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original_model_results.json

witw78
Apr 21st, 2025
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  1. [
  2.     {
  3.         "question_structure": {
  4.             "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.",
  5.             "sub_question_1": "Find the original length $l_0$ of the spring.",
  6.             "sub_question_2": "Determine the spring constant $k$ of the spring."
  7.         },
  8.         "answer": [
  9.             "10 cm",
  10.             "1000 N/m"
  11.         ],
  12.         "model_output": [
  13.             "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. Find the original length $l_0$ of the spring. The equilibrium length $l_0$ is equal to the compression of the spring. The force of magnitude $F_1$ is equal to the force of magnitude $F_2$. The force of magnitude $F_1$ is in the stretching or compression of the spring. The length of the spring is in the force of magnitude $F_2$. The length of the spring is equal to the force of magnitude $F_1$.\nThe force of magnitude $",
  14.             "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. Determine the spring constant $k$ of the spring. The spring constant $C$ is within the elastic limit. The elastic limit is a theoretical limit.\nThe problem is to determine the spring constant $C$ is within the spring. The spring constant $F_2$ is within the elastic limit. The elastic limit is a limit to the size of the force $F_1$ that can be applied to stretch the spring. The spring's spring constant is a limit to the size of the force $F_1$ that"
  15.         ]
  16.     },
  17.     {
  18.         "question_structure": {
  19.             "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 $\\mathrm{g}\\!=\\!10\\mathrm{m}/\\mathrm{s}^{2}$.",
  20.             "sub_question_1": "What is the duration of time it takes for the object to reach the ground?",
  21.             "sub_question_2": "What is the magnitude of the object's velocity upon impact with the ground?",
  22.             "sub_question_3": "What is the distance the object falls during its last 1 second of motion?"
  23.         },
  24.         "answer": [
  25.             "3s",
  26.             "30m/s",
  27.             "25m"
  28.         ],
  29.         "model_output": [
  30.             "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 $\\mathrm{g}\\!=\\!10\\mathrm{m}/\\mathrm{s}^{2}$. What is the duration of time it takes for the object to reach the ground? Step 1: 45 m/s. The acceleration due to the ground, undergoing free fall motion, with the acceleration due to the ground, is given by $\\mathrm{g}=\\!10\\mathrm{m}/\\mathrm{s}$. The duration of time it takes for the object to reach the ground, is given by $\\mathrm{t}=\\!\\mathrm{1}$. The time it takes for the object to reach the ground, is given by $\\mathrm",
  31.             "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 $\\mathrm{g}\\!=\\!10\\mathrm{m}/\\mathrm{s}^{2}$. 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 acceleration of $g=10\\text{ m}/\\text{s}^{2}$, of the ground? \n\n## Step 1\nTo find the velocity of the object, we need to know the force of gravity, which is a constant acceleration of $g=10\\text{ m}/\\text{s}^{2}$, and the direction of the ground",
  32.             "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 $\\mathrm{g}\\!=\\!10\\mathrm{m}/\\mathrm{s}^{2}$. What is the distance the object falls during its last 1 second of motion? The acceleration due to gravity is given by $\\mathrm{g}=\\!10\\mathrm{m}/\\mathrm{s}^{2}$.\n## Step 1\nTo find the velocity of the object, we first need to know the distance the object has been falling. This is given by $v in the equation $\\Delta=\\!45\\mathrm{m}/\\mathrm{s} in the equation $\\Delta=\\!45\\mathrm{m}/\\mathrm{s} in"
  33.         ]
  34.     },
  35.     {
  36.         "question_structure": {
  37.             "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.",
  38.             "sub_question_1": "The distance this little bird flies",
  39.             "sub_question_2": "The average speed of this small bird's flight"
  40.         },
  41.         "answer": [
  42.             "$400\\mathrm{m}$",
  43.             "$10\\mathrm{m/s}$"
  44.         ],
  45.         "model_output": [
  46.             "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. The distance this little bird flies is $0.5\\mathrm{m}$ and the cars are $600\\mathrm{m}$ apart. The two cars are $600\\mathrm{m}$ apart and the bird is $600\\mathrm{m}$ apart.\nNow, the problem is to find the distance between the two cars, the distance between the two cars, and the distance between the bird and the car. The distance between the bird and the front of Car B. The distance between the bird",
  47.             "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. The average speed of this small bird's flight is $30\\mathrm{m/s}$ and the cars stop at a speed of $30\\mathrm{m/s}$.\nFirst, we need to find the average speed of the bird. The average speed of the car is $20\\mathrm{m/s}$ and the bird is flying at a speed of $30\\mathrm{m/s}$.\nThe average time for the bird to cover the front of Car A to fly beyond Car B, and immediately stop the front"
  48.         ]
  49.     },
  50.     {
  51.         "question_structure": {
  52.             "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: $E^{2}=(p c)^{2}+\\left(m c^{2}\\right)^{2}$",
  53.             "sub_question_1": "Determine $E_p$ in terms of $m_p$, $m_{\\Delta}$, and $E_b$. You may assume that $E_b$ is small.",
  54.             "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.",
  55.             "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 $m_{\\Delta} c^{2}=1232 \\mathrm{MeV}$."
  56.         },
  57.         "answer": [
  58.             "$\\frac{m_{\\Delta}^{2}-m_{p}^{2}}{4 E_{b}}$",
  59.             "$\\approx 1.17 \\times 10^{-3} \\mathrm{eV}$",
  60.             "$E_{p} \\approx 1.4 \\times 10^{20} \\mathrm{eV}$"
  61.         ],
  62.         "model_output": [
  63.             "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: $E^{2}=(p c)^{2}+\\left(m c^{2}\\right)^{2}$ Determine $E_p$ in terms of $m_p$, $m_{\\Delta}$, and $E_b$. You may assume that $E_b$ is small. The collision results in the formation of a new particle with mass $m_p$, and the energy is small. The Lorentz factor is $\\frac{1}{\\sqrt{1-\\beta^{2} \\approx 1+\\beta^{2}$ for $|\\theta| \\ll 1$\n$\\sin \\theta \\approx 1+\\theta$ for $|x| \\ll 1$\n$\\tan \\theta \\approx 1+\\theta$ for $|",
  64.             "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: $E^{2}=(p c)^{2}+\\left(m c^{2}\\right)^{2}$ 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, writing your answer in electronvolgar shift the momentum of the Lorentz factor, the relativistic momentum, which is an oscillation of the Lorentz force, which is an oscillation of the Lorentz collision, which is an annihilation of the Lorentz factor, the relativistic mass, which is an annihilation of the Lorentz force, which is an oscillation of the Lorentz factor, the relativistic",
  65.             "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: $E^{2}=(p c)^{2}+\\left(m c^{2}\\right)^{2}$ 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 collision is given by $E_b$.\nThe relativistic momentum is given by $E_b$.\nThe speed of the motion is given by $e_b$.\nThe velocity of the Lorentz factor is given by $E_b$.\nThe momentum is given by $k_{\\mathrm{A}$.\nThe energy of the momentum is given by $k_{\\mathrm{B}$.\nThe mass of the momentum is given by $k_{"
  66.         ]
  67.     },
  68.     {
  69.         "question_structure": {
  70.             "context": "China's first lunar exploration satellite, \"Chang'e-1,\" was launched in 2007 from the Xichang Satellite Launch Center by the \"Long March 3A\" carrier rocket. Assuming the satellite's orbit is circular and its altitude above the lunar surface is equal to the Moon's radius, it is known that the satellite's orbital period around the Moon is T, the Moon's radius is R, and the gravitational constant is G.",
  71.             "sub_question_1": "What is the mass of the Moon?",
  72.             "sub_question_2": "What is the density of the Moon?"
  73.         },
  74.         "answer": [
  75.             "$\\frac{32\\pi^{2}R^{3}}{G T^{2}}$",
  76.             "$\\frac{24\\pi}{G T^{2}}$"
  77.         ],
  78.         "model_output": [
  79.             "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. What is the mass of the Moon? What is the mass of the Moon? What is the radius of the Moon? What is the distance to the Moon? What is the velocity of the Moon? What is the orbital speed of the Moon? What is the surface area of the Moon? What is the volume of the Moon? What is the lunar distance to the Moon? What is the lunar velocity? What is the orbital period of the Moon? What is the lunar time? What is the lunar time? What is",
  80.             "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. What is the density of the Moon? The density of the Moon is the Moon's mass, the mass of the Moon is the Moon's volume, the volume of the Moon is the Moon's surface area, the surface of the Moon is the Moon's gravity, the gravity of the Moon is the Moon's surface area, the area of the Moon is the Moon's volume, the volume of the Moon is the Moon's mass, the mass of the Moon is the Moon's radius, the size of the Moon is"
  81.         ]
  82.     },
  83.     {
  84.         "question_structure": {
  85.             "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.",
  86.             "sub_question_1": "What is the magnitude of the uniform electric field strength?",
  87.             "sub_question_2": "What is the potential difference $U_{AB}$ between points A and B?",
  88.             "sub_question_3": "If the potential at point O is taken as zero, what is the maximum potential energy of the charged ball?"
  89.         },
  90.         "answer": [
  91.             "$\\frac{\\sqrt{3}mg}{q}$",
  92.             "$-\\frac{\\sqrt{3}mgL}{2q}$",
  93.             "$\\frac{\\sqrt{3}mgL}{2}$"
  94.         ],
  95.         "model_output": [
  96.             "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. What is the magnitude of the uniform electric field strength? The electric field is a function of the ball at point B is a function of the ball at point B is a function of the ball at point B is a function of the ball at point B is a function of the ball at point B is a function of the ball at point B is a function of the ball at point B is a function of the ball at point B is a function of the ball at point B is a function of the ball at point B is a function",
  97.             "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. What is the potential difference $U_{AB}$ between points A and B? The ball is the potential difference between the points A and B? The ball is the potential difference between the points A and B? The ball is the potential difference between the points C and D. The ball is the potential difference between the points E. The ball is the potential difference between the points F. The ball is the potential difference between the points C. The ball is the potential difference between the points L. The ball is the potential difference between the points L. The ball",
  98.             "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. If the potential at point O is taken as zero, what is the maximum potential energy of the charged ball? The potential energy of the ball is the maximum potential energy of the charged ball is the maximum potential energy of the charged ball? The potential energy of the ball is the maximum potential energy of the charged ball? The potential energy of the ball is the maximum potential energy of the charged ball? The potential energy of the ball is the maximum potential energy of the charged ball? The potential energy of the ball is the maximum potential energy of the charged ball? The potential energy of the string is"
  99.         ]
  100.     },
  101.     {
  102.         "question_structure": {
  103.             "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 $a_{A} = 2 \\, \\mathbf{m/s}^{2}$.",
  104.             "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.",
  105.             "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?"
  106.         },
  107.         "answer": [
  108.             "$100\\mathrm{m}$",
  109.             "$66\\mathrm{m}$"
  110.         ],
  111.         "model_output": [
  112.             "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 $a_{A} = 2 \\, \\mathbf{m/s}^{2}$. The driver of car A needs to start braking at least how far away from the toll booth window to avoid violating regulations. Note that the speed of the vehicle is accelerated at a constant speed of v_{0} = 5 \\, \\mathrm{m/s}^{2}$. The answer to the problem is not difficult to understand why the driver of car A needs to be changed to avoid the toll station to avoid the driver of car A getting into the problem is not easy to understand why the toll station is not able to be decelerated to avoid the driver of car A getting on the",
  113.             "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 $a_{A} = 2 \\, \\mathbf{m/s}^{2}$. 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? The answer to the problem is in the form of a toll station, and the driver of car B, and the minimum distance between the two cars and the maximum speed of the toll station, and the acceleration of the toll booth, and the deceleration of the toll station, and the distance of the tolling of the tolling of the tolling of the tolling of the braking of the tolling of the accelerations of the speed of the tolling of the passing"
  114.         ]
  115.     },
  116.     {
  117.         "question_structure": {
  118.             "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.",
  119.             "sub_question_1": "Find the magnetic flux $\\Phi_{1}$ passing through the coil.",
  120.             "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."
  121.         },
  122.         "answer": [
  123.             "BL^2",
  124.             "$\\frac{4BL^2}{\\pi}$"
  125.         ],
  126.         "model_output": [
  127.             "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. Find the magnetic flux $\\Phi_{1}$ passing through the coil. \n\nGiven that the coil is a is placed in a uniform magnetic field with magnetic induction $B$, we want to find the magnetic flux $\\Phi_{1}$ passing through the coil. \n\nThe magnetic flux $\\Phi_{1}$ is placed in a uniform magnetic field with magnetic induction $B$, we want to find the magnetic flux $\\Phi_{2}$ passing through the coil. \n\nThe magnetic flux $\\Phi_{2}$ is placed in a uniform magnetic field with magnetic induction $\\",
  128.             "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. 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. Then the magnetic flux $\\Phi$ is measured by the coil.\nAnswer 3 to the question of the flux $\\Phi$ is\nThe flux $\\Phi$ is\nA square coil with a side length $L$ is\nThe flux $\\Phi$ is\nThe flux $\\Phi$ is\nThe flux $\\Phi$ is\nThe flux $\\Phi$ is\nThe flux $\\Phi$ is\nThe flux $\\Phi$ is\nThe flux $\\Phi$ is\nThe"
  129.         ]
  130.     },
  131.     {
  132.         "question_structure": {
  133.             "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 $R=99\\Omega$.",
  134.             "sub_question_1": "Write the expression for the instantaneous value of alternating current; do not add any other content.",
  135.             "sub_question_2": "The power consumed by the external resistor; do not add any other content.",
  136.             "sub_question_3": "The power of external forces."
  137.         },
  138.         "answer": [
  139.             "i = 6.28 sin(100πt) (A)",
  140.             "198π² W",
  141.             "200π² W"
  142.         ],
  143.         "model_output": [
  144.             "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 $R=99\\Omega$. Write the expression for the instantaneous value of alternating current; do not add any other content. The value of the measurement of the angle of the magnetic field of the velocity of the angular displacement of the instantaneous value of the resistance of the external circuit of the coil of the direction of the rotation of the rotation of the torque of the tension of the stress of the strain of the strain of the strain of the stress of the strain of the strain of the strain of the strain of the torsion of the torque of the rotation of the angular displacement of the velocity of the instantaneous value",
  145.             "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 $R=99\\Omega$. The power consumed by the external resistor; do not add any other content. The rotor of a sinusoidal generator is a square coil with $n=100$ turns and side length $L=20\\mathrm{cm}$. The magnetic field is a square coil with $B=0.5\\mathrm{T}$ turns and the direction of the induction is $\\omega=100\\pi$. The velocity of the action of an angular generator is a square coil with $a=1$ turns and the resistance of the external force is $R=99",
  146.             "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 $R=99\\Omega$. The power of external forces. The angular velocity of the magnetic field is $M=1\\Omega$. The uniform velocity of the rotor is $N=1\\Omega$.\n\nThe problem is to find the angle of the magnetic field, the angle of the rotor, the direction of the power of the external forces, and the velocity of the internal forces. The solution is to find the angle of the power of the rotor of the magnetic field of the velocity of the resistance of the coil of the timing of"
  147.         ]
  148.     },
  149.     {
  150.         "question_structure": {
  151.             "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 $100\\Omega$.",
  152.             "sub_question_1": "What is the current on the transmission line?",
  153.             "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)?"
  154.         },
  155.         "answer": [
  156.             "$10A$",
  157.             "1:50"
  158.         ],
  159.         "model_output": [
  160.             "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 $100\\Omega$. What is the current on the transmission line? By the AC generator\n## Step 1: Calculate the voltage of the transmission line\nThe voltage of the transmission line is given by the equation $\\frac{V}{\\Omega} = \\frac{V}{\\Omega}$. The voltage of the transmission line is given by the equation $\\frac{V}{\\Omega} = \\frac{V}{\\Omega}$.\n## Step 2: Calculate the resistance of the transmission line\nThe resistance of the transmission line is",
  161.             "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 $100\\Omega$. What is the turns ratio of the step-up transformer required for power transmission (assuming the transformer used is an ideal transformer)? $100\\%$\n## Step 1: Calculate the voltage of the transmission line\nThe voltage of the transmission line is given by the voltage of the transmission line is given by the voltage of the transmission line is given by the voltage of the transmission line is given by the voltage of the transmission line is given by the voltage of the transmission line is given by the voltage of the transmission line is given by the voltage of the transmission line is given by the voltage of the transmission line"
  162.         ]
  163.     },
  164.     {
  165.         "question_structure": {
  166.             "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 $\\triangle\\mathrm{t}\\!=\\!4.0\\mathrm{s}$.",
  167.             "sub_question_1": "What are the average velocities of the glider as it passes through each of the two photogates?",
  168.             "sub_question_2": "Estimate the magnitude of the glider's acceleration.",
  169.             "sub_question_3": "Estimate the distance between the two photogates."
  170.         },
  171.         "answer": [
  172.             "0.10m/s, 0.20m/s",
  173.             "0.025m/s²",
  174.             "0.60m"
  175.         ],
  176.         "model_output": [
  177.             "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 $\\triangle\\mathrm{t}\\!=\\!4.0\\mathrm{s}$. What are the average velocities of the glider as it passes through each of the two photogates? \n## Step 1: To determine the acceleration of a glider on a shading plate\nThe average velocity of the glider as it passes through the first photogate\nThe average velocity of the glider as it passes through the second photogate\nThe acceleration of the glider as it passes through the third photogate\nThe acceleration of the glider as it passes through the fourth photogate\nThe average acceleration of the gliders as they pass through",
  178.             "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 $\\triangle\\mathrm{t}\\!=\\!4.0\\mathrm{s}$. Estimate the magnitude of the glider's acceleration. The time to pass through the second photogate as $\\triangle\\mathrm{t}\\!=\\!3.0\\mathrm{s}$. The time to pass through the first photogate as $\\triangle\\mathrm{t}\\!=\\!5.0\\mathrm{s}$. The time to pass through the second photogate as $\\triangle\\mathrm{t}\\!=\\!6.0\\mathrm{s$$. The time to pass through the third photog",
  179.             "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 $\\triangle\\mathrm{t}\\!=\\!4.0\\mathrm{s}$. Estimate the distance between the two photogates. The time interval from the start of the third photogate to the end of the fourth photogate is $\\Delta\\mathrm{t}\\!=\\!5\\mathrm{s}$. The time to pass through the fifth photogate is $\\Pi\\mathrm{t}\\!=\\!6\\mathrm{s$.\nThe acceleration of the glider is $\\mu\\mathrm{t}\\!=\\!7\\mathrm{s}$, and the time to pass through the second"
  180.         ]
  181.     },
  182.     {
  183.         "question_structure": {
  184.             "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.",
  185.             "sub_question_1": "What is the wavelength of the electromagnetic wave emitted by the black box?",
  186.             "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?"
  187.         },
  188.         "answer": [
  189.             "8000m",
  190.             "$4.5\\times10^{-9}F$"
  191.         ],
  192.         "model_output": [
  193.             "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. What is the wavelength of the electromagnetic wave emitted by the black box? The wavelength of the electromagnetic wave emitted by the black box? The speed of the electromagnetic wave emitted by the electromagnetic wave?\n\n## Step 1: Identify the given information\nThe problem provides information about a plane crash and asks for a black box to be analyzed for 30 days. The black box is used to determine the cause of the accident.\n\n## Step 2: Determine the location of the black box\nThe black box is used to emit the electromagnetic wave, and the speed",
  194.             "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. 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? The answer is a mystery, but it is a mystery. The black box can automatically emit the signals, and the self-inductance coefficient of the coil is $\\mathrm{L} = 4.0$ m/s. The speed of the light in the vacuum is $\\mathrm{c} = 3.0$ m/s, and the electromagnetic wave frequency is $\\mathrm{f} = 30$ kHz, and the frequency of the light is $\\mathrm{"
  195.         ]
  196.     },
  197.     {
  198.         "question_structure": {
  199.             "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.",
  200.             "sub_question_1": "Determine the pressure of the gas inside the furnace chamber at room temperature after the argon gas has been injected.",
  201.             "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."
  202.         },
  203.         "answer": [
  204.             "$3.2 × 10^7 Pa$",
  205.             "$1.6 × 10^8 Pa$"
  206.         ],
  207.         "model_output": [
  208.             "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. Determine the pressure of the gas inside the furnace chamber at room temperature after the argon gas has been injected. The bottle of the gas was not a pressure vessel, but a container. The pressure of the gas was not a function of the bottle, but a device. The room temperature was not a pressure, but a value. The furnace was not a pressure, but a device. The chamber was not a pressure, but a container. The bottle was not a pressure, but a vessel. The pressure was not a function, but a device. The gas was not a pressure, but",
  209.             "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. 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 bottle is a container with a narrow neck, and the pressure of the bottle is the pressure that the gas inside the bottle exerts on the gas outside. The pressure of the bottle is the pressure that the gas inside the bottle exerts on the gas outside. The pressure of the bottle is the pressure that the gas inside the bottle exerts on the gas outside. The pressure of the bottle is the pressure that the gas inside the bottle exerts on the gas outside. The"
  210.         ]
  211.     },
  212.     {
  213.         "question_structure": {
  214.             "context": "A particle starts from rest and undergoes uniformly accelerated linear motion. The displacement of the particle in the first second is $3\\mathrm{m}$.",
  215.             "sub_question_1": "What is the magnitude of the acceleration of a particle's motion?",
  216.             "sub_question_2": "What is the displacement of the particle in the first 3 seconds?",
  217.             "sub_question_3": "When the displacement is $12\\mathrm{m}$, what is the velocity of the particle?"
  218.         },
  219.         "answer": [
  220.             "$6\\mathrm{m}/\\mathrm{s}^{2}$",
  221.             "27m",
  222.             "12m/s"
  223.         ],
  224.         "model_output": [
  225.             "A particle starts from rest and undergoes uniformly accelerated linear motion. The displacement of the particle in the first second is $3\\mathrm{m}$. What is the magnitude of the acceleration of a particle's motion? The displacement of a particle in the first second is $3\\mathrm{m}$. What is the acceleration of a particle in the first second? The acceleration of a particle in the first second is $3\\mathrm{m}$. The displacement of a particle in the first second is $3\\mathrm{m}$. The displacement of a particle in the first second is $3\\mathrm{m}$. The displacement of a particle in the first second is $3",
  226.             "A particle starts from rest and undergoes uniformly accelerated linear motion. The displacement of the particle in the first second is $3\\mathrm{m}$. What is the displacement of the particle in the first 3 seconds? What is the displacement of the particle in the first second?\n## Step 1: The displacement of the particle in the first second is given by $\\frac{\\mathrm{u}}$.\n$\\frac{\\mathrm{u}}$ = $\\frac{\\mathrm{u}}$.\n## Step 2: The displacement of the particle in the first second is given by $\\frac{\\mathrm{u}}$.\n## Step 3: The displacement of the particle in the first second",
  227.             "A particle starts from rest and undergoes uniformly accelerated linear motion. The displacement of the particle in the first second is $3\\mathrm{m}$. When the displacement is $12\\mathrm{m}$, what is the velocity of the particle? \n## Step 1\nThe displacement of the particle in the first second is $12\\mathrm{m}$. When the displacement of the particle in the first second is $12\\mathrm{m}$, what is the displacement of the particle in the first second is $12\\mathrm{m}$? \n## Step 2\nThe displacement of the particle in the first second is $12\\mathrm{m}$? The displacement of the particle in the first second"
  228.         ]
  229.     },
  230.     {
  231.         "question_structure": {
  232.             "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.",
  233.             "sub_question_1": "What is the turns ratio of the primary coil to the secondary coil in a step-up transformer?",
  234.             "sub_question_2": "What is the transmission current in A?"
  235.         },
  236.         "answer": [
  237.             "1:20",
  238.             "0.90A"
  239.         ],
  240.         "model_output": [
  241.             "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. What is the turns ratio of the primary coil to the secondary coil in a step-up transformer? If the secondary coil is used, the energy loss of the transformer is not considered. The turns ratio of the primary coil to the secondary coil in a step-up transformer is not considered. The power output of a power plant is $200\\mathrm{kW}$, and the output voltage is $11\\mathrm{kV}$. If the high voltage transmission at $220\\mathrm{kV}$ is used, the energy loss of the transformer is not considered. The turns ratio of",
  242.             "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. What is the transmission current in A? The transmission current is $11\\mathrm{kA}$, and the transmission voltage is $12\\mathrm{kA}$.\nThe transmission current is $11\\mathrm{kA}$, and the transmission voltage is $12\\mathrm{kA}$.\nThe transmission voltage is $12\\mathrm{kA}$.\nThe transmission voltage is $12\\mathrm{kA}$.\nThe transmission voltage is $12\\mathrm{kA}$.\nThe transmission current is $12\\mathrm{kA"
  243.         ]
  244.     },
  245.     {
  246.         "question_structure": {
  247.             "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.",
  248.             "sub_question_1": "What is the resistance of the bulb when it is glowing normally?",
  249.             "sub_question_2": "What is the voltage across the primary coil of the transformer?",
  250.             "sub_question_3": "What are the currents passing through the primary and secondary coils of the transformer?"
  251.         },
  252.         "answer": [
  253.             "$806.7 \\Omega$",
  254.             "660V",
  255.             "9.1A"
  256.         ],
  257.         "model_output": [
  258.             "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. What is the resistance of the bulb when it is glowing normally? The resistance of the bulb is 3:1. The resistance of the bulb is 4:1. The resistance of the bulb is 1:1. The resistance of the bulb is 3:1. The resistance of the bulb is 4:1. The resistance of the bulb is 5:1. The resistance of the bulb is 5:1. The resistance of the bulb is 6:1. The resistance of the bulb is 7",
  259.             "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. What is the voltage across the primary coil of the transformer? The voltage of the transformer is used to power the bulbs, and the specifications of the transformer are operating normally. The voltage of the transformer is used to power the bulbs, and the turn ratio of the transformer is used to power the secondary coil. The voltage of the transformer is used to power the primary coil, and the specifications of the transformer are operating normally. The voltage of the transformer is used to power the secondary coil, and the turn ratio of the transformer is used to power",
  260.             "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. What are the currents passing through the primary and secondary coils of the transformer? The secondary coil is operating at 10kW, and the primary coil is 3W. The transformer is used to power the secondary coil, and the operating voltage is 220V. The transformer is used to power the primary coil, and the operating current is 10kW. The transformer is used to power the secondary coil, and the operating voltage is 220V. The transformer is used to power the primary coil, and the secondary current is 20k"
  261.         ]
  262.     },
  263.     {
  264.         "question_structure": {
  265.             "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\".",
  266.             "sub_question_1": "Find the magnitude of the displacement of A in the first 3 seconds, $x_{1}$",
  267.             "sub_question_2": "Find the maximum distance between A and B within the first 3 seconds.",
  268.             "sub_question_3": "To avoid collision, the condition for the acceleration $a_{0}$ when B starts to decelerate must satisfy:"
  269.         },
  270.         "answer": [
  271.             "$39\\mathrm{m}$",
  272.             "$27\\mathrm{m}$",
  273.             "$a_{0}\\geq 6\\mathrm{m}/\\mathrm{s}^{2}$"
  274.         ],
  275.         "model_output": [
  276.             "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\". Find the magnitude of the displacement of A in the first 3 seconds, $x_{1}$, and $y_{2}$, which are the given values of the displacement of A in the second 2 seconds, $x_{1}$, and $y_{2}$, which are the given values of the displacement of A in the third 3 seconds, $x_{1}$, and $y_{2}$, which are the given values of the displacement of A in the fourth 4 seconds, $x_{1}$, and $y_{2",
  277.             "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\". Find the maximum distance between A and B within the first 3 seconds. The velocity of B is $v_{1}=4\\mathrm{m}/\\mathrm{s}$, and the distance between A and B is $a_{1}=3\\mathrm{m}/\\mathrm{s}$.\nThe velocity of B is $v_{2}=2\\mathrm{m}/\\mathrm{s}$, and the distance between A and B is $v_{3}=3\\mathrm{m}/\\mathrm{s}$.\nThe velocity of B is $",
  278.             "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\". To avoid collision, the condition for the acceleration $a_{0}$ when B starts to decelerate must satisfy: \\begin{equation*}\n\\begin{align}\n\\begin{equation}\n\\begin{array| A | C \\begin{table} \\begin{tabular}{| l | l | C | l |}\n\\hline\n\\begin{table} \\begin{array} | l | l | l | l | l | l | l | l | l | l | l | l | l | l | l | l | l |"
  279.         ]
  280.     },
  281.     {
  282.         "question_structure": {
  283.             "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.",
  284.             "sub_question_1": "Find the kinetic energy of the electron.",
  285.             "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.",
  286.             "sub_question_3": "Find the equivalent current $I$ formed by the motion of an electron around the nucleus."
  287.         },
  288.         "answer": [
  289.             "$\\frac{k e^2}{2r}$",
  290.             "$-\\frac{k e^2}{2r}$",
  291.             "$\\frac{e^2}{2 \\pi r}\\sqrt{\\frac{k}{mr}}$"
  292.         ],
  293.         "model_output": [
  294.             "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. Find the kinetic energy of the electron. The kinetic energy of the electron is not the same. The kinetic energy of the electron is not the same. The kinetic energy of the electron is not the same. The kinetic energy of the electron is not the same. The kinetic energy of the electron is not the same. The kinetic energy of the electron is not the same. The kinetic energy of the electron is not the same. The kinetic energy of the electron is not the same. The kinetic energy of the electron is not",
  295.             "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. 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 $e_{p} = \\frac{k}{m}$. The energy of the proton is $m_{p} = \\frac{k}{e}$.\nBrowse D. Choose the energy of the electron. The energy of the proton is $m_{p} = \\frac{k}{e}$. The energy of the neutron is $E_{p} = \\frac{k}{e}$. The energy of the alpha particle is $\\alpha_{",
  296.             "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. Find the equivalent current $I$ formed by the motion of an electron around the nucleus. The motion of the electron is $m$, the motion of the electron is $e$, the motion of the electron is $e$, the motion of the electron is $\\omega$, the motion of the electron is $\\phi$, and the motion of the electron is $\\Phi$.\nThe electron is a subatomic particle. The mass of the electron is $M$, the charge of the electron is $Q$, the electrostatic force is $q$, the motion of the electron is"
  297.         ]
  298.     },
  299.     {
  300.         "question_structure": {
  301.             "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 $2x$.",
  302.             "sub_question_1": "Find the ratio of the amplitudes of the two oscillations."
  303.         },
  304.         "answer": [
  305.             "1/2"
  306.         ],
  307.         "model_output": [
  308.             "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 $2x$. Find the ratio of the amplitudes of the two oscillations. The ratio of the amplitude of the first oscillation to the the second is the ratio of the first is constant, and the ratio of the first is the, and Find the ratio of the first is, and Find the ratio of the amplitude of the first is, and Find the ratio of the amplitude of the first is, and Find the ratio of the amplitude of the first is, and Find the ratio of the amplitude of the first is, and Find the ratio of the amplitude"
  309.         ]
  310.     },
  311.     {
  312.         "question_structure": {
  313.             "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:",
  314.             "sub_question_1": "What is the average velocity of object A throughout the entire process?",
  315.             "sub_question_2": "What is the average speed of A throughout the entire process?",
  316.             "sub_question_3": "What is the average speed of person A moving from point $A$ to point $B$?",
  317.             "sub_question_4": "What is the average speed of A moving from point $B$ to point $C$?"
  318.         },
  319.         "answer": [
  320.             "$5\\mathrm{m/s}$, direction is $37^{\\circ}$ west of north.",
  321.             "$7\\mathrm{m/s}$",
  322.             "$8\\mathrm{m/s}$, direction north",
  323.             "$6\\mathrm{m/s}$"
  324.         ],
  325.         "model_output": [
  326.             "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: What is the average velocity of object A throughout the entire process? The average velocity of object A is the speed at which it is the same point $B$ is the speed at which the average time $A$ is the time $B$ is the time $C$ is the distance $40\\mathrm{m}$ to reach point $B$ is the time $B$ is the speed at which the average time $A$ is the time $C$ is the distance $40\\mathrm{m}$ to reach point $B",
  327.             "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: What is the average speed of A throughout the entire process?  Find: The average time it takes for A to reach B, and the time it takes for A to reach C.  The average time it takes for A to reach B, and the time it takes for C to reach A.  The average time it takes for B to reach A.  The average time it takes for C to reach A.  The average time it takes for D to reach C.  The average time it takes for E to reach F.",
  328.             "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: What is the average speed of person A moving from point $A$ to point $B$? \n## Step 1: \nTo find the average speed of person A moving from point $A$ to point $B$.\n## Step 1: \nTo find the average speed of person A moving from point $A$ to point $B$.\n## Step 2: \nTo find the average time it takes for person A to reach point $B$.\n## Step 3: \nTo find the average distance from point $A$ to reach point $",
  329.             "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: What is the average speed of A moving from point $B$ to point $C$? \n## Step 1:  Find the distance from point A to point B\nThe distance from point A to point B is given by the formula distance = d = A - B. \n## Step 2:  Find the distance from point B to point C\nThe distance from point B to point C is given by the formula distance = d = C - B. \n## Step 3:  Find the distance from point C to point A\nThe distance from"
  330.         ]
  331.     },
  332.     {
  333.         "question_structure": {
  334.             "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.",
  335.             "sub_question_1": "What is the mass of the Earth?",
  336.             "sub_question_2": "What is the centripetal acceleration of a satellite orbiting around the center of the Earth?",
  337.             "sub_question_3": "What is the orbital speed of a satellite as it revolves around the center of the Earth?"
  338.         },
  339.         "answer": [
  340.             "$M={\\frac{g R^{2}}{G}}$",
  341.             "$a=\\frac{R^{2}g}{\\left(R+h\\right)^{2}}$",
  342.             "$v=R\\sqrt{\\frac{g}{R+h}}$"
  343.         ],
  344.         "model_output": [
  345.             "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. What is the mass of the Earth? The mass of the Earth's surface is not a function of the Earth's surface, but the mass of the Earth's surface is a function of the Earth's surface.\n## Step 1: Understand the problem\nThe problem is asking for the calculation of the Earth's surface area, which is a function of the Earth's surface. The formula is $A = \\sqrt{h} - 1$, where $h$ is the height of the Earth, and $R",
  346.             "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. What is the centripetal acceleration of a satellite orbiting around the center of the Earth? What is the launch speed of a rocket in a circular motion at a high velocity? What is the velocity of a rocket in a high orbit? What is the orbital velocity of a rocket in a high-speed motion? What is the launch speed of a rocket in a circular motion? What is the orbital velocity of a rocket in a high-speed motion? What is the speed of a rocket in a high-speed motion? What is the velocity of a rocket in a high-speed motion?",
  347.             "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. What is the orbital speed of a satellite as it revolves around the center of the Earth? The orbital speed of a satellite as it revolves around the center of the Earth is the same as the orbital speed of a satellite as it revolves around the center of the Earth is the same as the gravitational acceleration of the Earth's surface is the same as the circular motion of the Earth's surface is the same as the satellite as it revolves around the center of the Earth is the same as the final orbital velocity of the satellite as it revolves around the center of the Earth is the same"
  348.         ]
  349.     },
  350.     {
  351.         "question_structure": {
  352.             "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 $2\\mathrm{m}/\\mathrm{s}^{2}$.",
  353.             "sub_question_1": "The speed of the car after braking for 2 seconds.",
  354.             "sub_question_2": "The minimum distance for a car to stop before the zebra crossing when braking",
  355.             "sub_question_3": "The displacement of a car braking for 3 seconds."
  356.         },
  357.         "answer": [
  358.             "$4m/s$",
  359.             "$16m$",
  360.             "$15m$"
  361.         ],
  362.         "model_output": [
  363.             "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 $2\\mathrm{m}/\\mathrm{s}^{2}$. The speed of the car after braking for 2 seconds. The pedestrian, being a pedestrian, was driving at an acceleration of $1\\mathrm{m}/\\mathrm{h}$, and the brakes were closed. The brakes were closed. The car was a pedestrian, and the driver was a motorist. The driver was a driver. The speed was a motorist. The acceleration was a motorist. The motion was a motorist. The motion was a motor. The braking was a motorist. The braking was a motor",
  364.             "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 $2\\mathrm{m}/\\mathrm{s}^{2}$. The minimum distance for a car to stop before the zebra crossing when braking, and the pedestrian was not aware of the car in to cross the street. The driver of the car was not responsible for the pedestrian, and the vehicle was not responsible for the zebra. The car stopped a short distance, and the pedestrian stopped a very small angle, and the vehicle was not responsible for the pedestrian. The driver of the car was not aware of the pedestrian, and the car was not responsible for the zebra. The pedestrian stopped a short distance, and",
  365.             "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 $2\\mathrm{m}/\\mathrm{s}^{2}$. The displacement of a car braking for 3 seconds. The pedestrian was not wearing a helmet with a speed of $10\\mathrm{m}/\\mathrm{h}$ and of $8\\mathrm{m/s}$ in a car braking for 3 seconds. The acceleration of a pedestrian was not wearing a helmet with a speed of $10\\mathrm{m}/\\mathrm{s}$.\n\n## Step 1\nTo build a civilized city, it is advocated that motor vehicles yield to pedestrians. A driver was driving at a speed"
  366.         ]
  367.     },
  368.     {
  369.         "question_structure": {
  370.             "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.",
  371.             "sub_question_1": "The magnitude of the acceleration $\\mathbf{a}_1$ during the car's acceleration process.",
  372.             "sub_question_2": "The magnitude of the acceleration $\\mathbf{a}_2$ during the braking process of the car."
  373.         },
  374.         "answer": [
  375.             "$2\\mathrm{m}/\\mathrm{s}^{2}$ ",
  376.             "$5\\mathrm{m}/\\mathrm{s}^{2}$ "
  377.         ],
  378.         "model_output": [
  379.             "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. The magnitude of the acceleration $\\mathbf{a}_1$ during the car's acceleration process. The magnitude of the braking time $\\mathbf{t}_1$ is not taken into account. The displacement of the driver $\\mathbf{a}$ during the acceleration process. The displacement of the passenger $\\mathbf{a}$ during the braking time $\\mathbf{t}$ is not taken into account. of the driver $\\mathbf{a}$ during the acceleration process. The displacement of the passenger $\\mathbf{a}$ during the deceleration process. The",
  380.             "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. The magnitude of the acceleration $\\mathbf{a}_2$ during the braking process of the car. The driver's reaction time during the braking process of the car. The magnitude of the acceleration $\\mathbf{a}$ during the braking process of the car. The magnitude of the acceleration $\\mathbf{a}$ during the braking process of the car. The magnitude of the acceleration $\\mathbf{a}$ during the braking process of the car. The magnitude of the acceleration $\\mathbf{a}$ during the braking process of the car. The magnitude of the acceleration $\\math"
  381.         ]
  382.     },
  383.     {
  384.         "question_structure": {
  385.             "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.",
  386.             "sub_question_1": "What is the work $w$ done by the athlete on the basketball during the dribbling process?\n",
  387.             "sub_question_2": "What is the magnitude of the force applied by the athlete on the basketball when dribbling?"
  388.         },
  389.         "answer": [
  390.             "4.5J",
  391.             "9N"
  392.         ],
  393.         "model_output": [
  394.             "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. What is the work $w$ done by the athlete on the basketball during the dribbling process? 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 $h_2 = 1.8\\mathrm{m}$.\nThe gravitational acceleration is $g = \\frac{m}{g_{\\mathrm{}}}$ is the same as the gravitational constant, and it rebounds",
  395.             "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. What is the magnitude of the force applied by the athlete on the basketball when dribbling? \\begin{align} 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 by the athlete. The magnitude of the force applied by the athlete is $F_A = F_{\\text{left}} = \\begin{array}{\\text{left}} = \\begin{array}{\\text{left}} ="
  396.         ]
  397.     },
  398.     {
  399.         "question_structure": {
  400.             "context": "An object placed on a horizontal ground has a mass of 5 kg, and the kinetic friction coefficient between the object and the ground is 0.2. After being subjected to a horizontal pulling force of 15 N, it starts moving from rest ($g=10\\mathrm{m}/\\mathrm{s}^{2}$).",
  401.             "sub_question_1": "The magnitude of the acceleration of an object's motion.",
  402.             "sub_question_2": "The displacement magnitude of the object after 5s",
  403.             "sub_question_3": "At the end of 5 seconds, the external force is removed. How much farther can the object move?"
  404.         },
  405.         "answer": [
  406.             "$1\\mathrm{m}/\\mathrm{s}^{2}$",
  407.             "$12.5\\mathrm{m}$",
  408.             "$6.25\\mathrm{m}$"
  409.         ],
  410.         "model_output": [
  411.             "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 ($g=10\\mathrm{m}/\\mathrm{s}^{2}$). The magnitude of the acceleration of an object's motion. The magnitude of the acceleration of an object's motion. \n\nAn object placed on a horizontal force of 15 N, is 0.2. The magnitude of the acceleration of an object's motion. \n\n## Step 1\nDetermine the object's motion.\nThe object's motion is given by the equation $\\mu = \\frac{m}{g}$.\n\n## Step 2\nCalculate the object's motion.\nThe motion is given by the equation $m = \\",
  412.             "An object placed on a horizontal ground has a mass of 5 kg, and the kinetic friction coefficient between the object and the ground is 0.2. After being subjected to a horizontal pulling force of 15 N, it starts moving from rest ($g=10\\mathrm{m}/\\mathrm{s}^{2}$). The displacement magnitude of the object after 5s is 0.2. The acceleration of the object is a horizontal force of 15 N, and the displacement of the object is a horizontal force of 5 kg. The velocity of the object is a horizontal force of 5 kg. The magnitude of the object is a horizontal force of 5 kg.\n\n## Step 1\nDetermine the object's velocity.\nThe object's velocity is a function of the object's velocity, and the velocity of the object is a",
  413.             "An object placed on a horizontal ground has a mass of 5 kg, and the kinetic friction coefficient between the object and the ground is 0.2. After being subjected to a horizontal pulling force of 15 N, it starts moving from rest ($g=10\\mathrm{m}/\\mathrm{s}^{2}$). At the end of 5 seconds, the external force is removed. How much farther can the object move? [Hint: $\\mathrm{F}_{1} = 1.5 \\mathrm{m}/\\mathrm{s}^{2}$]\n\n## Step 1\nFirst, we need to find the initial velocity of the object when the external force is removed. We have the equation for the velocity of an object under the influence of gravity. We have that \\[ v = \\frac{d^{2} \\text{g}} \\text{F}_{1} = "
  414.         ]
  415.     },
  416.     {
  417.         "question_structure": {
  418.             "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:",
  419.             "sub_question_1": "The time the small ball is in the air",
  420.             "sub_question_2": "The speed and direction of the small ball when it hits the ground.",
  421.             "sub_question_3": "The power of gravity during the ball's landing process"
  422.         },
  423.         "answer": [
  424.             "$0.4s$",
  425.             "$5m/s$, the angle between the velocity and the horizontal direction is $53^{\\circ}$",
  426.             "$40W$"
  427.         ],
  428.         "model_output": [
  429.             "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: The time the small ball is in the air resistance.\n## Step 1\nDetermine the velocity of the ball as it is thrown horizontally.\n$R = \\text{m/s}$\n\n## Step 2\nMeasure the velocity of the ball as it is thrown horizontally.\n$R = \\text{m/s}$\n\n## Step 3\nDetermine the time the ball as it is thrown horizontally.\n$R = \\text{m/s}$\n\n## Step 4\nMeasure the velocity of the ball as",
  430.             "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: The speed and direction of the small ball when it hits the ground. The velocity of the ground is $1.2 \\, \\text{m/s}$. The problem is to find the time it takes for the ball to stop at the ground. The answer is to $0.5 \\text{s}$.\nTo find the time it takes for the ball to stop at the ground. The answer is to $0.5 \\text{m/s}$. The problem is to find the time it takes for the ball to stop at the",
  431.             "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: The power of gravity during the ball's landing process.\n\n## Step 1:  First, we need to find the equation for the horizontal velocity of the ball. We know that the horizontal of the gravity during the ball's motion is negligible. The equation for the power of the velocity of the velocity of the velocity of the velocity of the velocity of the velocity of the velocity of the velocity of the velocity of the velocity of the velocity of the acceleration of the acceleration of the acceleration of the acceleration of the acceleration of the acceleration of"
  432.         ]
  433.     },
  434.     {
  435.         "question_structure": {
  436.             "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 $\\mathbf{g}=10\\mathbf{m}/\\mathbf{s}^{2}$.",
  437.             "sub_question_1": "Calculate the total time it takes for the ball to fall.",
  438.             "sub_question_2": "Calculate the displacement of the ball during the final 2 seconds of its descent."
  439.         },
  440.         "answer": [
  441.             "5s",
  442.             "80m"
  443.         ],
  444.         "model_output": [
  445.             "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 $\\mathbf{g}=10\\mathbf{m}/\\mathbf{s}^{2}$. Calculate the total time it takes for the ball to fall. The displacement of the ball is $0.1 second. The displacement of the ball is $0.1 second. The displacement of the ball is $0.1 second. The displacement of the ball is $0.1 second. The displacement of the ball is $0.1 second. The displacement of the ball is $0.1 second. The displacement of the ball is $0.1 second. The time it takes for the ball to fall. The displacement",
  446.             "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 $\\mathbf{g}=10\\mathbf{m}/\\mathbf{s}^{2}$. Calculate the displacement of the ball during the final 2 seconds of its descent. The displacement of the ball is given by the displacement of the ball from the displacement of the ball is given by the displacement of the ball is given by the displacement of the ball is given by the displacement of the ball is given by the displacement of the ball is given by the displacement of the ball is given by the displacement of the ball is given by the displacement of the ball is given by the displacement of the ball is given by the displacement of the ball is given by the displacement"
  447.         ]
  448.     },
  449.     {
  450.         "question_structure": {
  451.             "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.",
  452.             "sub_question_1": "What are the potential differences between AB, BC, and CA?",
  453.             "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?"
  454.         },
  455.         "answer": [
  456.             "200 V, 300 V, 500 V",
  457.             "200 V, -300 V, -6×10^-4 J, -9×10^-4 J"
  458.         ],
  459.         "model_output": [
  460.             "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. What are the potential differences between AB, BC, and CA? \n## Step 1:  To find the difference between the electric field and the charge of $ q = -3 \\times 10^{-4} \\, J.  The electric field force is given by F = -3 \\times 10^{-4} \\text{C} \\text{C} \\text{J} \\text{N} \\text{p} \\text{d} \\text{C} \\text{b} \\text",
  461.             "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. 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? To the potential charge with a charge of $ \\frac{ \\text{J}}{The potential energy of the charge with a charge of $ \\frac{ \\text{C}}{The potential energy of the charge with a charge of $ \\frac{ \\text{E}}{The potential charge with a charge of $ \\frac{ \\text{a}}{The potential charge with a charge of $ \\frac{ \\text{o}}{The potential charge with a"
  462.         ]
  463.     },
  464.     {
  465.         "question_structure": {
  466.             "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.",
  467.             "sub_question_1": "(a) Where should a pin be placed on the optical axis such that its image is formed at the same place?",
  468.             "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."
  469.         },
  470.         "answer": [
  471.             "$15 cm$",
  472.             "$1.16 cm$"
  473.         ],
  474.         "model_output": [
  475.             "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) Where should a pin be placed on the optical axis such that its image is formed at the same place? (b) What is the optical axis of the image of the convex lens? (c) What is the optical axis of the convex lens? (a) What is the optical axis of the convex lens? (a) What is the optical axis of the convex mirror? (a) What is the refractive index of the convex mirror? (a) What is the refractive index of the convex lens? (a) What is the focal length of the convex mirror?",
  476.             "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. (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 the lens is a convex surface with a refractive index of $2.5$ and a convex surface with a refractive index of $2.5$ is a convex surface with a refractive index of $2.5$ and a convex surface with a refractive index of $2.5$ is a convex surface with a refractive index of $2.5$ is a convex surface with a refractive index of $2.5$"
  477.         ]
  478.     },
  479.     {
  480.         "question_structure": {
  481.             "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:",
  482.             "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?",
  483.             "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?"
  484.         },
  485.         "answer": [
  486.             "The bow should face the direction perpendicular to the riverbank, $36s$, $90\\sqrt{5}\\mathrm{m}$.",
  487.             "The bow should be deflected $30^{\\circ}$ upstream, $24\\sqrt{3}\\mathrm{s}$, $180\\mathrm{m}$."
  488.         ],
  489.         "model_output": [
  490.             "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: 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? How much will the boat be able to carry out the tasks assigned to the boat to cross the river? How long will it take? What is the displacement? How much will the boat be able to carry out the tasks assigned to the boat to cross the river? How long will it take? What is the displacement? How much will the displacement be able to carry out the tasks assigned to the boat to cross the river? How long will it take? What is the displacement?",
  491.             "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: 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 buoyancy of the boat in the water? The buoyancy of the boat in the water? The buoyancy of the boat in the water? The buoyance of the boat in the water? The buoyance of the boat in the water? The buoyance of the boat in the water? The buoyance of the boat in the water? The buoyance of the boat in the water? The buoyance of the boat in the water? The buoyance of"
  492.         ]
  493.     },
  494.     {
  495.         "question_structure": {
  496.             "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.",
  497.             "sub_question_1": "What is the voltage measured across the secondary coil using an AC voltmeter?"
  498.         },
  499.         "answer": [
  500.             "100V"
  501.         ],
  502.         "model_output": [
  503.             "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. 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.\n## Step 1\nTo find the value of the inductance of the secondary coil, we need to first calculate the value of the inductance of the primary coil. This is the value of the inductance of the inductance of the secondary coil.\n## Step 2\nTo find the voltage of the secondary coil, we need to first calculate the voltage of the induct"
  504.         ]
  505.     }
  506. ]
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