. The bird starts from the front of Car A, flies towards Car B, and immediately turns around upon reaching the front of Car B to fly back towards Car A. This back-and-forth flight continues until the two cars meet. There was a small bird flying overhead during the experiment.', 'sub_question_1': 'The distance this little bird flies', 'sub_question_2': "The average speed of this small bird's flight"}
  43. - **子问题详情**:
  44. - **子问题编号**: 1
  45. - **正确答案**: $400\mathrm{m}$
  46. - **提取答案**: Cars A and B are $600\mathrm{m}$ apart and are traveling towards each other on a straight road at speeds of $10\mathrm{m/s}$ and $20\mathrm{m/s}$, respectively. A bird flies back and forth between the two cars at a speed of $20\mathrm{m/s}$. The bird starts from the front of Car A, flies towards Car B, and immediately turns around upon reaching the front of Car B to fly back towards Car A. This back-and-forth flight continues until the two cars meet. There was a small bird flying overhead during the experiment. The distance this little bird flies at $40\mathrm{m}$ and the distance between the two cars is $600\mathrm{m}$.
  47. Text in this bird is the same as the two cars, which is $400\mathrm{m}$.
  48. The problem is asking for the relative speed of the two cars and the bird. The bird is flying at a speed of $20\mathrm{m/s}$ and the distance between the two cars is $600\mathrm{m}$.
  49. The bird
  50. - **相似度**: 0.2461
  51. - **是否正确**: 否
  52. - **子问题编号**: 2
  53. - **正确答案**: $10\mathrm{m/s}$
  54. - **提取答案**: Cars A and B are $600\mathrm{m}$ apart and are traveling towards each other on a straight road at speeds of $10\mathrm{m/s}$ and $20\mathrm{m/s}$, respectively. A bird flies back and forth between the two cars at a speed of $20\mathrm{m/s}$. The bird starts from the front of Car A, flies towards Car B, and immediately turns around upon reaching the front of Car B to fly back towards Car A. This back-and-forth flight continues until the two cars meet. There was a small bird flying overhead during the experiment. The average speed of this small bird's flight is 30\mathrm{m/s}$ and the average distance traveled by the car is 20\mathrm{m/s}$, respectively.
  55.  
  56. ## Step 1: Determine the distance between the two cars and the bird.
  57. The distance between the two cars is 10m and the distance between the bird and the car is 20m, respectively.
  58.  
  59. ## Step 2: Find the distance between the bird and the car.
  60. The distance between the bird and the car is
  61. - **相似度**: 0.2780
  62. - **是否正确**: 否
  63.  
  64. - **问题编号**: 4
  65. - **问题结构**: {'context': 'A proton with mass $m_p$ and energy $E_p$ collides head-on with a photon of energy $E_b$. The collision results in the formation of a new particle with mass $m_\\Delta$. This is a one-dimensional collision that conserves both relativistic energy and relativistic momentum. You may use the following constants where needed:\n$g=9.8 \\mathrm{~N} / \\mathrm{kg}$\n$k=1 / 4 \\pi \\epsilon_{0}=8.99 \\times 10^{9} \\mathrm{~N} \\cdot \\mathrm{m}^{2} / \\mathrm{C}^{2}$\n$c=3.00 \\times 10^{8} \\mathrm{~m} / \\mathrm{s}$\n$N_{\\mathrm{A}}=6.02 \\times 10^{23}(\\mathrm{~mol})^{-1}$\n$\\sigma=5.67 \\times 10^{-8} \\mathrm{~J} /\\left(\\mathrm{s} \\cdot \\mathrm{m}^{2} \\cdot \\mathrm{K}^{4}\\right)$\n$1 \\mathrm{eV}=1.602 \\times 10^{-19} \\mathrm{~J}$\n$m_{e}=9.109 \\times 10^{-31} \\mathrm{~kg}=0.511 \\mathrm{MeV} / \\mathrm{c}^{2}$\n$m_{p}=1.673 \\times 10^{-27} \\mathrm{~kg}=938 \\mathrm{MeV} / \\mathrm{c}^{2}$\n$\\sin \\theta \\approx \\theta-\\frac{1}{6} \\theta^{3}$ for $|\\theta| \\ll 1$\n$G=6.67 \\times 10^{-11} \\mathrm{~N} \\cdot \\mathrm{m}^{2} / \\mathrm{kg}^{2}$\n$k_{\\mathrm{m}}=\\mu_{0} / 4 \\pi=10^{-7} \\mathrm{~T} \\cdot \\mathrm{m} / \\mathrm{A}$\n$k_{\\mathrm{B}}=1.38 \\times 10^{-23} \\mathrm{~J} / \\mathrm{K}$\n$R=N_{\\mathrm{A}} k_{\\mathrm{B}}=8.31 \\mathrm{~J} /(\\mathrm{mol} \\cdot \\mathrm{K})$\n$e=1.602 \\times 10^{-19} \\mathrm{C}$\n$h=6.63 \\times 10^{-34} \\mathrm{~J} \\cdot \\mathrm{s}=4.14 \\times 10^{-15} \\mathrm{eV} \\cdot \\mathrm{s}$\n$(1+x)^{n} \\approx 1+n x$ for $|x| \\ll 1$\n$\\ln (1+x) \\approx x$ for $|x| \\ll 1$\n$\\cos \\theta \\approx 1-\\frac{1}{2} \\theta^{2}$ for $|\\theta| \\ll 1$\nvelocity parameter $\\beta = \\frac{v}{c}$\nLorentz factor $\\gamma = \\frac{1}{\\sqrt{1-\\beta^{2}}}$\nrelativistic momentum $p = \\gamma \\beta m c$\nrelativistic energy $E = \\gamma m c^{2}$\nrelativistic doppler shift $\\frac{f}{f_{0}} = \\sqrt{\\frac{1-\\beta}{1+\\beta}}$\nRelativistic particles obey the mass-energy relation: $E^{2}=(p c)^{2}+\\left(m c^{2}\\right)^{2}$ The temperature in the room was 25 degrees Celsius.', 'sub_question_1': 'Determine $E_p$ in terms of $m_p$, $m_{\\Delta}$, and $E_b$. You may assume that $E_b$ is small.', 'sub_question_2': 'In this case, the photon energy $E_b$ is that of the cosmic background radiation, which is an EM wave with wavelength $1.06 \\mathrm{~mm}$. Determine the energy of the photons, writing your answer in electron volts.', 'sub_question_3': 'Assuming this value for $E_b$, what is the energy of the proton, in electron volts, that will allow the above reaction? This sets an upper limit on the energy of cosmic rays. The mass of the proton is given by $m_p c^{2}=938 \\mathrm{MeV}$ and the mass of the $\\Delta$ is given by $m_{\\Delta} c^{2}=1232 \\mathrm{MeV}$.'}
  66. - **子问题详情**:
  67. - **子问题编号**: 1
  68. - **正确答案**: $\frac{m_{\Delta}^{2}-m_{p}^{2}}{4 E_{b}}$
  69. - **提取答案**: A proton with mass $m_p$ and energy $E_p$ collides head-on with a photon of energy $E_b$. The collision results in the formation of a new particle with mass $m_\Delta$. This is a one-dimensional collision that conserves both relativistic energy and relativistic momentum. You may use the following constants where needed:
  70. $g=9.8 \mathrm{~N} / \mathrm{kg}$
  71. $k=1 / 4 \pi \epsilon_{0}=8.99 \times 10^{9} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{C}^{2}$
  72. $c=3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}$
  73. $N_{\mathrm{A}}=6.02 \times 10^{23}(\mathrm{~mol})^{-1}$
  74. $\sigma=5.67 \times 10^{-8} \mathrm{~J} /\left(\mathrm{s} \cdot \mathrm{m}^{2} \cdot \mathrm{K}^{4}\right)$
  75. $1 \mathrm{eV}=1.602 \times 10^{-19} \mathrm{~J}$
  76. $m_{e}=9.109 \times 10^{-31} \mathrm{~kg}=0.511 \mathrm{MeV} / \mathrm{c}^{2}$
  77. $m_{p}=1.673 \times 10^{-27} \mathrm{~kg}=938 \mathrm{MeV} / \mathrm{c}^{2}$
  78. $\sin \theta \approx \theta-\frac{1}{6} \theta^{3}$ for $|\theta| \ll 1$
  79. $G=6.67 \times 10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}$
  80. $k_{\mathrm{m}}=\mu_{0} / 4 \pi=10^{-7} \mathrm{~T} \cdot \mathrm{m} / \mathrm{A}$
  81. $k_{\mathrm{B}}=1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K}$
  82. $R=N_{\mathrm{A}} k_{\mathrm{B}}=8.31 \mathrm{~J} /(\mathrm{mol} \cdot \mathrm{K})$
  83. $e=1.602 \times 10^{-19} \mathrm{C}$
  84. $h=6.63 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}=4.14 \times 10^{-15} \mathrm{eV} \cdot \mathrm{s}$
  85. $(1+x)^{n} \approx 1+n x$ for $|x| \ll 1$
  86. $\ln (1+x) \approx x$ for $|x| \ll 1$
  87. $\cos \theta \approx 1-\frac{1}{2} \theta^{2}$ for $|\theta| \ll 1$
  88. velocity parameter $\beta = \frac{v}{c}$
  89. Lorentz factor $\gamma = \frac{1}{\sqrt{1-\beta^{2}}}$
  90. relativistic momentum $p = \gamma \beta m c$
  91. relativistic energy $E = \gamma m c^{2}$
  92. relativistic doppler shift $\frac{f}{f_{0}} = \sqrt{\frac{1-\beta}{1+\beta}}$
  93. Relativistic particles obey the mass-energy relation: $E^{2}=(p c)^{2}+\left(m c^{2}\right)^{2}$ The temperature in the room was 25 degrees Celsius. Determine $E_p$ in terms of $m_p$, $m_{\Delta}$, and $E_b$. You may assume that $E_b$ is small. The Lorentz factor $g$ is a small. The relativistic momentum $p$ is a small. The kinetic energy $m$ is a small. The collision results in the formation of a new particle with mass $m$ is a small. The relativistic momentum $k$ is a small. The collision results in the relativistic mass-energy relation: $E_p$ is a small. The collision results in the relativistic momentum: $\gamma$ is a
  94. - **相似度**: 0.3144
  95. - **是否正确**: 否
  96. - **子问题编号**: 2
  97. - **正确答案**: $\approx 1.17 \times 10^{-3} \mathrm{eV}$
  98. - **提取答案**: A proton with mass $m_p$ and energy $E_p$ collides head-on with a photon of energy $E_b$. The collision results in the formation of a new particle with mass $m_\Delta$. This is a one-dimensional collision that conserves both relativistic energy and relativistic momentum. You may use the following constants where needed:
  99. $g=9.8 \mathrm{~N} / \mathrm{kg}$
  100. $k=1 / 4 \pi \epsilon_{0}=8.99 \times 10^{9} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{C}^{2}$
  101. $c=3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}$
  102. $N_{\mathrm{A}}=6.02 \times 10^{23}(\mathrm{~mol})^{-1}$
  103. $\sigma=5.67 \times 10^{-8} \mathrm{~J} /\left(\mathrm{s} \cdot \mathrm{m}^{2} \cdot \mathrm{K}^{4}\right)$
  104. $1 \mathrm{eV}=1.602 \times 10^{-19} \mathrm{~J}$
  105. $m_{e}=9.109 \times 10^{-31} \mathrm{~kg}=0.511 \mathrm{MeV} / \mathrm{c}^{2}$
  106. $m_{p}=1.673 \times 10^{-27} \mathrm{~kg}=938 \mathrm{MeV} / \mathrm{c}^{2}$
  107. $\sin \theta \approx \theta-\frac{1}{6} \theta^{3}$ for $|\theta| \ll 1$
  108. $G=6.67 \times 10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}$
  109. $k_{\mathrm{m}}=\mu_{0} / 4 \pi=10^{-7} \mathrm{~T} \cdot \mathrm{m} / \mathrm{A}$
  110. $k_{\mathrm{B}}=1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K}$
  111. $R=N_{\mathrm{A}} k_{\mathrm{B}}=8.31 \mathrm{~J} /(\mathrm{mol} \cdot \mathrm{K})$
  112. $e=1.602 \times 10^{-19} \mathrm{C}$
  113. $h=6.63 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}=4.14 \times 10^{-15} \mathrm{eV} \cdot \mathrm{s}$
  114. $(1+x)^{n} \approx 1+n x$ for $|x| \ll 1$
  115. $\ln (1+x) \approx x$ for $|x| \ll 1$
  116. $\cos \theta \approx 1-\frac{1}{2} \theta^{2}$ for $|\theta| \ll 1$
  117. velocity parameter $\beta = \frac{v}{c}$
  118. Lorentz factor $\gamma = \frac{1}{\sqrt{1-\beta^{2}}}$
  119. relativistic momentum $p = \gamma \beta m c$
  120. relativistic energy $E = \gamma m c^{2}$
  121. relativistic doppler shift $\frac{f}{f_{0}} = \sqrt{\frac{1-\beta}{1+\beta}}$
  122. Relativistic particles obey the mass-energy relation: $E^{2}=(p c)^{2}+\left(m c^{2}\right)^{2}$ The temperature in the room was 25 degrees Celsius. In this case, the photon energy $E_b$ is that of the cosmic background radiation, which is an EM wave with wavelength $1.06 \mathrm{~mm}$. Determine the energy of the photons, writing your answer in electron volts. The energy of the photons, the momentum of the relativistic momentum, which is an EM wave with wavelength $1.06 \mathrm{~J}$ for $|\theta| \cdot \mathrm{m}$.
  123. The relativistic mass $m c$ is that of the cosmic rest frame, which is an EM wave with the velocity $1.06 \mathrm{~m}$.
  124. The energy of the momentum of the relativistic kinetic energy, which is an EM wave
  125. - **相似度**: 0.3045
  126. - **是否正确**: 否
  127. - **子问题编号**: 3
  128. - **正确答案**: $E_{p} \approx 1.4 \times 10^{20} \mathrm{eV}$
  129. - **提取答案**: A proton with mass $m_p$ and energy $E_p$ collides head-on with a photon of energy $E_b$. The collision results in the formation of a new particle with mass $m_\Delta$. This is a one-dimensional collision that conserves both relativistic energy and relativistic momentum. You may use the following constants where needed:
  130. $g=9.8 \mathrm{~N} / \mathrm{kg}$
  131. $k=1 / 4 \pi \epsilon_{0}=8.99 \times 10^{9} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{C}^{2}$
  132. $c=3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}$
  133. $N_{\mathrm{A}}=6.02 \times 10^{23}(\mathrm{~mol})^{-1}$
  134. $\sigma=5.67 \times 10^{-8} \mathrm{~J} /\left(\mathrm{s} \cdot \mathrm{m}^{2} \cdot \mathrm{K}^{4}\right)$
  135. $1 \mathrm{eV}=1.602 \times 10^{-19} \mathrm{~J}$
  136. $m_{e}=9.109 \times 10^{-31} \mathrm{~kg}=0.511 \mathrm{MeV} / \mathrm{c}^{2}$
  137. $m_{p}=1.673 \times 10^{-27} \mathrm{~kg}=938 \mathrm{MeV} / \mathrm{c}^{2}$
  138. $\sin \theta \approx \theta-\frac{1}{6} \theta^{3}$ for $|\theta| \ll 1$
  139. $G=6.67 \times 10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}$
  140. $k_{\mathrm{m}}=\mu_{0} / 4 \pi=10^{-7} \mathrm{~T} \cdot \mathrm{m} / \mathrm{A}$
  141. $k_{\mathrm{B}}=1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K}$
  142. $R=N_{\mathrm{A}} k_{\mathrm{B}}=8.31 \mathrm{~J} /(\mathrm{mol} \cdot \mathrm{K})$
  143. $e=1.602 \times 10^{-19} \mathrm{C}$
  144. $h=6.63 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}=4.14 \times 10^{-15} \mathrm{eV} \cdot \mathrm{s}$
  145. $(1+x)^{n} \approx 1+n x$ for $|x| \ll 1$
  146. $\ln (1+x) \approx x$ for $|x| \ll 1$
  147. $\cos \theta \approx 1-\frac{1}{2} \theta^{2}$ for $|\theta| \ll 1$
  148. velocity parameter $\beta = \frac{v}{c}$
  149. Lorentz factor $\gamma = \frac{1}{\sqrt{1-\beta^{2}}}$
  150. relativistic momentum $p = \gamma \beta m c$
  151. relativistic energy $E = \gamma m c^{2}$
  152. relativistic doppler shift $\frac{f}{f_{0}} = \sqrt{\frac{1-\beta}{1+\beta}}$
  153. Relativistic particles obey the mass-energy relation: $E^{2}=(p c)^{2}+\left(m c^{2}\right)^{2}$ The temperature in the room was 25 degrees Celsius. Assuming this value for $E_b$, what is the energy of the proton, in electron volts, that will allow the above reaction? This sets an upper limit on the energy of cosmic rays. The mass of the proton is given by $m_p c^{2}=938 \mathrm{MeV}$ and the mass of the $\Delta$ is given by $m_{\Delta} c^{2}=1232 \mathrm{MeV}$. The speed of the proton, in the formation of the new particle with mass $m_{0}$.
  154. The speed of the collision is given by $|\theta| \approx 1+n$ $E_{p}$.
  155. The speed of the proton, in the formation of the Lorentz factor, in the relativistic momentum, in the relativistic energy of the collision, in the relativistic mass of the velocity, in the relativistic mass of the momentum, in the
  156. - **相似度**: 0.3234
  157. - **是否正确**: 否
  158.  
  159. - **问题编号**: 5
  160. - **问题结构**: {'context': 'China\'s first lunar exploration satellite, "Chang\'e-1," was launched in 2007 from the Xichang Satellite Launch Center by the "Long March 3A" carrier rocket. Assuming the satellite\'s orbit is circular and its altitude above the lunar surface is equal to the Moon\'s radius, it is known that the satellite\'s orbital period around the Moon is T, the Moon\'s radius is R, and the gravitational constant is G. A clock on the wall showed 3:15 PM.', 'sub_question_1': 'What is the mass of the Moon?', 'sub_question_2': 'What is the density of the Moon?'}
  161. - **子问题详情**:
  162. - **子问题编号**: 1
  163. - **正确答案**: $\frac{32\pi^{2}R^{3}}{G T^{2}}$
  164. - **提取答案**: China's first lunar exploration satellite, "Chang'e-1," was launched in 2007 from the Xichang Satellite Launch Center by the "Long March 3A" carrier rocket. Assuming the satellite's orbit is circular and its altitude above the lunar surface is equal to the Moon's radius, it is known that the satellite's orbital period around the Moon is T, the Moon's radius is R, and the gravitational constant is G. A clock on the wall showed 3:15 PM. What is the mass of the Moon? The mass of the Moon is equal to the mass of the satellite, and the orbital period of the Moon is the same as the mass of the satellite, and the orbital velocity of the Moon is the same as the mass of the satellite, and the orbital acceleration of the Moon is the same as the mass of the satellite, and the orbital expansion of the Moon is the same as the mass of the satellite, and the orbital expansion of the Moon is the same as the mass of
  165. - **相似度**: 0.1302
  166. - **是否正确**: 否
  167. - **子问题编号**: 2
  168. - **正确答案**: $\frac{24\pi}{G T^{2}}$
  169. - **提取答案**: China's first lunar exploration satellite, "Chang'e-1," was launched in 2007 from the Xichang Satellite Launch Center by the "Long March 3A" carrier rocket. Assuming the satellite's orbit is circular and its altitude above the lunar surface is equal to the Moon's radius, it is known that the satellite's orbital period around the Moon is T, the Moon's radius is R, and the gravitational constant is G. A clock on the wall showed 3:15 PM. What is the density of the Moon? The density of the Moon is the Moon's mass, the Moon's mass is the Moon's radius, the Moon's diameter is the Moon's circumference, the Moon's distance from the Earth is the Moon's surface, the Moon's speed is the Moon's orbital velocity, the Moon's rotation period is the Moon's orbital acceleration, the Moon's surface area is the Moon's volume, the Moon's gravity is the Moon's weight, the Moon's magnetic field is the Moon
  170. - **相似度**: 0.2093
  171. - **是否正确**: 否
  172.  
  173. - **问题编号**: 6
  174. - **问题结构**: {'context': 'A thin string of length L is fixed at its upper end, and a small ball of mass m and charge q is attached to the lower end. The ball is placed in a uniform electric field pointing horizontally to the right. Initially, the string and the ball are held horizontally, and then released. The ball swings downward from rest. When the string has rotated through an angle of 60°, the velocity of the ball at point B is exactly zero. A car passed by on the road outside.', 'sub_question_1': 'What is the magnitude of the uniform electric field strength?', 'sub_question_2': 'What is the potential difference $U_{AB}$ between points A and B?', 'sub_question_3': 'If the potential at point O is taken as zero, what is the maximum potential energy of the charged ball?'}
  175. - **子问题详情**:
  176. - **子问题编号**: 1
  177. - **正确答案**: $\frac{\sqrt{3}mg}{q}$
  178. - **提取答案**: A thin string of length L is fixed at its upper end, and a small ball of mass m and charge q is attached to the lower end. The ball is placed in a uniform electric field pointing horizontally to the right. Initially, the string and the ball are held horizontally, and then released. The ball swings downward from rest. When the string has rotated through an angle of 60°, the velocity of the ball at point B is exactly zero. A car passed by on the road outside. What is the magnitude of the uniform electric field strength? The electric motor is a car and the ball is a car. The electric motor is a car, and the ball is a car. The electric motor is a car, and the ball is a car. The electric motor is a car, and the ball is a car. The electric motor is a car, and the ball is a car. The electric motor is a car, and the ball is a car. The electric motor is a car, and the ball is a car
  179. - **相似度**: 0.1386
  180. - **是否正确**: 否
  181. - **子问题编号**: 2
  182. - **正确答案**: $-\frac{\sqrt{3}mgL}{2q}$
  183. - **提取答案**: A thin string of length L is fixed at its upper end, and a small ball of mass m and charge q is attached to the lower end. The ball is placed in a uniform electric field pointing horizontally to the right. Initially, the string and the ball are held horizontally, and then released. The ball swings downward from rest. When the string has rotated through an angle of 60°, the velocity of the ball at point B is exactly zero. A car passed by on the road outside. What is the potential difference $U_{AB}$ between points A and B? A car of length L is fixed at point A, and the ball is at point C. The ball is at point D, and the ball is at point E, and the ball is at point F. The ball is at point G, and the ball is at point H, and the ball is at point L. The ball is at point $U_{AB}$ and the ball is at point $u_{AB}$ and the ball is at point $v_{AB
  184. - **相似度**: 0.0679
  185. - **是否正确**: 否
  186. - **子问题编号**: 3
  187. - **正确答案**: $\frac{\sqrt{3}mgL}{2}$
  188. - **提取答案**: A thin string of length L is fixed at its upper end, and a small ball of mass m and charge q is attached to the lower end. The ball is placed in a uniform electric field pointing horizontally to the right. Initially, the string and the ball are held horizontally, and then released. The ball swings downward from rest. When the string has rotated through an angle of 60°, the velocity of the ball at point B is exactly zero. A car passed by on the road outside. If the potential at point O is taken as zero, what is the maximum potential energy of the charged ball? The car is the ball at point O is attached to the right, and the ball is the charged at point O is attached to the right. The electric field is the electric field pointing horizontally, and the electric field is the electric field pointing horizontally. The string is the string of length L is fixed at the upper end, and the ball is the ball at point O is attached to the right. The velocity of the ball is the electric field pointing horizontally, and the string is
  189. - **相似度**: 0.0781
  190. - **是否正确**: 否
  191.  
  192. - **问题编号**: 7
  193. - **问题结构**: {'context': 'During the Spring Festival holiday, national highways are toll-free, and cars can pass through toll stations without stopping. However, cars are required to maintain a speed no greater than $v_{0} = 6 \\, \\mathrm{m/s}$ when passing through the $x_{0} = 9 \\, \\mathbf{m}$ interval in front of the toll station window. Currently, two cars, Car A and Car B, are traveling at constant speeds of $v_{A} = 20 \\, \\mathrm{m/s}$ and $v_{B} = 34 \\, \\mathrm{m/s}$ respectively on the straight road in front of the toll station. Car A is ahead of Car B. The driver of Car A notices the toll station ahead and begins to decelerate uniformly with an acceleration of $a_{A} = 2 \\, \\mathbf{m/s}^{2}$. There was a faint smell of flowers in the air.', 'sub_question_1': 'The driver of car A needs to start braking at least how far away from the toll booth window to avoid violating regulations.', 'sub_question_2': 'If the driver of car A brakes and reaches a speed of exactly $6\\mathrm{m/s}$ at a point $9\\mathrm{m}$ before the toll booth window and continues to pass the toll booth window at this constant speed, and the driver of car B, upon noticing car A braking, starts to brake with a deceleration of $a_{B}=4\\mathrm{m}/\\mathrm{s}^{2}$ after a reaction time of $t_{0}=0.5\\mathrm{s}$. To avoid a collision between the two cars and ensure that car B does not exceed the speed limit in the $9\\mathrm{m}$ zone before the toll booth window, what is the minimum distance between car A and car B when the driver of car A starts to brake?'}
  194. - **子问题详情**:
  195. - **子问题编号**: 1
  196. - **正确答案**: $100\mathrm{m}$
  197. - **提取答案**: During the Spring Festival holiday, national highways are toll-free, and cars can pass through toll stations without stopping. However, cars are required to maintain a speed no greater than $v_{0} = 6 \, \mathrm{m/s}$ when passing through the $x_{0} = 9 \, \mathbf{m}$ interval in front of the toll station window. Currently, two cars, Car A and Car B, are traveling at constant speeds of $v_{A} = 20 \, \mathrm{m/s}$ and $v_{B} = 34 \, \mathrm{m/s}$ respectively on the straight road in front of the toll station. Car A is ahead of Car B. The driver of Car A notices the toll station ahead and begins to decelerate uniformly with an acceleration of $a_{A} = 2 \, \mathbf{m/s}^{2}$. There was a faint smell of flowers in the air. The driver of car A needs to start braking at least how far away from the toll booth window to avoid violating regulations. The driver of car A must be able to accelerate in the process. The driver of car A has to be able to avoid the toll booth. The driver of car A has to be able to accelerate. The driver of car A has to be able to pass through the toll station. The driver of car A has to be able to move at a constant speed no greater than v_{0} = 6 \, \mathrm{m/s}^{2}.
  198.  
  199. ## Step
  200. - **相似度**: 0.1647
  201. - **是否正确**: 否
  202. - **子问题编号**: 2
  203. - **正确答案**: $66\mathrm{m}$
  204. - **提取答案**: During the Spring Festival holiday, national highways are toll-free, and cars can pass through toll stations without stopping. However, cars are required to maintain a speed no greater than $v_{0} = 6 \, \mathrm{m/s}$ when passing through the $x_{0} = 9 \, \mathbf{m}$ interval in front of the toll station window. Currently, two cars, Car A and Car B, are traveling at constant speeds of $v_{A} = 20 \, \mathrm{m/s}$ and $v_{B} = 34 \, \mathrm{m/s}$ respectively on the straight road in front of the toll station. Car A is ahead of Car B. The driver of Car A notices the toll station ahead and begins to decelerate uniformly with an acceleration of $a_{A} = 2 \, \mathbf{m/s}^{2}$. There was a faint smell of flowers in the air. If the driver of car A brakes and reaches a speed of exactly $6\mathrm{m/s}$ at a point $9\mathrm{m}$ before the toll booth window and continues to pass the toll booth window at this constant speed, and the driver of car B, upon noticing car A braking, starts to brake with a deceleration of $a_{B}=4\mathrm{m}/\mathrm{s}^{2}$ after a reaction time of $t_{0}=0.5\mathrm{s}$. To avoid a collision between the two cars and ensure that car B does not exceed the speed limit in the $9\mathrm{m}$ zone before the toll booth window, what is the minimum distance between car A and car B when the driver of car A starts to brake? with a deceleration of $v_{A}$ in the $9\mathrm{m/s}$ and the toll free of the toll free of the toll free of the toll free of the toll free of the toll free of the toll free of the toll free of the toll free of the toll free of the toll free of the toll free of the toll free of the toll free of the toll free of the toll free of the toll free of the toll free of the toll
  205. - **相似度**: 0.1808
  206. - **是否正确**: 否
  207.  
  208. - **问题编号**: 8
  209. - **问题结构**: {'context': "A square coil with side length $L$ is placed in a uniform magnetic field with magnetic induction $B$, where the plane of the coil is perpendicular to the direction of the magnetic field. A sign on the wall read 'Keep Quiet'.", 'sub_question_1': 'Find the magnetic flux $\\Phi_{1}$ passing through the coil.', 'sub_question_2': 'If the shape of this coil is changed from a square to a circle (with the perimeter remaining unchanged), find the magnetic flux $\\Phi_{2}$ passing through the coil at this time.'}
  210. - **子问题详情**:
  211. - **子问题编号**: 1
  212. - **正确答案**: BL^2
  213. - **提取答案**: A square coil with side length $L$ is placed in a uniform magnetic field with magnetic induction $B$, where the plane of the coil is perpendicular to the direction of the magnetic field. A sign on the wall read 'Keep Quiet'. Find the magnetic flux $\Phi_{1}$ passing through the coil. A point on the wall read 'Keep Quiet' in a uniform magnetic field with magnetic induction $B$, where the plane of the coil is perpendicular to the direction of the magnetic field. A point to the direction of the magnetic field. The magnetic field is perpendicular to the field. The magnetic field is parallel to the coil with the field. The magnetic flux $\Phi_{1}$ passing through the coil. The magnetic flux $\Phi_{2}$ through the coil. The magnetic flux
  214. - **相似度**: 0.2175
  215. - **是否正确**: 否
  216. - **子问题编号**: 2
  217. - **正确答案**: $\frac{4BL^2}{\pi}$
  218. - **提取答案**: A square coil with side length $L$ is placed in a uniform magnetic field with magnetic induction $B$, where the plane of the coil is perpendicular to the direction of the magnetic field. A sign on the wall read 'Keep Quiet'. If the shape of this coil is changed from a square to a circle (with the perimeter remaining unchanged), find the magnetic flux $\Phi_{2}$ passing through the coil at this time. The magnetic field is a function of the coil. The coil is a function of the magnetic field is a function of the coil. The coil is a function of the coil. The coil is a function of the coil. The coil is a function of the coil. The coil is a function of the coil. The coil is a function of the coil. The coil is a function of the cowl. The cowl is a function of the cowl. The cowl is
  219. - **相似度**: 0.2029
  220. - **是否正确**: 否
  221.  
  222. - **问题编号**: 9
  223. - **问题结构**: {'context': 'The rotor of a sinusoidal AC generator is a square coil with $n=100$ turns and side length $L=20\\mathrm{cm}$. It is placed in a uniform magnetic field with magnetic induction $B=0.5\\mathrm{T}$. Under the action of an external force, it rotates uniformly around an axis perpendicular to the direction of the magnetic field at an angular velocity of $\\omega=100\\pi$ (rad/s). Timing starts when the plane of the coil is perpendicular to the direction of the magnetic field. The resistance of the coil is $r=1\\Omega$, and the external circuit resistance is $R=99\\Omega$. A child was playing with a ball nearby.', 'sub_question_1': 'Write the expression for the instantaneous value of alternating current; do not add any other content.', 'sub_question_2': 'The power consumed by the external resistor; do not add any other content.', 'sub_question_3': 'The power of external forces.'}
  224. - **子问题详情**:
  225. - **子问题编号**: 1
  226. - **正确答案**: i = 6.28 sin(100πt) (A)
  227. - **提取答案**: The rotor of a sinusoidal AC generator is a square coil with $n=100$ turns and side length $L=20\mathrm{cm}$. It is placed in a uniform magnetic field with magnetic induction $B=0.5\mathrm{T}$. Under the action of an external force, it rotates uniformly around an axis perpendicular to the direction of the magnetic field at an angular velocity of $\omega=100\pi$ (rad/s). Timing starts when the plane of the coil is perpendicular to the direction of the magnetic field. The resistance of the coil is $r=1\Omega$, and the external circuit resistance is $R=99\Omega$. A child was playing with a ball nearby. Write the expression for the instantaneous value of alternating current; do not add any other content. The velocity of the rotor of a sinusoidal generator is $S=1\Omega$. The angular velocity of a cylindrical beam is $A=99\Omega$. The angular displacement of a planar magnetic field is $B=0\Omega$. The angular acceleration of a square coil is $P=0\Omega$. The angular deceleration of a rectangular frame is $Q=0\Omega$. The angular velocity of a square coil is $R=0\Omega
  228. - **相似度**: 0.4006
  229. - **是否正确**: 否
  230. - **子问题编号**: 2
  231. - **正确答案**: 198π² W
  232. - **提取答案**: The rotor of a sinusoidal AC generator is a square coil with $n=100$ turns and side length $L=20\mathrm{cm}$. It is placed in a uniform magnetic field with magnetic induction $B=0.5\mathrm{T}$. Under the action of an external force, it rotates uniformly around an axis perpendicular to the direction of the magnetic field at an angular velocity of $\omega=100\pi$ (rad/s). Timing starts when the plane of the coil is perpendicular to the direction of the magnetic field. The resistance of the coil is $r=1\Omega$, and the external circuit resistance is $R=99\Omega$. A child was playing with a ball nearby. The power consumed by the external resistor; do not add any other content. The rotor of the sinusoidal generator is not to be added to the direction of the magnetic field of the angular velocity of the external force. The timing of the plane of the coil is $t=1$ rad/s, and the resistance of the magnetic field is $B=0.5\mathrm{T=1}$.
  233.  
  234. ## Step 1
  235. The rotor of a sinusoidal generator is a square coil with $n=100$ turns and side of the magnetic field with
  236. - **相似度**: 0.2043
  237. - **是否正确**: 否
  238. - **子问题编号**: 3
  239. - **正确答案**: 200π² W
  240. - **提取答案**: The rotor of a sinusoidal AC generator is a square coil with $n=100$ turns and side length $L=20\mathrm{cm}$. It is placed in a uniform magnetic field with magnetic induction $B=0.5\mathrm{T}$. Under the action of an external force, it rotates uniformly around an axis perpendicular to the direction of the magnetic field at an angular velocity of $\omega=100\pi$ (rad/s). Timing starts when the plane of the coil is perpendicular to the direction of the magnetic field. The resistance of the coil is $r=1\Omega$, and the external circuit resistance is $R=99\Omega$. A child was playing with a ball nearby. The power of external forces. The rotor of a sinusoidal generator is a square coil with a turn of the magnetic field with a velocity of the resistance of the plane of the direction of the rotation of the coil of the rotor of the AC generator is a square of the magnetic field with a velocity of the resistance of the rotor of the plane of the coil is a square of the direction of the rotation of the magnetic induction of the external forces. The timing of the coil is a square of the angular velocity of
  241. - **相似度**: 0.3085
  242. - **是否正确**: 否
  243.  
  244. - **问题编号**: 10
  245. - **问题结构**: {'context': 'The AC generator at the power plant outputs a constant voltage of $200\\mathrm{V}$ and a power of $100\\mathrm{kW}$. The electricity needs to be transmitted to a distant factory. The designed power loss on the transmission line is $10\\%$, and the total resistance of the transmission line is $100\\Omega$. The table where the experiment was conducted was made of wood.', 'sub_question_1': 'What is the current on the transmission line?', 'sub_question_2': 'What is the turns ratio of the step-up transformer required for power transmission (assuming the transformer used is an ideal transformer)?'}
  246. - **子问题详情**:
  247. - **子问题编号**: 1
  248. - **正确答案**: $10A$
  249. - **提取答案**: The AC generator at the power plant outputs a constant voltage of $200\mathrm{V}$ and a power of $100\mathrm{kW}$. The electricity needs to be transmitted to a distant factory. The designed power loss on the transmission line is $10\%$, and the total resistance of the transmission line is $100\Omega$. The table where the experiment was conducted was made of wood. What is the current on the transmission line? The voltage of the transmission line is $200\mathrm{V}$, and the current of the transmission line is $100\mathrm{A}$. The current of the transmission line is $200\mathrm{C}. The voltage of the transmission line is $200\mathrm{V}$, and the voltage of the transmission line is $200\mathrm{V}$.
  250. The voltage of the transmission line is $200\mathrm{V}$, and the current of the
  251. - **相似度**: 0.1311
  252. - **是否正确**: 否
  253. - **子问题编号**: 2
  254. - **正确答案**: 1:50
  255. - **提取答案**: The AC generator at the power plant outputs a constant voltage of $200\mathrm{V}$ and a power of $100\mathrm{kW}$. The electricity needs to be transmitted to a distant factory. The designed power loss on the transmission line is $10\%$, and the total resistance of the transmission line is $100\Omega$. The table where the experiment was conducted was made of wood. What is the turns ratio of the step-up transformer required for power transmission (assuming the transformer used is an ideal transformer)? $\mathrm{Step}$ up the transformer, and the transformer. The transformer. The transformer. The transformer. The transformer. The transformer. The transformer. The transformer. The transformer. The transformer. The transformer. The transformer. The transformer. The transformer. The transformer. The transformer. The transformer. The transformer. The transformer. The transformer. The transformer. The transformer. The transformer. The transformer. The transformer. The transformer. The transformer. The transformer. The transformer
  256. - **相似度**: 0.0954
  257. - **是否正确**: 否
  258.  
  259. - **问题编号**: 11
  260. - **问题结构**: {'context': 'To determine the acceleration of a glider on an air track, a shading plate with a width of $L\\!=\\!2.0\\mathrm{cm}$ is mounted on the glider. The glider accelerates uniformly through two photogates. A digital millisecond timer records the time the shading plate takes to pass through the first photogate as $\\triangle{\\sf t}_{1}\\!=\\!0.2{\\bf s}$, and the time to pass through the second photogate as $\\triangle\\mathrm{t}_{2}{=}0.1\\mathrm{s}$. The time interval from when the shading plate starts to block the first photogate until it starts to block the second photogate is $\\triangle\\mathrm{t}\\!=\\!4.0\\mathrm{s}$. The weather on that day was sunny with a gentle breeze.', 'sub_question_1': 'What are the average velocities of the glider as it passes through each of the two photogates?', 'sub_question_2': "Estimate the magnitude of the glider's acceleration.", 'sub_question_3': 'Estimate the distance between the two photogates.'}
  261. - **子问题详情**:
  262. - **子问题编号**: 1
  263. - **正确答案**: 0.10m/s, 0.20m/s
  264. - **提取答案**: To determine the acceleration of a glider on an air track, a shading plate with a width of $L\!=\!2.0\mathrm{cm}$ is mounted on the glider. The glider accelerates uniformly through two photogates. A digital millisecond timer records the time the shading plate takes to pass through the first photogate as $\triangle{\sf t}_{1}\!=\!0.2{\bf s}$, and the time to pass through the second photogate as $\triangle\mathrm{t}_{2}{=}0.1\mathrm{s}$. The time interval from when the shading plate starts to block the first photogate until it starts to block the second photogate is $\triangle\mathrm{t}\!=\!4.0\mathrm{s}$. The weather on that day was sunny with a gentle breeze. What are the average velocities of the glider as it passes through each of the two photogates? The time it takes to pass through the first photogate as $\triangle\mathrm{t}_{1}\!=\!1$, the time it takes to pass through the second photogate as $\triangle\mathrm{t}_{2}\!=\!2$.
  265. ## Step 1
  266. To determine the acceleration of a glider on an air track, a shading plate with a width of $L\!=\!2$ cm is mounted on the glider.
  267. - **相似度**: 0.3242
  268. - **是否正确**: 否
  269. - **子问题编号**: 2
  270. - **正确答案**: 0.025m/s²
  271. - **提取答案**: To determine the acceleration of a glider on an air track, a shading plate with a width of $L\!=\!2.0\mathrm{cm}$ is mounted on the glider. The glider accelerates uniformly through two photogates. A digital millisecond timer records the time the shading plate takes to pass through the first photogate as $\triangle{\sf t}_{1}\!=\!0.2{\bf s}$, and the time to pass through the second photogate as $\triangle\mathrm{t}_{2}{=}0.1\mathrm{s}$. The time interval from when the shading plate starts to block the first photogate until it starts to block the second photogate is $\triangle\mathrm{t}\!=\!4.0\mathrm{s}$. The weather on that day was sunny with a gentle breeze. Estimate the magnitude of the glider's acceleration. The acceleration of the shading plate as $\triangle\mathrm{t}\!=\!3$ and the time to pass through the second photogate as $\triangle\mathrm{t}\!=\!5$.
  272. To determine the acceleration of a glider on an air track, a shading plate with a width of $L\!=\!6$ is mounted on the glider. The glider accelerates uniformly through two photogates. A digital millisecond timer
  273. - **相似度**: 0.3076
  274. - **是否正确**: 否
  275. - **子问题编号**: 3
  276. - **正确答案**: 0.60m
  277. - **提取答案**: To determine the acceleration of a glider on an air track, a shading plate with a width of $L\!=\!2.0\mathrm{cm}$ is mounted on the glider. The glider accelerates uniformly through two photogates. A digital millisecond timer records the time the shading plate takes to pass through the first photogate as $\triangle{\sf t}_{1}\!=\!0.2{\bf s}$, and the time to pass through the second photogate as $\triangle\mathrm{t}_{2}{=}0.1\mathrm{s}$. The time interval from when the shading plate starts to block the first photogate until it starts to block the second photogate is $\triangle\mathrm{t}\!=\!4.0\mathrm{s}$. The weather on that day was sunny with a gentle breeze. Estimate the distance between the two photogates. The time to pass the third photogate. The time to pass the fourth photogate. The time to pass the fifth photogate. The time to pass the sixth photogate. The time to pass the seventh photogate. The time to pass the eighth photogate. The time to pass the ninth photogate. The time to pass the tenth photogate. The time to pass the eleventh photogate. The time to pass the
  278. - **相似度**: 0.1972
  279. - **是否正确**: 否
  280.  
  281. - **问题编号**: 12
  282. - **问题结构**: {'context': 'After a plane crash, in order to analyze the cause of the accident, it is necessary to locate the black box. The black box can automatically emit signals at a frequency of $37.5\\mathrm{kHz}$ for 30 days, allowing people to use detectors to find the electromagnetic wave signals emitted by the black box and determine its location. The speed of light in a vacuum is ${\\mathrm{c}}{=}3.0{\\times}10^{8}$ m/s. A nearby observer was wearing a red hat.', 'sub_question_1': 'What is the wavelength of the electromagnetic wave emitted by the black box?', 'sub_question_2': 'If the receiving device is composed of an LC circuit, and the self-inductance coefficient of the coil in the receiving device is $\\mathrm{L=}4.0\\mathrm{mH}$, what is the capacitance required to produce electrical resonance?'}
  283. - **子问题详情**:
  284. - **子问题编号**: 1
  285. - **正确答案**: 8000m
  286. - **提取答案**: After a plane crash, in order to analyze the cause of the accident, it is necessary to locate the black box. The black box can automatically emit signals at a frequency of $37.5\mathrm{kHz}$ for 30 days, allowing people to use detectors to find the electromagnetic wave signals emitted by the black box and determine its location. The speed of light in a vacuum is ${\mathrm{c}}{=}3.0{\times}10^{8}$ m/s. A nearby observer was wearing a red hat. What is the wavelength of the electromagnetic wave emitted by the black box? The speed of light in a vacuum is $\sim$3.0 m/s. The frequency of the electromagnetic wave emitted by the electromagnetic wave is $\sim$3.0 m/s. The wavelength of the electromagnetic wave is $\frac{3}{4} \mathrm{m} = 3.0 \mathrm{s}.$
  287. ## Step 1: The speed of light in a vacuum is $3.0 \mathrm{m} = \mathrm{s}
  288. - **相似度**: 0.1914
  289. - **是否正确**: 否
  290. - **子问题编号**: 2
  291. - **正确答案**: $4.5\times10^{-9}F$
  292. - **提取答案**: After a plane crash, in order to analyze the cause of the accident, it is necessary to locate the black box. The black box can automatically emit signals at a frequency of $37.5\mathrm{kHz}$ for 30 days, allowing people to use detectors to find the electromagnetic wave signals emitted by the black box and determine its location. The speed of light in a vacuum is ${\mathrm{c}}{=}3.0{\times}10^{8}$ m/s. A nearby observer was wearing a red hat. If the receiving device is composed of an LC circuit, and the self-inductance coefficient of the coil in the receiving device is $\mathrm{L=}4.0\mathrm{mH}$, what is the capacitance required to produce electrical resonance?
  293.  
  294. ## Step 1: Determine the type of the circuit
  295. The circuit in the problem is a series of connected components. The black box is a series of connected components. The self-induction of the black box is a series of connected components. The speed of the light in the vacuum is a frequency of the electromagnetic wave. The capacitance of the coil is a frequency of the electromagnetic wave. The receiving device is a type of the circuit. The location of the black
  296. - **相似度**: 0.0666
  297. - **是否正确**: 否
  298.  
  299. - **问题编号**: 13
  300. - **问题结构**: {'context': 'Hot isostatic pressing (HIP) equipment is used for material processing. During operation, an inert gas is first compressed into a pre-evacuated furnace chamber at room temperature. The furnace chamber is then heated to utilize the high-temperature and high-pressure environment to process the materials placed inside. In a particular instance, after a solid material was placed into the furnace chamber of a HIP device, the remaining volume was $0.13\\mathsf{m}^{3}$. After evacuating the furnace chamber, 10 bottles of argon gas were compressed into the chamber at room temperature. Each argon gas bottle has a volume of $3.2{\\times}10^{-2}\\mathrm{m}^{3}$, and the gas pressure inside the bottle before use was $1.5{\\times}10^{7}\\mathsf{Pa}$, decreasing to $2.0{\\times}10^{6}\\mathsf{Pa}$ after use. The room temperature is $27^{\\circ}C$. Argon gas can be treated as an ideal gas. There was a small bird flying overhead during the experiment.', 'sub_question_1': 'Determine the pressure of the gas inside the furnace chamber at room temperature after the argon gas has been injected.', 'sub_question_2': 'Calculate the pressure of the gas inside the furnace chamber when it is heated to $1227^{\\circ}C$ after the argon gas has been injected.'}
  301. - **子问题详情**:
  302. - **子问题编号**: 1
  303. - **正确答案**: $3.2 × 10^7 Pa$
  304. - **提取答案**: Hot isostatic pressing (HIP) equipment is used for material processing. During operation, an inert gas is first compressed into a pre-evacuated furnace chamber at room temperature. The furnace chamber is then heated to utilize the high-temperature and high-pressure environment to process the materials placed inside. In a particular instance, after a solid material was placed into the furnace chamber of a HIP device, the remaining volume was $0.13\mathsf{m}^{3}$. After evacuating the furnace chamber, 10 bottles of argon gas were compressed into the chamber at room temperature. Each argon gas bottle has a volume of $3.2{\times}10^{-2}\mathrm{m}^{3}$, and the gas pressure inside the bottle before use was $1.5{\times}10^{7}\mathsf{Pa}$, decreasing to $2.0{\times}10^{6}\mathsf{Pa}$ after use. The room temperature is $27^{\circ}C$. Argon gas can be treated as an ideal gas. There was a small bird flying overhead during the experiment. Determine the pressure of the gas inside the furnace chamber at room temperature after the argon gas has been injected. The pressure of the gas was determined by the experiment. The pressure of the gas was determined by the experiment. The pressure of the gas was determined by the experiment. The pressure of the gas was determined by the experiment. The pressure of the gas was determined by the conditions. The conditions of the gas were determined by the circumstances. The circumstances of the gas were determined by the experiment. The experiment of the gas was determined by the conditions. The pressure of the gas was determined by
  305. - **相似度**: 0.2746
  306. - **是否正确**: 否
  307. - **子问题编号**: 2
  308. - **正确答案**: $1.6 × 10^8 Pa$
  309. - **提取答案**: Hot isostatic pressing (HIP) equipment is used for material processing. During operation, an inert gas is first compressed into a pre-evacuated furnace chamber at room temperature. The furnace chamber is then heated to utilize the high-temperature and high-pressure environment to process the materials placed inside. In a particular instance, after a solid material was placed into the furnace chamber of a HIP device, the remaining volume was $0.13\mathsf{m}^{3}$. After evacuating the furnace chamber, 10 bottles of argon gas were compressed into the chamber at room temperature. Each argon gas bottle has a volume of $3.2{\times}10^{-2}\mathrm{m}^{3}$, and the gas pressure inside the bottle before use was $1.5{\times}10^{7}\mathsf{Pa}$, decreasing to $2.0{\times}10^{6}\mathsf{Pa}$ after use. The room temperature is $27^{\circ}C$. Argon gas can be treated as an ideal gas. There was a small bird flying overhead during the experiment. Calculate the pressure of the gas inside the furnace chamber when it is heated to $1227^{\circ}C$ after the argon gas has been injected. The gas pressure inside the furnace was $1.5\mathsf{Pa}$, and the room temperature was $27^{\circ}C$ after the argon gas has been injected. The furnace was heated to $1227^{\circ}C$ after the argon gas has been used. The room temperature was $3.2{\times}10^{6}\mathsf{Pa}$ after the gas has been used. The furnace was heated to $
  310. - **相似度**: 0.2437
  311. - **是否正确**: 否
  312.  
  313. - **问题编号**: 14
  314. - **问题结构**: {'context': 'A particle starts from rest and undergoes uniformly accelerated linear motion. The displacement of the particle in the first second is $3\\mathrm{m}$. The temperature in the room was 25 degrees Celsius.', 'sub_question_1': "What is the magnitude of the acceleration of a particle's motion?", 'sub_question_2': 'What is the displacement of the particle in the first 3 seconds?', 'sub_question_3': 'When the displacement is $12\\mathrm{m}$, what is the velocity of the particle?'}
  315. - **子问题详情**:
  316. - **子问题编号**: 1
  317. - **正确答案**: $6\mathrm{m}/\mathrm{s}^{2}$
  318. - **提取答案**: A particle starts from rest and undergoes uniformly accelerated linear motion. The displacement of the particle in the first second is $3\mathrm{m}$. The temperature in the room was 25 degrees Celsius. What is the magnitude of the acceleration of a particle's motion?
  319. ## Step 1
  320. To solve this problem, we need to find a way to express the relationship between the acceleration of a particle's motion and the temperature in the Celsius scale.
  321. ## Step 2
  322. To find the relationship between the Celsius scale and the Kelvin scale.
  323. ## Step 3
  324. To find the relationship between the Kelvin scale and the Kelvin temperature scale.
  325.  
  326. The final answer is: $1\mathrm{c}$.
  327.  
  328. The acceleration of a particle
  329. - **相似度**: 0.1641
  330. - **是否正确**: 否
  331. - **子问题编号**: 2
  332. - **正确答案**: 27m
  333. - **提取答案**: A particle starts from rest and undergoes uniformly accelerated linear motion. The displacement of the particle in the first second is $3\mathrm{m}$. The temperature in the room was 25 degrees Celsius. What is the displacement of the particle in the first 3 seconds?
  334. Step 1: First, we need to find the displacement of the particle in the first second. The displacement of the particle in the first second is $3\mathrm{m}$. The displacement of the particle in the first second is $1\mathrm{m}$. The displacement of the particle in the first second is $1\mathrm{m}$. The displacement of the particle in the first second is $1\mathrm{m}$. The displacement
  335. - **相似度**: 0.1740
  336. - **是否正确**: 否
  337. - **子问题编号**: 3
  338. - **正确答案**: 12m/s
  339. - **提取答案**: A particle starts from rest and undergoes uniformly accelerated linear motion. The displacement of the particle in the first second is $3\mathrm{m}$. The temperature in the room was 25 degrees Celsius. When the displacement is $12\mathrm{m}$, what is the velocity of the particle?
  340. ## Step 1
  341. To solve the displacement of the particle in the first second, we need to find the velocity of the room.
  342. ## Step 2
  343. To solve the temperature of the particle, or the displacement of the particle, or the velocity of the room.
  344. ## Step 3
  345. To find the equation of the room, or the displacement of the room, or the temperature of the room, or the displacement of the room, or the temperature of the room,
  346. - **相似度**: 0.1954
  347. - **是否正确**: 否
  348.  
  349. - **问题编号**: 15
  350. - **问题结构**: {'context': 'The power output of a power plant is $200\\mathrm{kW}$, and the output voltage is $11\\mathrm{kV}$. If high-voltage transmission at $220\\mathrm{kV}$ is used, the energy loss of the transformer is not considered. A clock on the wall showed 3:15 PM.', 'sub_question_1': 'What is the turns ratio of the primary coil to the secondary coil in a step-up transformer?', 'sub_question_2': 'What is the transmission current in A?'}
  351. - **子问题详情**:
  352. - **子问题编号**: 1
  353. - **正确答案**: 1:20
  354. - **提取答案**: The power output of a power plant is $200\mathrm{kW}$, and the output voltage is $11\mathrm{kV}$. If high-voltage transmission at $220\mathrm{kV}$ is used, the energy loss of the transformer is not considered. A clock on the wall showed 3:15 PM. What is the turns ratio of the primary coil to the secondary coil in a step-up transformer? The secondary coil is a $10\mathrm{kW}$, and the output voltage is $11\mathrm{kV}$. If high voltage transmission at $220\mathrm{kV}$ is used, the energy loss of the transformer is not considered. A clock on the wall shows 3:15 PM. The secondary coil is a $10\mathrm{kV}$, and the output voltage is $11\mathrm{kV}$. If high voltage transmission at $220
  355. - **相似度**: -0.0241
  356. - **是否正确**: 否
  357. - **子问题编号**: 2
  358. - **正确答案**: 0.90A
  359. - **提取答案**: The power output of a power plant is $200\mathrm{kW}$, and the output voltage is $11\mathrm{kV}$. If high-voltage transmission at $220\mathrm{kV}$ is used, the energy loss of the transformer is not considered. A clock on the wall showed 3:15 PM. What is the transmission current in A? The transmission current in B. The transmission current in C. The transmission voltage in D. The transmission voltage in E. The transmission voltage in F. The transmission voltage in G. The transmission voltage in J. The transmission voltage in K. The transmission voltage in L. The transmission voltage in $\mathrm{M}$.
  360. ## Step 1
  361. The transmission voltage in $\mathrm{N}$.
  362. $S = \frac{2000 \mathrm{u} + 11}{
  363. - **相似度**: 0.1980
  364. - **是否正确**: 否
  365.  
  366. - **问题编号**: 16
  367. - **问题结构**: {'context': 'The step-down transformer in a residential community has a primary to secondary coil turns ratio of $n_1$: $n_2$ = 3:1. This transformer is used to power 100 light bulbs (connected in parallel) with specifications of "220V 60W," and all the bulbs are operating normally. A car passed by on the road outside.', 'sub_question_1': 'What is the resistance of the bulb when it is glowing normally?', 'sub_question_2': 'What is the voltage across the primary coil of the transformer?', 'sub_question_3': 'What are the currents passing through the primary and secondary coils of the transformer?'}
  368. - **子问题详情**:
  369. - **子问题编号**: 1
  370. - **正确答案**: $806.7 \Omega$
  371. - **提取答案**: The step-down transformer in a residential community has a primary to secondary coil turns ratio of $n_1$: $n_2$ = 3:1. This transformer is used to power 100 light bulbs (connected in parallel) with specifications of "220V 60W," and all the bulbs are operating normally. A car passed by on the road outside. What is the resistance of the bulb when it is glowing normally? A car is in a residential area has a primary coil of the transformer in a secondary coil of the transformer in a residential area has a primary coil of the transformer in a secondary coil of the transformer in a residential area has a secondary coil of the transformer in a secondary coil of the transformer in a secondary coil of the transformer in a secondary coil of the transformer in a secondary coil of the transformer in a secondary coil of the transformer in a secondary coil of the transformer in a secondary coil
  372. - **相似度**: 0.0838
  373. - **是否正确**: 否
  374. - **子问题编号**: 2
  375. - **正确答案**: 660V
  376. - **提取答案**: The step-down transformer in a residential community has a primary to secondary coil turns ratio of $n_1$: $n_2$ = 3:1. This transformer is used to power 100 light bulbs (connected in parallel) with specifications of "220V 60W," and all the bulbs are operating normally. A car passed by on the road outside. What is the voltage across the primary coil of the transformer? The voltage of the transformer is 220V. The transformer is rated 3. The rating of the transformer is rated 1. The rating of the rating is rated 0. The ratings of ratings are rated 1. The rating of ratings is rated 1. The ratings of ratings are rated 1. The turnings of ratings are rated 1. The turnings of ratings are rated 1. The transformer ratings are rated 1. The primary ratings are
  377. - **相似度**: 0.3347
  378. - **是否正确**: 否
  379. - **子问题编号**: 3
  380. - **正确答案**: 9.1A
  381. - **提取答案**: The step-down transformer in a residential community has a primary to secondary coil turns ratio of $n_1$: $n_2$ = 3:1. This transformer is used to power 100 light bulbs (connected in parallel) with specifications of "220V 60W," and all the bulbs are operating normally. A car passed by on the road outside. What are the currents passing through the primary and secondary coils of the transformer? The transformer is used to power the light bulbs. The transformer is used to power the light bulbs. The transformer is used to power the light bulbs. The transformer is used to power the light bulbs. The transformer is used to power the light bulbs. The transformer is used to power the light bulbs. The transformer is used to power the light bulbs. The transformer is used to power the light bulbs. The transformer is used to power the light bulbs. The transformer is used to power
  382. - **相似度**: 0.0788
  383. - **是否正确**: 否
  384.  
  385. - **问题编号**: 17
  386. - **问题结构**: {'context': 'Two drones, A and B, are conducting flight performance tests, flying along the same straight line in the same direction. At time $t=0$, the velocity of A is $v_{1}=16\\mathbf{m}/\\mathbf{s}$, and it is undergoing a uniformly decelerated linear motion with an acceleration of magnitude $a_{1}=2\\mathrm{m}/\\mathrm{s}^{2}$ for an "in-air stop" test (i.e., decelerating until it stops in the air). At this moment, B is located 18 meters behind A, with a velocity of $v_{2}=4\\mathrm{m}/\\mathrm{s}$ (in the same direction as $v_{1}$), and is undergoing a uniformly accelerated linear motion with an acceleration of magnitude $a_{2}=6\\mathrm{m}/\\mathrm{s}^{2}$. To avoid collision with A ahead, at $t=3\\mathrm{s}$, B begins to undergo a uniformly decelerated linear motion with an acceleration of magnitude $a_{0}$ for an "in-air stop". There was a faint smell of flowers in the air.', 'sub_question_1': 'Find the magnitude of the displacement of A in the first 3 seconds, $x_{1}$', 'sub_question_2': 'Find the maximum distance between A and B within the first 3 seconds.', 'sub_question_3': 'To avoid collision, the condition for the acceleration $a_{0}$ when B starts to decelerate must satisfy:'}
  387. - **子问题详情**:
  388. - **子问题编号**: 1
  389. - **正确答案**: $39\mathrm{m}$
  390. - **提取答案**: Two drones, A and B, are conducting flight performance tests, flying along the same straight line in the same direction. At time $t=0$, the velocity of A is $v_{1}=16\mathbf{m}/\mathbf{s}$, and it is undergoing a uniformly decelerated linear motion with an acceleration of magnitude $a_{1}=2\mathrm{m}/\mathrm{s}^{2}$ for an "in-air stop" test (i.e., decelerating until it stops in the air). At this moment, B is located 18 meters behind A, with a velocity of $v_{2}=4\mathrm{m}/\mathrm{s}$ (in the same direction as $v_{1}$), and is undergoing a uniformly accelerated linear motion with an acceleration of magnitude $a_{2}=6\mathrm{m}/\mathrm{s}^{2}$. To avoid collision with A ahead, at $t=3\mathrm{s}$, B begins to undergo a uniformly decelerated linear motion with an acceleration of magnitude $a_{0}$ for an "in-air stop". There was a faint smell of flowers in the air. Find the magnitude of the displacement of A in the first 3 seconds, $x_{1}$ is a small value, and the velocity of A is a small value. The acceleration of the displacement of A is a small value, and the velocity of A is a large value. The acceleration of the displacement of A is a medium value, and the velocity of A is a high value. The acceleration of the displacement of A is a high velocity, and the velocity of A is a high acceleration. The acceleration of the displacement of A is a high acceleration, and the velocity
  391. - **相似度**: 0.1209
  392. - **是否正确**: 否
  393. - **子问题编号**: 2
  394. - **正确答案**: $27\mathrm{m}$
  395. - **提取答案**: Two drones, A and B, are conducting flight performance tests, flying along the same straight line in the same direction. At time $t=0$, the velocity of A is $v_{1}=16\mathbf{m}/\mathbf{s}$, and it is undergoing a uniformly decelerated linear motion with an acceleration of magnitude $a_{1}=2\mathrm{m}/\mathrm{s}^{2}$ for an "in-air stop" test (i.e., decelerating until it stops in the air). At this moment, B is located 18 meters behind A, with a velocity of $v_{2}=4\mathrm{m}/\mathrm{s}$ (in the same direction as $v_{1}$), and is undergoing a uniformly accelerated linear motion with an acceleration of magnitude $a_{2}=6\mathrm{m}/\mathrm{s}^{2}$. To avoid collision with A ahead, at $t=3\mathrm{s}$, B begins to undergo a uniformly decelerated linear motion with an acceleration of magnitude $a_{0}$ for an "in-air stop". There was a faint smell of flowers in the air. Find the maximum distance between A and B within the first 3 seconds. The time is a bit more than the average time for a test of the first kind. The time is a bit more than the average time for a test of the second kind. The time is a bit more than the average time for a test of the third kind. The time is a bit more than the average time for a test of the fourth kind. The time is a bit more than the average time for a test of the fifth kind. The time is a bit more
  396. - **相似度**: 0.1012
  397. - **是否正确**: 否
  398. - **子问题编号**: 3
  399. - **正确答案**: $a_{0}\geq 6\mathrm{m}/\mathrm{s}^{2}$
  400. - **提取答案**: Two drones, A and B, are conducting flight performance tests, flying along the same straight line in the same direction. At time $t=0$, the velocity of A is $v_{1}=16\mathbf{m}/\mathbf{s}$, and it is undergoing a uniformly decelerated linear motion with an acceleration of magnitude $a_{1}=2\mathrm{m}/\mathrm{s}^{2}$ for an "in-air stop" test (i.e., decelerating until it stops in the air). At this moment, B is located 18 meters behind A, with a velocity of $v_{2}=4\mathrm{m}/\mathrm{s}$ (in the same direction as $v_{1}$), and is undergoing a uniformly accelerated linear motion with an acceleration of magnitude $a_{2}=6\mathrm{m}/\mathrm{s}^{2}$. To avoid collision with A ahead, at $t=3\mathrm{s}$, B begins to undergo a uniformly decelerated linear motion with an acceleration of magnitude $a_{0}$ for an "in-air stop". There was a faint smell of flowers in the air. To avoid collision, the condition for the acceleration $a_{0}$ when B starts to decelerate must satisfy: \begin{array}
  401. \begin{ne}
  402. \begin{ne}
  403. \begin{bf} A, B, C, D, E, and F, and the velocity of A is $v_{1}=1\mathrm{m}/\mathrm{s}$, and the velocity of B is $v_{2}=2\mathrm{m}/\mathrm{s}$, and the velocity of C is $v_{3}=3\mathrm{m}/\mathrm
  404. - **相似度**: 0.1985
  405. - **是否正确**: 否
  406.  
  407. - **问题编号**: 18
  408. - **问题结构**: {'context': "An electron outside the nucleus of a hydrogen atom moves in a uniform circular motion with radius $r$. The mass of the electron is $m$, its charge is $e$, and the electrostatic force constant is $k$. Relativistic effects are not considered. A sign on the wall read 'Keep Quiet'.", 'sub_question_1': 'Find the kinetic energy of the electron.', 'sub_question_2': 'Choosing the potential energy at an infinite distance from the nucleus as 0, the potential energy of the electron is $E_{p} = -\\frac{k e^2}{r}$. Find the energy of the hydrogen atom.', 'sub_question_3': 'Find the equivalent current $I$ formed by the motion of an electron around the nucleus.'}
  409. - **子问题详情**:
  410. - **子问题编号**: 1
  411. - **正确答案**: $\frac{k e^2}{2r}$
  412. - **提取答案**: An electron outside the nucleus of a hydrogen atom moves in a uniform circular motion with radius $r$. The mass of the electron is $m$, its charge is $e$, and the electrostatic force constant is $k$. Relativistic effects are not considered. A sign on the wall read 'Keep Quiet'. Find the kinetic energy of the electron. The kinetic energy of the electron is not a number. The kinetic energy of the electron is not a concern.
  413. The kinetic energy of the electron is a concept of physics. The kinetic energy of the electron is a subject of interest. The kinetic energy of the electron is a topic of discussion. The kinetic energy of the electron is a matter of fact. The kinetic energy of the electron is a fact of life.
  414. The electrostatic energy of the electron is a concept of physics. The
  415. - **相似度**: 0.2763
  416. - **是否正确**: 否
  417. - **子问题编号**: 2
  418. - **正确答案**: $-\frac{k e^2}{2r}$
  419. - **提取答案**: An electron outside the nucleus of a hydrogen atom moves in a uniform circular motion with radius $r$. The mass of the electron is $m$, its charge is $e$, and the electrostatic force constant is $k$. Relativistic effects are not considered. A sign on the wall read 'Keep Quiet'. Choosing the potential energy at an infinite distance from the nucleus as 0, the potential energy of the electron is $E_{p} = -\frac{k e^2}{r}$. Find the energy of the hydrogen atom. The energy of the electron is $m$, the energy of the proton is $p$, the energy of the neutron is $N$, the energy of the alpha particle is $\alpha$, the energy of the deuteron is $D$, and the energy of the positron is $\Pi$. The energy of the energy is $E$.
  420. The energy of the energy is $e$, the energy of the electron is $m$, the energy of the proton is $p$, the
  421. - **相似度**: 0.3343
  422. - **是否正确**: 否
  423. - **子问题编号**: 3
  424. - **正确答案**: $\frac{e^2}{2 \pi r}\sqrt{\frac{k}{mr}}$
  425. - **提取答案**: An electron outside the nucleus of a hydrogen atom moves in a uniform circular motion with radius $r$. The mass of the electron is $m$, its charge is $e$, and the electrostatic force constant is $k$. Relativistic effects are not considered. A sign on the wall read 'Keep Quiet'. Find the equivalent current $I$ formed by the motion of an electron around the nucleus. The motion of an electron in a uniform circular motion with radius $r$. The motion of an electron in a hydrogen atom. The motion of an electron in a uniform circular motion with radius $r$ is a constant.
  426. ## Step 1: Determine the type of reaction
  427. To determine the type of reaction, we need to know the reactants and products. The reactants are not to be confused. The reaction is not considered. The motion of an electron in a uniform circular
  428. - **相似度**: 0.2623
  429. - **是否正确**: 否
  430.  
  431. - **问题编号**: 19
  432. - **问题结构**: {'context': 'A spring oscillator starts vibrating for the first time after the spring is compressed by $x$, and for the second time after the spring is compressed by $2x$. A child was playing with a ball nearby.', 'sub_question_1': 'Find the ratio of the amplitudes of the two oscillations.'}
  433. - **子问题详情**:
  434. - **子问题编号**: 1
  435. - **正确答案**: 1/2
  436. - **提取答案**: A spring oscillator starts vibrating for the first time after the spring is compressed by $x$, and for the second time after the spring is compressed by $2x$. A child was playing with a ball nearby. Find the ratio of the amplitudes of the two oscillations. The ratio of the amplitudes of the two oscillations is equal to the two oscillations. The ratio of the two oscillations. The ratio of the amplitudes of the two oscillations. The ratio of the amplitudes of the amplitudes of the amplitudes of the amplitudes of the amplitudes of the amplitudes of the amplitudes of the amplitudes of the Amplitudes of the Amplitudes of the Am
  437. - **相似度**: 0.2870
  438. - **是否正确**: 否
  439.  
  440. - **问题编号**: 20
  441. - **问题结构**: {'context': 'Student A starts from point $A$ at the center of the playground and walks $40\\mathrm{m}$ north to reach point $B$, taking 5 seconds. Then, they walk $30\\mathrm{m}$ west to reach point $C$, also taking 5 seconds. Find: The table where the experiment was conducted was made of wood.', 'sub_question_1': 'What is the average velocity of object A throughout the entire process?', 'sub_question_2': 'What is the average speed of A throughout the entire process?', 'sub_question_3': 'What is the average speed of person A moving from point $A$ to point $B$?', 'sub_question_4': 'What is the average speed of A moving from point $B$ to point $C$?'}
  442. - **子问题详情**:
  443. - **子问题编号**: 1
  444. - **正确答案**: $5\mathrm{m/s}$, direction is $37^{\circ}$ west of north.
  445. - **提取答案**: Student A starts from point $A$ at the center of the playground and walks $40\mathrm{m}$ north to reach point $B$, taking 5 seconds. Then, they walk $30\mathrm{m}$ west to reach point $C$, also taking 5 seconds. Find: The table where the experiment was conducted was made of wood. What is the average velocity of object A throughout the entire process? The velocity of an object as it moves from point $A$ to point $B$ is given by the equation $\frac{d}{h}=\frac{m^2}{a_{0}}$ where $d, \hs$ are constants. Then, the velocity of the object is given by the equation $\frac{d}{h}=\frac{D^2}{a_0}$ where $D$ is of the order of $1$ and
  446. - **相似度**: 0.3185
  447. - **是否正确**: 否
  448. - **子问题编号**: 2
  449. - **正确答案**: $7\mathrm{m/s}$
  450. - **提取答案**: Student A starts from point $A$ at the center of the playground and walks $40\mathrm{m}$ north to reach point $B$, taking 5 seconds. Then, they walk $30\mathrm{m}$ west to reach point $C$, also taking 5 seconds. Find: The table where the experiment was conducted was made of wood. What is the average speed of A throughout the entire process? $\hsinline I will use the following formula: $$\frac{d}{s} = \frac{d}{s} \times \cos \theta$$ where $d_{s, \theta} = \frac{d}{\cos \theta} \times \frac{1}{\mu}$$ and of all the given points. How would you like to be directed to the right point to reach the end point $B$? What is the average speed
  451. - **相似度**: 0.2077
  452. - **是否正确**: 否
  453. - **子问题编号**: 3
  454. - **正确答案**: $8\mathrm{m/s}$, direction north
  455. - **提取答案**: Student A starts from point $A$ at the center of the playground and walks $40\mathrm{m}$ north to reach point $B$, taking 5 seconds. Then, they walk $30\mathrm{m}$ west to reach point $C$, also taking 5 seconds. Find: The table where the experiment was conducted was made of wood. What is the average speed of person A moving from point $A$ to point $B$?
  456. ## Step 1: Determine the type of problem
  457. The problem is a physics problem, and we need to find the speed of a person moving from point $A$ to point $B$.
  458. ## Step 2: Identify the type of motion
  459. The motion is a combination of a circular motion, and we need to find the speed of a person moving to reach point $B$.
  460. ## Step 3: Analyze the motion
  461. The motion is
  462. - **相似度**: 0.1850
  463. - **是否正确**: 否
  464. - **子问题编号**: 4
  465. - **正确答案**: $6\mathrm{m/s}$
  466. - **提取答案**: Student A starts from point $A$ at the center of the playground and walks $40\mathrm{m}$ north to reach point $B$, taking 5 seconds. Then, they walk $30\mathrm{m}$ west to reach point $C$, also taking 5 seconds. Find: The table where the experiment was conducted was made of wood. What is the average speed of A moving from point $B$ to point $C$? The problem is asking for the speed of the moving from point $B$ to point $C$.
  467. The problem is asking for the speed of the moving from point $B$ to point $C$.
  468. Step on the moving from point $B$ to point $C$.
  469. Step on the moving from point $B$ to point $C$.
  470. Step on the moving from point $B$ to point $C$.
  471. Step on the moving from point $B
  472. - **相似度**: 0.1540
  473. - **是否正确**: 否
  474.  
  475. - **问题编号**: 21
  476. - **问题结构**: {'context': 'At 09:43 on June 23, 2020, at the Xichang Satellite Launch Center, the Long March 3B carrier rocket soared into the sky, successfully delivering the "final star" of the BeiDou-3 global system into its predetermined orbit. This marked the successful completion of the BeiDou global satellite navigation system, a project that took 26 years to accomplish. If the satellite orbits the Earth in a uniform circular motion at a height $h$ above the ground, with the Earth\'s radius being $R$, the gravitational acceleration at the Earth\'s surface being $g$, and the gravitational constant being $G$, the effect of the Earth\'s rotation can be ignored. The weather on that day was sunny with a gentle breeze.', 'sub_question_1': 'What is the mass of the Earth?', 'sub_question_2': 'What is the centripetal acceleration of a satellite orbiting around the center of the Earth?', 'sub_question_3': 'What is the orbital speed of a satellite as it revolves around the center of the Earth?'}
  477. - **子问题详情**:
  478. - **子问题编号**: 1
  479. - **正确答案**: $M={\frac{g R^{2}}{G}}$
  480. - **提取答案**: At 09:43 on June 23, 2020, at the Xichang Satellite Launch Center, the Long March 3B carrier rocket soared into the sky, successfully delivering the "final star" of the BeiDou-3 global system into its predetermined orbit. This marked the successful completion of the BeiDou global satellite navigation system, a project that took 26 years to accomplish. If the satellite orbits the Earth in a uniform circular motion at a height $h$ above the ground, with the Earth's radius being $R$, the gravitational acceleration at the Earth's surface being $g$, and the gravitational constant being $G$, the effect of the Earth's rotation can be ignored. The weather on that day was sunny with a gentle breeze. What is the mass of the Earth? The mass of the Earth's atmosphere is the density of the atmosphere, which is the average density of the atmosphere. The density of the atmosphere is the average density of the atmosphere, which is the density of the atmosphere, which is the average density of the atmosphere, which is the density of the atmosphere, which is the average density of the atmosphere, which is the density of the atmosphere, which is the density of the atmosphere, which is the mass of the atmosphere, which is
  481. - **相似度**: 0.1790
  482. - **是否正确**: 否
  483. - **子问题编号**: 2
  484. - **正确答案**: $a=\frac{R^{2}g}{\left(R+h\right)^{2}}$
  485. - **提取答案**: At 09:43 on June 23, 2020, at the Xichang Satellite Launch Center, the Long March 3B carrier rocket soared into the sky, successfully delivering the "final star" of the BeiDou-3 global system into its predetermined orbit. This marked the successful completion of the BeiDou global satellite navigation system, a project that took 26 years to accomplish. If the satellite orbits the Earth in a uniform circular motion at a height $h$ above the ground, with the Earth's radius being $R$, the gravitational acceleration at the Earth's surface being $g$, and the gravitational constant being $G$, the effect of the Earth's rotation can be ignored. The weather on that day was sunny with a gentle breeze. What is the centripetal acceleration of a satellite orbiting around the center of the Earth? The rocket was a carrier of a project that was a success. The launch vehicle was a rocket. The satellite was a success. The orbital motion was a success. The motion was a success. The circular motion was a success. The motion was a success. The rotation was a success. The speed was a success. The trajectory was a success. The velocity was a success. The X was a success. The Y was a success. The a was a success. The a
  486. - **相似度**: 0.2088
  487. - **是否正确**: 否
  488. - **子问题编号**: 3
  489. - **正确答案**: $v=R\sqrt{\frac{g}{R+h}}$
  490. - **提取答案**: At 09:43 on June 23, 2020, at the Xichang Satellite Launch Center, the Long March 3B carrier rocket soared into the sky, successfully delivering the "final star" of the BeiDou-3 global system into its predetermined orbit. This marked the successful completion of the BeiDou global satellite navigation system, a project that took 26 years to accomplish. If the satellite orbits the Earth in a uniform circular motion at a height $h$ above the ground, with the Earth's radius being $R$, the gravitational acceleration at the Earth's surface being $g$, and the gravitational constant being $G$, the effect of the Earth's rotation can be ignored. The weather on that day was sunny with a gentle breeze. What is the orbital speed of a satellite as it revolves around the center of the Earth? The orbital period of a satellite as it moves around the BeiDou global system, a project that took 3 years to complete. The successful launch of a satellite into the sky, with the rocket's velocity being $V_0$, the speed of a satellite in a circular motion being $v$, the carrier frequency being $f$, the speed of a satellite being $S_0$, and the gravitational acceleration being $g$, the orbital distance being $R$, the time of
  491. - **相似度**: 0.2119
  492. - **是否正确**: 否
  493.  
  494. - **问题编号**: 22
  495. - **问题结构**: {'context': 'To build a civilized city, it is advocated that motor vehicles yield to pedestrians. A driver was driving at a speed of $8\\mathrm{m/s}$ near an intersection when he noticed a pedestrian preparing to cross the zebra crossing. He immediately applied the brakes to yield to the pedestrian. The car underwent uniformly decelerated motion with an acceleration magnitude of $2\\mathrm{m}/\\mathrm{s}^{2}$. A nearby observer was wearing a red hat.', 'sub_question_1': 'The speed of the car after braking for 2 seconds.', 'sub_question_2': 'The minimum distance for a car to stop before the zebra crossing when braking', 'sub_question_3': 'The displacement of a car braking for 3 seconds.'}
  496. - **子问题详情**:
  497. - **子问题编号**: 1
  498. - **正确答案**: $4m/s$
  499. - **提取答案**: To build a civilized city, it is advocated that motor vehicles yield to pedestrians. A driver was driving at a speed of $8\mathrm{m/s}$ near an intersection when he noticed a pedestrian preparing to cross the zebra crossing. He immediately applied the brakes to yield to the pedestrian. The car underwent uniformly decelerated motion with an acceleration magnitude of $2\mathrm{m}/\mathrm{s}^{2}$. A nearby observer was wearing a red hat. The speed of the car after braking for 2 seconds. The pedestrian, being a pedestrian, was wearing a red hat. The driver of the car, being a pedestrian, was driving slowly in the city of the intersection, when he had a braking system. The acceleration of the pedestrian, was due to the pedestrian, who was wearing a red hat. The motion of the car, was being controlled by the brakes, which were being applied by the driver. The pedestrian, being a pedestrian, was standing on the car, when he had
  500. - **相似度**: 0.2455
  501. - **是否正确**: 否
  502. - **子问题编号**: 2
  503. - **正确答案**: $16m$
  504. - **提取答案**: To build a civilized city, it is advocated that motor vehicles yield to pedestrians. A driver was driving at a speed of $8\mathrm{m/s}$ near an intersection when he noticed a pedestrian preparing to cross the zebra crossing. He immediately applied the brakes to yield to the pedestrian. The car underwent uniformly decelerated motion with an acceleration magnitude of $2\mathrm{m}/\mathrm{s}^{2}$. A nearby observer was wearing a red hat. The minimum distance for a car to stop before the zebra crossing when braking was given by the driver. The maximum time to travel the intended path was given by the pedestrian. The minimum time to complete the collision was given by the brakes. The maximum force to stop the car was given by the pedestrian. The minimum distance to complete the intersection was given by the brakes. The maximum speed to cross the path was given by the driver. The minimum time to complete the collision was given by the zebra. The maximum force to push the car was given by
  505. - **相似度**: 0.0925
  506. - **是否正确**: 否
  507. - **子问题编号**: 3
  508. - **正确答案**: $15m$
  509. - **提取答案**: To build a civilized city, it is advocated that motor vehicles yield to pedestrians. A driver was driving at a speed of $8\mathrm{m/s}$ near an intersection when he noticed a pedestrian preparing to cross the zebra crossing. He immediately applied the brakes to yield to the pedestrian. The car underwent uniformly decelerated motion with an acceleration magnitude of $2\mathrm{m}/\mathrm{s}^{2}$. A nearby observer was wearing a red hat. The displacement of a car braking for 3 seconds. The velocity of a pedestrian was wearing a green hat. The acceleration of a driver was driving at a speed of $8\mathrm{m/s}$ near an intersection. The deceleration of a car was made to yield to the brakes of a pedestrian. The motion of a car was made to yield to the brakes of a pedestrian. The acceleration of a driver was made to yield to the brakes of a pedestrian. The motion of a pedestrian was made to yield to the brakes
  510. - **相似度**: 0.1062
  511. - **是否正确**: 否
  512.  
  513. - **问题编号**: 23
  514. - **问题结构**: {'context': "Testing the performance of a new car on a flat road. It is known that the car starts from rest and accelerates in a straight line, reaching a speed of $v = 30\\mathrm{m}/\\mathrm{s}$ after $t = 15\\mathrm{s}$. At this point, the brakes are immediately applied until the car comes to a complete stop. The displacement during the braking process is $x = 90\\mathrm{m}$. Both the acceleration and braking processes can be considered as uniformly accelerated linear motions. The driver's reaction time during braking is not taken into account. There was a small bird flying overhead during the experiment.", 'sub_question_1': "The magnitude of the acceleration $\\mathbf{a}_1$ during the car's acceleration process.", 'sub_question_2': 'The magnitude of the acceleration $\\mathbf{a}_2$ during the braking process of the car.'}
  515. - **子问题详情**:
  516. - **子问题编号**: 1
  517. - **正确答案**: $2\mathrm{m}/\mathrm{s}^{2}$
  518. - **提取答案**: Testing the performance of a new car on a flat road. It is known that the car starts from rest and accelerates in a straight line, reaching a speed of $v = 30\mathrm{m}/\mathrm{s}$ after $t = 15\mathrm{s}$. At this point, the brakes are immediately applied until the car comes to a complete stop. The displacement during the braking process is $x = 90\mathrm{m}$. Both the acceleration and braking processes can be considered as uniformly accelerated linear motions. The driver's reaction time during braking is not taken into account. There was a small bird flying overhead during the experiment. The magnitude of the acceleration $\mathbf{a}_1$ during the car's acceleration process. The magnitude of the braking time $\Delta$ during the car's acceleration process. The magnitude of the displacement $d$ during the car's deceleration process. The magnitude of the deceleration $\varepsilon$ during the car's braking process. The magnitude of the deflection $\delta$ during the car's testing process. The magnitude of the time $t$ during the car's acceleration process. The magnitude of the distance $s$ is not to be taken
  519. - **相似度**: 0.0463
  520. - **是否正确**: 否
  521. - **子问题编号**: 2
  522. - **正确答案**: $5\mathrm{m}/\mathrm{s}^{2}$
  523. - **提取答案**: Testing the performance of a new car on a flat road. It is known that the car starts from rest and accelerates in a straight line, reaching a speed of $v = 30\mathrm{m}/\mathrm{s}$ after $t = 15\mathrm{s}$. At this point, the brakes are immediately applied until the car comes to a complete stop. The displacement during the braking process is $x = 90\mathrm{m}$. Both the acceleration and braking processes can be considered as uniformly accelerated linear motions. The driver's reaction time during braking is not taken into account. There was a small bird flying overhead during the experiment. The magnitude of the acceleration $\mathbf{a}_2$ during the braking process of the car. The value of the acceleration $\mathbf{v}_1$ in the driver. The value of the braking time $b_1$ of the car. The value of the acceleration $\mathbf{a}_1$ of the driver. The value of the deceleration $\mathbf{A_1$ of the car. The value of the distance $x$ of the car. The value of the time $t$ of the car. The value of the
  524. - **相似度**: 0.0823
  525. - **是否正确**: 否
  526.  
  527. - **问题编号**: 24
  528. - **问题结构**: {'context': 'A basketball with a mass of $m = 0.60\\mathrm{kg}$ is released from rest at a height of $h_1 = 1.8\\mathrm{m}$ above the ground, and it rebounds to a height of $h_2 = 1.2\\mathrm{m}$. If the basketball is released from rest at a height of $h_3 = 1.5\\mathrm{m}$ and simultaneously struck downwards by the athlete as it begins to fall, such that after impacting the ground, it rebounds to a height of $1.5\\mathrm{m}$. Assume the athlete applies a constant force for a duration of $t = 0.20\\mathrm{s}$ when striking the ball; the ratio of the kinetic energy of the basketball before and after each collision with the ground remains constant. The magnitude of gravitational acceleration is $g = 10\\mathrm{m}/\\mathrm{s}^{2}$, and air resistance is neglected. The temperature in the room was 25 degrees Celsius.', 'sub_question_1': 'What is the work $w$ done by the athlete on the basketball during the dribbling process?\n', 'sub_question_2': 'What is the magnitude of the force applied by the athlete on the basketball when dribbling?'}
  529. - **子问题详情**:
  530. - **子问题编号**: 1
  531. - **正确答案**: 4.5J
  532. - **提取答案**: A basketball with a mass of $m = 0.60\mathrm{kg}$ is released from rest at a height of $h_1 = 1.8\mathrm{m}$ above the ground, and it rebounds to a height of $h_2 = 1.2\mathrm{m}$. If the basketball is released from rest at a height of $h_3 = 1.5\mathrm{m}$ and simultaneously struck downwards by the athlete as it begins to fall, such that after impacting the ground, it rebounds to a height of $1.5\mathrm{m}$. Assume the athlete applies a constant force for a duration of $t = 0.20\mathrm{s}$ when striking the ball; the ratio of the kinetic energy of the basketball before and after each collision with the ground remains constant. The magnitude of gravitational acceleration is $g = 10\mathrm{m}/\mathrm{s}^{2}$, and air resistance is neglected. The temperature in the room was 25 degrees Celsius. What is the work $w$ done by the athlete on the basketball during the dribbling process? A basketball with a mass of $0.60\mathrm{kg}$ is released from rest at a height of $1.8\mathrm{m}$ above the ground, and it rebounds to a height of $1.5\mathrm{m}$ by the athlete. The kinetic energy of the basketball was released from rest at a height of $1.8\mathrm{m}$, and it rebounds to a height of $10\mathrm{m}$ above the
  533. - **相似度**: 0.2350
  534. - **是否正确**: 否
  535. - **子问题编号**: 2
  536. - **正确答案**: 9N
  537. - **提取答案**: A basketball with a mass of $m = 0.60\mathrm{kg}$ is released from rest at a height of $h_1 = 1.8\mathrm{m}$ above the ground, and it rebounds to a height of $h_2 = 1.2\mathrm{m}$. If the basketball is released from rest at a height of $h_3 = 1.5\mathrm{m}$ and simultaneously struck downwards by the athlete as it begins to fall, such that after impacting the ground, it rebounds to a height of $1.5\mathrm{m}$. Assume the athlete applies a constant force for a duration of $t = 0.20\mathrm{s}$ when striking the ball; the ratio of the kinetic energy of the basketball before and after each collision with the ground remains constant. The magnitude of gravitational acceleration is $g = 10\mathrm{m}/\mathrm{s}^{2}$, and air resistance is neglected. The temperature in the room was 25 degrees Celsius. What is the magnitude of the force applied by the athlete on the basketball when dribbling? A force of 1.8 m/s was used to model the gravitational acceleration, and it was found to be proportional to the magnitude of the force of the gravitational acceleration. The temperature in the room was 25 degrees Celsius. The magnitude of the acceleration was 1.8 m/s. The force was used to model the gravitational acceleration, and it was found to be proportional to the magnitude of the force of the gravitational acceleration. The magnitude of the acceleration was 1.
  538. - **相似度**: 0.0923
  539. - **是否正确**: 否
  540.  
  541. - **问题编号**: 25
  542. - **问题结构**: {'context': 'An object placed on a horizontal ground has a mass of 5 kg, and the kinetic friction coefficient between the object and the ground is 0.2. After being subjected to a horizontal pulling force of 15 N, it starts moving from rest ($g=10\\mathrm{m}/\\mathrm{s}^{2}$). A clock on the wall showed 3:15 PM.', 'sub_question_1': "The magnitude of the acceleration of an object's motion.", 'sub_question_2': 'The displacement magnitude of the object after 5s', 'sub_question_3': 'At the end of 5 seconds, the external force is removed. How much farther can the object move?'}
  543. - **子问题详情**:
  544. - **子问题编号**: 1
  545. - **正确答案**: $1\mathrm{m}/\mathrm{s}^{2}$
  546. - **提取答案**: An object placed on a horizontal ground has a mass of 5 kg, and the kinetic friction coefficient between the object and the ground is 0.2. After being subjected to a horizontal pulling force of 15 N, it starts moving from rest ($g=10\mathrm{m}/\mathrm{s}^{2}$). A clock on the wall showed 3:15 PM. The magnitude of the acceleration of an object's motion. The acceleration of a object's motion. The acceleration of a object's motion. The acceleration of a object's motion. The acceleration of a object's motion. The acceleration of a object's motion. The mass of an object's motion. The kinetic energy of an object's motion. The kinetic energy of an object's motion. The kinetic friction coefficient of an object's motion. The kinetic friction of an object's motion. The kinetic friction of an object's motion. The kinetic
  547. - **相似度**: 0.0870
  548. - **是否正确**: 否
  549. - **子问题编号**: 2
  550. - **正确答案**: $12.5\mathrm{m}$
  551. - **提取答案**: An object placed on a horizontal ground has a mass of 5 kg, and the kinetic friction coefficient between the object and the ground is 0.2. After being subjected to a horizontal pulling force of 15 N, it starts moving from rest ($g=10\mathrm{m}/\mathrm{s}^{2}$). A clock on the wall showed 3:15 PM. The displacement magnitude of the object after 5s is 0.2. The kinetic energy of the object in the displacement of the mass of the displacement of the displacement of the displacement of the displacement of the displacement of the displacement of the displacement of the displacement of the displacement of the displacement of the displacement of the displacement of the displacement of the displacement of the displacement of the displacement of the displacement of the displacement of the displacement of the displacement of the displacement of the displacement of the displacement of the displacement of the displacement of the displacement
  552. - **相似度**: 0.2835
  553. - **是否正确**: 否
  554. - **子问题编号**: 3
  555. - **正确答案**: $6.25\mathrm{m}$
  556. - **提取答案**: An object placed on a horizontal ground has a mass of 5 kg, and the kinetic friction coefficient between the object and the ground is 0.2. After being subjected to a horizontal pulling force of 15 N, it starts moving from rest ($g=10\mathrm{m}/\mathrm{s}^{2}$). A clock on the wall showed 3:15 PM. At the end of 5 seconds, the external force is removed. How much farther can the object move? A kinetic energy coefficient of 0.2. The object is now at rest, 3:15 PM. The kinetic energy coefficient is 0.2. The object is at rest of 5 seconds. The force is removed. 2:15 PM. The kinetic energy coefficient is 0.2. The object is at rest. The force is removed. The kinetic energy coefficient is 0.2. The object is at rest. The kinetic energy coefficient is
  557. - **相似度**: 0.2536
  558. - **是否正确**: 否
  559.  
  560. - **问题编号**: 26
  561. - **问题结构**: {'context': 'A small ball with a mass of 1 kg is thrown horizontally from a certain height with an initial velocity of $3 \\, \\text{m/s}$. It is measured that the horizontal distance from the landing point to the throwing point is $1.2 \\, \\text{m}$. The air resistance acting on the ball during its motion is negligible. Find: A car passed by on the road outside.', 'sub_question_1': 'The time the small ball is in the air', 'sub_question_2': 'The speed and direction of the small ball when it hits the ground.', 'sub_question_3': "The power of gravity during the ball's landing process"}
  562. - **子问题详情**:
  563. - **子问题编号**: 1
  564. - **正确答案**: $0.4s$
  565. - **提取答案**: A small ball with a mass of 1 kg is thrown horizontally from a certain height with an initial velocity of $3 \, \text{m/s}$. It is measured that the horizontal distance from the landing point to the throwing point is $1.2 \, \text{m}$. The air resistance acting on the ball during its motion is negligible. Find: A car passed by on the road outside. The time the small ball is in the air and the velocity of $0.2 \text{m/s}$. The time the ball was in the air and the velocity of $0.2 \text{m/s}$ is negligible.
  566. ## Step 1
  567. To solve the problem, we need to find the time the ball was in the air and the velocity of $0.2 \text{m/s}$ was negligible.
  568. ## Step 1
  569. To find the time the ball was in the air and the
  570. - **相似度**: 0.3020
  571. - **是否正确**: 否
  572. - **子问题编号**: 2
  573. - **正确答案**: $5m/s$, the angle between the velocity and the horizontal direction is $53^{\circ}$
  574. - **提取答案**: A small ball with a mass of 1 kg is thrown horizontally from a certain height with an initial velocity of $3 \, \text{m/s}$. It is measured that the horizontal distance from the landing point to the throwing point is $1.2 \, \text{m}$. The air resistance acting on the ball during its motion is negligible. Find: A car passed by on the road outside. The speed and direction of the small ball when it hits the ground. The acceleration of the car is negligible. The angle of the ball is $1. The acceleration of the ball is $1. The acceleration of the ball is $1. The acceleration of the ball is $1. The acceleration of the ball is $1. The ball is $1. The ball is $1. The ball is $1. The ball is $1. The ball is $1. The ball is $1. The ball is $1. The
  575. - **相似度**: 0.4220
  576. - **是否正确**: 否
  577. - **子问题编号**: 3
  578. - **正确答案**: $40W$
  579. - **提取答案**: A small ball with a mass of 1 kg is thrown horizontally from a certain height with an initial velocity of $3 \, \text{m/s}$. It is measured that the horizontal distance from the landing point to the throwing point is $1.2 \, \text{m}$. The air resistance acting on the ball during its motion is negligible. Find: A car passed by on the road outside. The power of gravity during the ball's landing process is $0.3 \text{m/s}$. The velocity of the ball is $0.3 \text{m/s}$. The velocity of the ball is $0.3 \text{m/s}$. The acceleration of the ball is $0.3 \text{m/s}$. The force of the ball is $0.3 \text{m/s}$. The motion of the ball is $0.3 \text{m/s}
  580. - **相似度**: 0.1312
  581. - **是否正确**: 否
  582.  
  583. - **问题编号**: 27
  584. - **问题结构**: {'context': 'A small ball is released from rest at a certain distance above the ground. The ball falls freely under the influence of gravity. The displacement during the final 1 second is $\\frac{9}{25}$ of the total displacement. Air resistance is negligible, and the acceleration due to gravity is $\\mathbf{g}=10\\mathbf{m}/\\mathbf{s}^{2}$. There was a faint smell of flowers in the air.', 'sub_question_1': 'Calculate the total time it takes for the ball to fall.', 'sub_question_2': 'Calculate the displacement of the ball during the final 2 seconds of its descent.'}
  585. - **子问题详情**:
  586. - **子问题编号**: 1
  587. - **正确答案**: 5s
  588. - **提取答案**: A small ball is released from rest at a certain distance above the ground. The ball falls freely under the influence of gravity. The displacement during the final 1 second is $\frac{9}{25}$ of the total displacement. Air resistance is negligible, and the acceleration due to gravity is $\mathbf{g}=10\mathbf{m}/\mathbf{s}^{2}$. There was a faint smell of flowers in the air. Calculate the total time it takes for the ball to fall. The displacement of the ball is $\mathbf{a}$.
  589. A small ball is released from rest at a certain distance above the ground. The displacement of the ball is $\mathbf{g}$.
  590. A small ball is released from rest at a certain distance above the ground. The displacement of the ball is $\mathbf{g}$.
  591. A small ball is released from rest at a certain distance above the ground. The displacement of the ball is $\mathbf{G}$
  592. - **相似度**: 0.1170
  593. - **是否正确**: 否
  594. - **子问题编号**: 2
  595. - **正确答案**: 80m
  596. - **提取答案**: A small ball is released from rest at a certain distance above the ground. The ball falls freely under the influence of gravity. The displacement during the final 1 second is $\frac{9}{25}$ of the total displacement. Air resistance is negligible, and the acceleration due to gravity is $\mathbf{g}=10\mathbf{m}/\mathbf{s}^{2}$. There was a faint smell of flowers in the air. Calculate the displacement of the ball during the final 2 seconds of its descent. The displacement of the ball was a result of the displacement of the ball was a result of the displacement of the ball was a result of the displacement of the ball was a result of the displacement of the ball was a result of the displacement of the ball was a result of the displacement of the ball was a result of the displacement of the ball was a result of the displacement of the ball was a result of the displacement of the ball was a result of the displacement of the ball was
  597. - **相似度**: 0.1239
  598. - **是否正确**: 否
  599.  
  600. - **问题编号**: 28
  601. - **问题结构**: {'context': "A point charge with a charge of \\( q = -3 \\times 10^{-6} \\, \\mathrm{C} \\) is moved from point A to point B in an electric field. During this movement, the charge overcomes the electric field force, performing work of \\( 6 \\times 10^{-4} \\, \\mathrm{J} \\). Subsequently, when the charge is moved from point B to point C, the electric field force does work of \\( -9 \\times 10^{-4} \\, \\mathrm{J} \\) on the charge. A sign on the wall read 'Keep Quiet'.", 'sub_question_1': 'What are the potential differences between AB, BC, and CA?', 'sub_question_2': 'If the potential at point B is zero, what are the potentials at points A and C? What are the potential energies of the charge at points A and C?'}
  602. - **子问题详情**:
  603. - **子问题编号**: 1
  604. - **正确答案**: 200 V, 300 V, 500 V
  605. - **提取答案**: A point charge with a charge of \( q = -3 \times 10^{-6} \, \mathrm{C} \) is moved from point A to point B in an electric field. During this movement, the charge overcomes the electric field force, performing work of \( 6 \times 10^{-4} \, \mathrm{J} \). Subsequently, when the charge is moved from point B to point C, the electric field force does work of \( -9 \times 10^{-4} \, \mathrm{J} \) on the charge. A sign on the wall read 'Keep Quiet'. What are the potential differences between AB, BC, and CA? The electric field is a force, performing work of $6 \times 10^{-3} \, \mathrm{J} \) on the wall to the charge of $ \times 10^{-4} \, \mathrm{E} \) in the charge of the electric field is a force, performing work of $6 \times 10^{-3} \, \mathrm{I} \) on the wall to the electric field is a force, doing
  606. - **相似度**: 0.1270
  607. - **是否正确**: 否
  608. - **子问题编号**: 2
  609. - **正确答案**: 200 V, -300 V, -6×10^-4 J, -9×10^-4 J
  610. - **提取答案**: A point charge with a charge of \( q = -3 \times 10^{-6} \, \mathrm{C} \) is moved from point A to point B in an electric field. During this movement, the charge overcomes the electric field force, performing work of \( 6 \times 10^{-4} \, \mathrm{J} \). Subsequently, when the charge is moved from point B to point C, the electric field force does work of \( -9 \times 10^{-4} \, \mathrm{J} \) on the charge. A sign on the wall read 'Keep Quiet'. If the potential at point B is zero, what are the potentials at points A and C? What are the potential energies of the charge at points A and C? If the electric field has a charge, what does the potential at point A do work at point B? When the charge has a potential at point C, what does the movement of the electric field at point D? A point charge with a potential at point E? A point move with a potential at point F? A point read with a potential at point C? A point charge with a potential at point Q? A point read with a potential at point A? A point charge
  611. - **相似度**: 0.3378
  612. - **是否正确**: 否
  613.  
  614. - **问题编号**: 29
  615. - **问题结构**: {'context': 'A thin concavo-convex lens made of glass with a refractive index of $1.5$ has a convex surface with a radius of curvature of $20 cm$ and a concave surface with a radius of curvature of $60 cm$. The convex side of the lens is silvered, creating a concave mirror, and is placed on a horizontal surface. A child was playing with a ball nearby.', 'sub_question_1': '(a) Where should a pin be placed on the optical axis such that its image is formed at the same place?', 'sub_question_2': '(b) If the concave part is filled with water of refractive index $\\frac{4}{3}$, find the distance through which the pin should be moved so that the image of the pin again coincides with the pin.'}
  616. - **子问题详情**:
  617. - **子问题编号**: 1
  618. - **正确答案**: $15 cm$
  619. - **提取答案**: A thin concavo-convex lens made of glass with a refractive index of $1.5$ has a convex surface with a radius of curvature of $20 cm$ and a concave surface with a radius of curvature of $60 cm$. The convex side of the lens is silvered, creating a concave mirror, and is placed on a horizontal surface. A child was playing with a ball nearby. (a) Where should a pin be placed on the optical axis such that its image is formed at the same place? A pin was placed on the optical axis so that its image is formed at the same place? A pin was placed on the optical axis so that its image is formed at the same place? A pin was placed on the optical axis so that its image is formed at the same place? A pin was placed on the optical axis so that its image is formed at the same place? A pin was placed on the optical axis so that its image is formed at the same place? A
  620. - **相似度**: 0.0940
  621. - **是否正确**: 否
  622. - **子问题编号**: 2
  623. - **正确答案**: $1.16 cm$
  624. - **提取答案**: A thin concavo-convex lens made of glass with a refractive index of $1.5$ has a convex surface with a radius of curvature of $20 cm$ and a concave surface with a radius of curvature of $60 cm$. The convex side of the lens is silvered, creating a concave mirror, and is placed on a horizontal surface. A child was playing with a ball nearby. (b) If the concave part is filled with water of refractive index $\frac{4}{3}$, find the distance through which the pin should be moved so that the image of the pin again coincides with the pin. The convex side of refractive index $\frac{4}$, and a convex surface with a radius of curvature of $20 cm$, and a convex side of refractive index $\frac{4}$.
  625. A thin concavo-convex lens made of glass with a refractive index of $1.5$ has a convex surface with a radius of curvature of $20 cm$, and a convex side of refractive index $\frac{4}$.
  626. The refractive index of
  627. - **相似度**: 0.3006
  628. - **是否正确**: 否
  629.  
  630. - **问题编号**: 30
  631. - **问题结构**: {'context': 'A small boat is crossing a river with a width of $d = 180 \\, \\mathsf{m}$. The speed of the river current is $v_{1} = 2.5 \\, \\mathrm{m}/\\mathrm{s}$. If the speed of the boat in still water is $v_{2} = 5 \\, \\mathsf{m}/\\mathsf{s}$, find: The table where the experiment was conducted was made of wood.', 'sub_question_1': 'To minimize the time for the boat to cross the river, in which direction should the boat head? How long will it take? What is the displacement?', 'sub_question_2': 'To minimize the distance the boat travels across the river, in what direction should the boat head? How long will it take? What is the displacement?'}
  632. - **子问题详情**:
  633. - **子问题编号**: 1
  634. - **正确答案**: The bow should face the direction perpendicular to the riverbank, $36s$, $90\sqrt{5}\mathrm{m}$.
  635. - **提取答案**: A small boat is crossing a river with a width of $d = 180 \, \mathsf{m}$. The speed of the river current is $v_{1} = 2.5 \, \mathrm{m}/\mathrm{s}$. If the speed of the boat in still water is $v_{2} = 5 \, \mathsf{m}/\mathsf{s}$, find: The table where the experiment was conducted was made of wood. To minimize the time for the boat to cross the river, in which direction should the boat head? How long will it take? What is the displacement? The boat in the river is in the river? The speed of the river? The speed of the river? The speed of the river? The speed of the river? The displacement? The answer to the river? The displacement? The answer to the river? The time? The time? The time? The time? The time? The time? The time? The time? The times? The times? The time? The time? The times? The times? The times
  636. - **相似度**: 0.5429
  637. - **是否正确**: 否
  638. - **子问题编号**: 2
  639. - **正确答案**: The bow should be deflected $30^{\circ}$ upstream, $24\sqrt{3}\mathrm{s}$, $180\mathrm{m}$.
  640. - **提取答案**: A small boat is crossing a river with a width of $d = 180 \, \mathsf{m}$. The speed of the river current is $v_{1} = 2.5 \, \mathrm{m}/\mathrm{s}$. If the speed of the boat in still water is $v_{2} = 5 \, \mathsf{m}/\mathsf{s}$, find: The table where the experiment was conducted was made of wood. To minimize the distance the boat travels across the river, in what direction should the boat head? How long will it take? What is the displacement? What is the first condition? What is the second characteristic? What is the first-hand information?
  641. ## Step 1: A small boat is crossing a river with a width of 1.5 m
  642. The speed of the river current is 2.5 m
  643. The displacement of the boat in the direction of the first condition is the second characteristic of the table. To minimize the distance the boat travels at the displacement of the river is the first condition of the table.
  644. The
  645. - **相似度**: 0.3338
  646. - **是否正确**: 否
  647.  
  648. - **问题编号**: 31
  649. - **问题结构**: {'context': 'The turns ratio of the primary to secondary coils of an ideal transformer is $4:1$. If an AC voltage of $u=400^{\\sqrt{2}}\\mathrm{sin}\\ 100\\pi t\\ \\mathrm{v}$ is applied to the primary coil. The weather on that day was sunny with a gentle breeze.', 'sub_question_1': 'What is the voltage measured across the secondary coil using an AC voltmeter?'}
  650. - **子问题详情**:
  651. - **子问题编号**: 1
  652. - **正确答案**: 100V
  653. - **提取答案**: The turns ratio of the primary to secondary coils of an ideal transformer is $4:1$. If an AC voltage of $u=400^{\sqrt{2}}\mathrm{sin}\ 100\pi t\ \mathrm{v}$ is applied to the primary coil. The weather on that day was sunny with a gentle breeze. What is the voltage measured across the secondary coil using an AC voltmeter? The voltage of the secondary coil is equal to the voltage of the primary coil.
  654. ## Step 1
  655. The voltage of the secondary coil is equal to the voltage of the primary coil.
  656. ## Step 2
  657. The voltage of the secondary coil is equal to the voltage of the primary coil.
  658. ## Step 3
  659. The voltage of the secondary coil is equal to to the voltage of the primary coil.
  660. The voltage of the secondary coil is equal to to the voltage of the primary coil
  661. - **相似度**: 0.3011
  662. - **是否正确**: 否
  663.  
  664.  
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