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modified_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. The spring was slightly rusted, which might affect its elastic coefficient, but it was assumed to be negligible in the experiment.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). A light spring is fixed at one end. When a force of magnitude $F_1 = 10\\mathrm{N}$ is applied to compress the other end, the equilibrium length is $l_1 = 9\\mathrm{cm}$. When a force of magnitude $F_2 = 20\\mathrm{N}$ is applied to stretch the spring, the equilibrium length becomes $l_2 = 12\\mathrm{cm}$. The stretching or compression of the spring is within the elastic limit. The spring was slightly rusted, which might affect its elastic coefficient, but it was assumed to be negligible in the experiment. Find the original length $l_0$ of the spring. The equilibrium length $l_0 = 10\\mathrm{cm}$ is fixed, but the stretched length $l_0 = 12\\mathrm{cm}$ is not. The spring constant is $C_s = 1\\mathrm{cm}$, but the spring coefficient is $k_0 = 9\\mathrm{cm}$.\nThe final answer is $\\boxed{F_1 = 10\\mathrm{cm}}$, but the spring with a force",
  14.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). A light spring is fixed at one end. When a force of magnitude $F_1 = 10\\mathrm{N}$ is applied to compress the other end, the equilibrium length is $l_1 = 9\\mathrm{cm}$. When a force of magnitude $F_2 = 20\\mathrm{N}$ is applied to stretch the spring, the equilibrium length becomes $l_2 = 12\\mathrm{cm}$. The stretching or compression of the spring is within the elastic limit. The spring was slightly rusted, which might affect its elastic coefficient, but it was assumed to be negligible in the experiment. Determine the spring constant $k$ of the spring. The spring was slightly rusted, which might affect its elastic coefficient, but it was assumed to be negligible in the experiment. The spring was slightly rusted, which might affect its elastic constant, but it was assumed to be negligible in the experiment. The spring constant was slightly rusted, which might affect its elastic coefficient, but it was assumed to be negligible in the experiment. The spring was slightly rusted, which might affect its elastic constant, but it was assumed to be"
  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 $\\mathrm{g}\\!=\\!10\\mathrm{m}/\\mathrm{s}^{2}$. There was a slight air resistance during the free - fall motion, although it was considered to have no significant impact on the result.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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 $\\mathrm{g}\\!=\\!10\\mathrm{m}/\\mathrm{s}^{2}$. There was a slight air resistance during the free - fall motion, although it was considered to have no significant impact on the result. What is the duration of time it takes for the object to reach the ground? The velocity of the object is given by the equation $\\frac{d}{t}{h} = \\frac{M}{R} = \\frac{a}{n}{c} = \\frac{b}{e} = \\frac{a}{f} = \\frac{A}{\\mathrm{m}} = \\frac{A}{\\mathrm{L}} = \\frac{a}{\\mathrm{G}} = \\frac{A}{\\mathrm{g",
  31.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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 $\\mathrm{g}\\!=\\!10\\mathrm{m}/\\mathrm{s}^{2}$. There was a slight air resistance during the free - fall motion, although it was considered to have no significant impact on the result. What is the magnitude of the object's velocity upon impact with the ground? The acceleration due to gravity is the acceleration due to gravity. The acceleration due to gravity is the acceleration due to gravity. The acceleration due to gravity is the acceleration due to gravity. The deceleration due to gravity is the deceleration due to gravity. The final answer due to gravity is the final answer due to gravity.\n## Step 1\nTo find the velocity of the object, we need to know the mass of the object, which is the mass of the object",
  32.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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 $\\mathrm{g}\\!=\\!10\\mathrm{m}/\\mathrm{s}^{2}$. There was a slight air resistance during the free - fall motion, although it was considered to have no significant impact on the result. What is the distance the object falls during its last 1 second of motion? The velocity of the object was given as $v=\\!10\\mathrm{m}/\\mathrm{s}$. The distance the object falls is given as $d=\\!10\\mathrm{m}/\\mathrm{s}$.\n\n## Balance\nThe velocity of the object is given as $v=\\!10\\mathrm{m}/\\mathrm{s}$, and the distance the object falls is given as $d=\\!10\\mathrm{m}/\\mathrm{s}$.\n\n"
  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. The road surface where the cars were moving had a small coefficient of friction, but it was ignored in this problem.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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 road surface where the cars were moving had a small coefficient of friction, but it was ignored in this problem. The distance this little bird flies at was a small bird, but it was not in this problem. The car's average speed was given by the bird, but the speed of the car was not. The distance the car travels is given by the bird, but the car is not. The road is a straight and smooth ride, but the car is not. The answer is given by the car, but the speed is not. The flight is not possible for the car, but the bike is a good option",
  47.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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 road surface where the cars were moving had a small coefficient of friction, but it was ignored in this problem. The average speed of this small bird's flight was not to be a problem. The average distance that the bird had to travel was not given, but it was a problem. The bird's flight path was not given, but it was a problem. The bird's flight was not given, but it was a problem. The car's speed was not given, but it was a problem. The problem was to be a problem, and the car was not given, but it was a problem. The problem was to be a"
  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: $E^{2}=(p c)^{2}+\\left(m c^{2}\\right)^{2}$ During the particle collision, there was a very small amount of energy loss due to a brief magnetic field interference, which was not accounted for in the calculations.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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: $E^{2}=(p c)^{2}+\\left(m c^{2}\\right)^{2}$ During the particle collision, there was a very small amount of energy loss due to a brief magnetic field interference, which was not accounted for in the calculations. Determine $E_p$ in terms of $m_p$, $m_{\\Delta}$, and $E_b$. You may assume that $E_b$ is small. The relativistic collision was a one-dimensional process, where the relativistic momentum was a small number of particles that were not in the relativistic energy, which was a large number of photons that were not in the relativistic momentum. The relativistic energy transfer was a relativistic process, where the relativistic velocity was a relativistic quantity, which was a relativistic mass was a relativistic momentum. The relativistic force was a relativistic power was a relativistic effect was a",
  64.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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: $E^{2}=(p c)^{2}+\\left(m c^{2}\\right)^{2}$ During the particle collision, there was a very small amount of energy loss due to a brief magnetic field interference, which was not accounted for in the calculations. 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 collision is the relativistic momentum, which is the relativistic force, which is the relativistic velocity, which is relativistic. The relativistic momentum is the relativistic kinetic energy, which is relativistic. The relativistic force is the relativistic momentum, which is relativistic. The relativistic motion is the relativistic velocity, which is relativistic. The relativistic motion is the relativistic kinetic energy, which is relativic. The relativistic motion",
  65.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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: $E^{2}=(p c)^{2}+\\left(m c^{2}\\right)^{2}$ During the particle collision, there was a very small amount of energy loss due to a brief magnetic field interference, which was not accounted for in the calculations. 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 Lorentz factor is given by $e \\mathrm{gamma} \\gamma$ for $|E| \\ll 1$, and the energy of the electron is given by $E \\cdot \\gamma$ for $|E| \\ll 1$. The energy of the photon is given by $h \\mathrm{H}$ for $|E| \\ll 1$. The energy of the neutron is given by $A \\mathrm{a}$ for $"
  66.         ]
  67.     },
  68.     {
  69.         "question_structure": {
  70.             "context": "China's first lunar exploration satellite, \"Chang'e-1,\" was launched in 2007 from the Xichang Satellite Launch Center by the \"Long March 3A\" carrier rocket. Assuming the satellite's orbit is circular and its altitude above the lunar surface is equal to the Moon's radius, it is known that the satellite's orbital period around the Moon is T, the Moon's radius is R, and the gravitational constant is G. The lunar surface has a thin layer of dust, which might cause a small change in the gravitational field, but it was not considered in this model.",
  71.             "sub_question_1": "What is the mass of the Moon?",
  72.             "sub_question_2": "What is the density of the Moon?"
  73.         },
  74.         "answer": [
  75.             "$\\frac{32\\pi^{2}R^{3}}{G T^{2}}$",
  76.             "$\\frac{24\\pi}{G T^{2}}$"
  77.         ],
  78.         "model_output": [
  79.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. The lunar surface has a thin layer of dust, which might cause a small change in the gravitational field, but it was not considered in this model. What is the mass of the Moon? The mass of the Moon is the mass of the Moon's radius, and the radius of the Moon's orbital period is the mass of the Moon's gravitational constant is the mass of the Moon's radius, and the radius of the Moon's orbital period is the mass of the Moon's gravitational field, but it was not considered in this model. What is the mass of the Moon? The mass of the Moon is the mass of the Moon's radius, and the radius of the",
  80.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. The lunar surface has a thin layer of dust, which might cause a small change in the gravitational field, but it was not considered in this model. What is the density of the Moon? The density of the Moon is about 5.5 km, and the lunar surface is not flat, it's got craters, which are circular and have a small size, and the Moon's surface is not smooth, it's got craters, which are circular and have a small scale, and the gravitational field is not uniform, it's got a small size, and the lunar surface is not flat, it's got craters, which are circular and have a small"
  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. There was a weak magnetic field around the charged ball, which could potentially affect its motion, but was assumed to be insignificant.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. There was a weak magnetic field around the charged ball, which could potentially affect its motion, but was assumed to be insignificant. What is the magnitude of the uniform electric field strength? The ball is placed in a horizontal electric field, and the string is attached to the lower end of the charged mass. The ball is released from rest, and the string is attached to the upper end of the charged mass. The electric motor is fixed at the upper end of the charged mass, and the string is attached to the lower end of the charged ball. The ball is placed in a horizontal electric field, and the string is attached to the upper end of the charged mass",
  97.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. There was a weak magnetic field around the charged ball, which could potentially affect its motion, but was assumed to be insignificant. What is the potential difference $U_{AB}$ between points A and B? What is the potential difference between the points C and D? What is the potential difference between the points E and F? (a question) What is the potential difference between the points 1 and 2? (a) What is the potential difference between the points 1 and 2? (b) The potential difference between the points 1 and 3? (c) The potential difference between the points 1 and 4? (d) The potential difference between",
  98.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. There was a weak magnetic field around the charged ball, which could potentially affect its motion, but was assumed to be insignificant. If the potential at point O is taken as zero, what is the maximum potential energy of the charged ball? The ball is placed in a uniform electric field, and the string is held horizontally at point B. The ball is released to the right, and the string is released. The ball is placed in a fixed electric field, and the charged string is attached to the upper end. The ball is placed in a uniform electric field, and the string is held horizontally at point B. The ball is placed in a fixed electric field, and the string is attached to the lower end. The"
  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 $a_{A} = 2 \\, \\mathbf{m/s}^{2}$. The toll station area had a very slight slope, but it was assumed to be a flat road in the analysis.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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 toll station area had a very slight slope, but it was assumed to be a flat road in the analysis. The driver of car A needs to start braking at least how far away from the toll booth window to avoid violating regulations. The toll road is wide and relatively smooth in the analysis. However, cars are required to maintain a speed and not to be at least a certain distance from the car A. The toll of car B is not too far from the toll of car A. The toll of car A is not too far from the toll of car B. The toll of car A is not too far from the toll of car. The toll of car A is not too far from the toll of car",
  113.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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 toll station area had a very slight slope, but it was assumed to be a flat road in the analysis. 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? To prevent a car A from colliding with a bicycle on the pedestrian crossing at the toll booth, a special speed for a driver of a run-out of a car from a toll booth, or a collision, and a path in the toll booth, or a rule of a right of way on the left, or a traffic light, or a traffic light, or a warning sign, or a warning flag, or a warning flag, or a warning whistle, or a warning marker"
  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. The magnetic field around the coil had a small non - uniformity, but it was considered uniform for simplicity in this problem.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. The magnetic field around the coil had a small non - uniformity, but it was considered uniform for simplicity in this problem. Find the magnetic flux $\\Phi_{1}$ passing through the coil. The magnetic field has a small radius, but it is considered uniform for simplicity. The magnetic field has a small length, but it is not perpendicular to the direction of the magnetic field. The magnetic coil has a small radius, but it is not perpendicular to the direction of the magnetic field. The magnetic field has a small length, but it is not perpendicular to the direction of the magnetic field. The magnetic field has a small radius, but it is not perpendicular to the direction of",
  128.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. The magnetic field around the coil had a small non - uniformity, but it was considered uniform for simplicity in this problem. If the shape of this coil is changed from a square to a circle (with the perimeter remaining unchanged), find the magnetic flux $\\Phi_{2}$ passing through the coil at this time. The magnetic field of the coil is a small problem, but the plane of the coil is perpendicular to the direction of the magnetic flux. The magnetic coil is a small problem, but the plane of the coil is perpendicular to the direction of the magnetic field of the coil is a small problem, but the magnetic flux is a small problem, but the plane of the coil is perpendicular to the direction of the magnetic induction of the coil is a small problem, but the magnetic coil is a"
  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 $R=99\\Omega$. The AC generator had a small amount of mechanical friction in its rotation, which was not considered in the power calculations.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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 AC generator had a small amount of mechanical friction in its rotation, which was not considered in the power calculations. Write the expression for the instantaneous value of alternating current; do not add any other content. The solution to the problem of the angular velocity of the rotor of the AC generator is $A=100\\mathrm{T}$, and the final answer is $\\boxed{\\text{N}}$.\nThe final answer is $\\boxed{\\text{N}}$. The final answer is $\\boxed{\\text{N}}$, and the final result is $\\boxed{\\text{N}}$. The final value is $\\boxed{\\text{N}}$, and the final result is $\\boxed",
  145.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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 AC generator had a small amount of mechanical friction in its rotation, which was not considered in the power calculations. The power consumed by the external resistor; do not add any other content. The content of the coil is not limited to the direction of the magnetic field. The magnetic force of the rotor is not limited to the length of the AC generator. The AC motor is not in the rotor of the direction of the external force. The resistance of the coil is not limited to the power of the magnetic field. The timing of the plane is not in the rotation of the direction of the external force. The content of the coil is not in the rotation of the magnetic",
  146.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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 AC generator had a small amount of mechanical friction in its rotation, which was not considered in the power calculations. The power of external forces. The power of the magnetic field. The magnetic induction of the rotor. The angular velocity of the coil. The angular momentum of the direction of the AC generator. The AC motor. The AC motor of the DC motor. The AC motor of the EM motor. The external forces. The power of the magnetic field. The power of the rotor. The resistance of the DC motor. The timing of the coil. The plane of the rotor. The angular momentum of the AC motor."
  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 $100\\Omega$. The transmission line had a small capacitance effect, but it was ignored in the power transmission analysis.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). The AC generator at the power plant outputs a constant voltage of $200\\mathrm{V}$ and a power of $100\\mathrm{kW}$. The electricity needs to be transmitted to a distant factory. The designed power loss on the transmission line is $10\\%$, and the total resistance of the transmission line is $100\\Omega$. The transmission line had a small capacitance effect, but it was ignored in the power transmission analysis. What is the current on the transmission line? The current on the transmission line is $100\\mathrm{kW}$.\n##  Step 1: Find the generator\nThe 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, and the designed power loss on the transmission line is $10\\%$. The total resistance of the transmission line is $100\\Omega$. The transmission line had a",
  161.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). The AC generator at the power plant outputs a constant voltage of $200\\mathrm{V}$ and a power of $100\\mathrm{kW}$. The electricity needs to be transmitted to a distant factory. The designed power loss on the transmission line is $10\\%$, and the total resistance of the transmission line is $100\\Omega$. The transmission line had a small capacitance effect, but it was ignored in the power transmission analysis. What is the turns ratio of the step-up transformer required for power transmission (assuming the transformer used is an ideal transformer)? The transformer is a transformer, and the transformer is a transformer. The transformer is a power transformer, and the power transformer is a power transformer. The power transformer is a transformer, and the transformers are power transformers. The power transmission is a transformer, and the transmission is a transformer. The turn-off transformer is a power-off, and the power-off is a power-off. The power- off transformer is a power-off, and the power+ is a power# transformer is a"
  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 $\\triangle\\mathrm{t}\\!=\\!4.0\\mathrm{s}$. The spring was slightly rusted, which might affect its elastic coefficient, but it was assumed to be negligible in the experiment.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). To determine the acceleration of a glider on an air track, a shading plate with a width of $L\\!=\\!2.0\\mathrm{cm}$ is mounted on the glider. The glider accelerates uniformly through two photogates. A digital millisecond timer records the time the shading plate takes to pass through the first photogate as $\\triangle{\\sf t}_{1}\\!=\\!0.2{\\bf s}$, and the time to pass through the second photogate as $\\triangle\\mathrm{t}_{2}{=}0.1\\mathrm{s}$. The time interval from when the shading plate starts to block the first photogate until it starts to block the second photogate is $\\triangle\\mathrm{t}\\!=\\!4.0\\mathrm{s}$. The spring was slightly rusted, which might affect its elastic coefficient, but it was assumed to be negligible in the experiment. What are the average velocities of the glider as it passes through each of the two photogates? What are the acceleration of the glider as it passes through the other two photogates? What are the average times of the shading plate as it passes through the other two photogates? What are the time intervals between the glider and the other two gliders? What are the time intervals between the glider and the other two photogates? What are the time intervals between the digital timer and the other two timers? What are the time intervals between the shading plate",
  178.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). To determine the acceleration of a glider on an air track, a shading plate with a width of $L\\!=\\!2.0\\mathrm{cm}$ is mounted on the glider. The glider accelerates uniformly through two photogates. A digital millisecond timer records the time the shading plate takes to pass through the first photogate as $\\triangle{\\sf t}_{1}\\!=\\!0.2{\\bf s}$, and the time to pass through the second photogate as $\\triangle\\mathrm{t}_{2}{=}0.1\\mathrm{s}$. The time interval from when the shading plate starts to block the first photogate until it starts to block the second photogate is $\\triangle\\mathrm{t}\\!=\\!4.0\\mathrm{s}$. The spring was slightly rusted, which might affect its elastic coefficient, but it was assumed to be negligible in the experiment. Estimate the magnitude of the glider's acceleration. The time it took to pass through the second photogate as $\\triangle\\mathrm{t}_{2}{=}0.1\\mathrm{s}$, and the time to pass through the first photogate as $\\triangle\\mathrm{t}_{1}{=}0.1\\mathrm{s$.\nThe acceleration of the glider was determined to be negligible, and the time it took to pass through the second photogate was $\\triangle\\mathrm{t}_{2}{",
  179.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). To determine the acceleration of a glider on an air track, a shading plate with a width of $L\\!=\\!2.0\\mathrm{cm}$ is mounted on the glider. The glider accelerates uniformly through two photogates. A digital millisecond timer records the time the shading plate takes to pass through the first photogate as $\\triangle{\\sf t}_{1}\\!=\\!0.2{\\bf s}$, and the time to pass through the second photogate as $\\triangle\\mathrm{t}_{2}{=}0.1\\mathrm{s}$. The time interval from when the shading plate starts to block the first photogate until it starts to block the second photogate is $\\triangle\\mathrm{t}\\!=\\!4.0\\mathrm{s}$. The spring was slightly rusted, which might affect its elastic coefficient, but it was assumed to be negligible in the experiment. Estimate the distance between the two photogates. The time between the two ends of the photogate is $\\Delta\\mathrm{t}\\!=\\!\\mathrm{t}_{2}\\mathrm{s}\\!=\\!\\mathrm{t}_{3}\\mathrm{s}\\!=\\!\\mathrm{t}_{4}\\mathrm{E}$. The time it takes to pass through the second photogate is $\\triangle\\mathrm{t}\\!=\\!\\mathrm{t}_{5}\\mathrm{N}\\!=\\!\\mathrm{t"
  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. There was a slight air resistance during the free - fall motion, although it was considered to have no significant impact on the result.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. There was a slight air resistance during the free - fall motion, although it was considered to have no significant impact on the result. What is the wavelength of the electromagnetic wave emitted by the black box? The frequency of the signal emitted by the electromagnetic wave is $\\frac{\\dmath}{\\begin{align} & \\text{Hz} & \\text{ and} & \\text{kHz} & \\text{ and} & \\text{m/s} & \\text{ and the speed of the signal emitted by the black box? The final answer is the location of the signal emitted by the electromagnetic wave is $\\frac{\\mathbf{d}{\\math",
  194.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. There was a slight air resistance during the free - fall motion, although it was considered to have no significant impact on the result. 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: The black box.\nThe question is such a difficult one, but the solution is not as simple, but the black box is not a simple answer. The answer is not a simple thing, but the black box is a simple thing. The answer is not a simple $\\mathrm{B}$, but the black box is a simple $\\mathrm{B}$.\nThe question is a simple question, but the answer is not a simple thing. The question is a"
  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. The road surface where the cars were moving had a small coefficient of friction, but it was ignored in this problem.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. The road surface where the cars were moving had a small coefficient of friction, but it was ignored in this problem. Determine the pressure of the gas inside the furnace chamber at room temperature after the argon gas has been injected. The gas was at a high pressure, but it was not used to process the materials placed inside the bottle before use. The volume of the gas was decreased, but it was not used to determine the pressure of the gas inside the furnace chamber at room temperature after the argon gas has been injected. The ideal gas was at a high pressure, but it was not used to process the materials placed inside the bottle before use. The coefficient of the gas was at a high temperature,",
  209.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. The road surface where the cars were moving had a small coefficient of friction, but it was ignored in this problem. 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 pressure of the gas is a function of the gas, and the pressure of the gas is a function of the gas.\n\n## Step 1: Calculate the pressure of the gas inside the furnace chamber.\nThe pressure of the gas inside the bottle is a function of the gas, and the coefficient of the gas is a function of the argon gas. The room temperature is $27^{\\circ} C$, and the coefficient of the gas is a function of the argon"
  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 $3\\mathrm{m}$. During the particle collision, there was a very small amount of energy loss due to a brief magnetic field interference, which was not accounted for in the calculations.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). A particle starts from rest and undergoes uniformly accelerated linear motion. The displacement of the particle in the first second is $3\\mathrm{m}$. During the particle collision, there was a very small amount of energy loss due to a brief magnetic field interference, which was not accounted for in the calculations. What is the magnitude of the acceleration of a particle's motion? The acceleration of a particle in a magnetic field?\n## Step 1:  Determine the type of motion\nWe need to determine the type of motion of the particle. The motion of a particle in a magnetic of $\\mathrm{m} = 3$ and of the acceleration of a particle in a magnetic of $\\mathrm{m}$.\n## Step 2:  Calculate the magnitude of the acceleration of a particle in a magnetic field of $\\mathrm{m}$.\nWe",
  226.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). A particle starts from rest and undergoes uniformly accelerated linear motion. The displacement of the particle in the first second is $3\\mathrm{m}$. During the particle collision, there was a very small amount of energy loss due to a brief magnetic field interference, which was not accounted for in the calculations. What is the displacement of the particle in the first 3 seconds? The displacement of the particle in the first 2 seconds? The displacement of the particle in the first 1 second? The displacement of the particle in the first 0.5 seconds? The displacement of the particle in the first 0.5 seconds? The displacement of the particle in the first 0.5 seconds? The displacement of the particle in the first 0.5 seconds? The displacement of the particle in the first 0.5 seconds? The displacement",
  227.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). A particle starts from rest and undergoes uniformly accelerated linear motion. The displacement of the particle in the first second is $3\\mathrm{m}$. During the particle collision, there was a very small amount of energy loss due to a brief magnetic field interference, which was not accounted for in the calculations. When the displacement is $12\\mathrm{m}$, what is the velocity of the particle? \\[ \\nonumber \\text{ }{3} \\text{m} \\text{ }{4} \\text{ }{5} \\text{ }{6} \\text{ }{8} \\text{ }{9} \\text{ }{10} \\text{ }{11} \\text{ }{12} \\text{ }{7} \\text{ }{10} \\text{ }{9} \\text"
  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. The lunar surface has a thin layer of dust, which might cause a small change in the gravitational field, but it was not considered in this model.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. The lunar surface has a thin layer of dust, which might cause a small change in the gravitational field, but it was not considered in this model. What is the turns ratio of the primary coil to the secondary coil in a step-up transformer? The secondary coil has a thin layer of dust, which is not considered in the gravitational field, but it is not a problem. 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, and the output voltage is $11\\mathrm{kV}$. If the power",
  242.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. The lunar surface has a thin layer of dust, which might cause a small change in the gravitational field, but it was not considered in this model. What is the transmission current in A? The transmission of a power plant is $200\\mathrm{kW}$, and the voltage of the transformer is $11\\mathrm{kV}$. If the power output is $200\\mathrm{kW}$, and the voltage is $11\\mathrm{kV}$, then the energy loss is not considered in this model. What is the transmission of a power plant? The voltage of a transformer is $11\\mathrm{kV}$, and the current is $200\\"
  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. There was a weak magnetic field around the charged ball, which could potentially affect its motion, but was assumed to be insignificant.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. There was a weak magnetic field around the charged ball, which could potentially affect its motion, but was assumed to be insignificant. What is the resistance of the bulb when it is glowing normally? The step-down transformer in a residential community has a primary to secondary coil turn ratio of $n_1$: $n_2$ = 3:1. This transformer is used to power 100 light bulbs, which are connected in parallel, with a specification of \"220V 60W,\" and all the bulbs are operating normally. There was a weak magnetic field around the charged ball, which could potentially affect its motion, but was assumed to be insignificant. The step",
  259.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. There was a weak magnetic field around the charged ball, which could potentially affect its motion, but was assumed to be insignificant. What is the voltage across the primary coil of the transformer? The step-down transformer in the residential area had a secondary coil with a ratio of 3:1. The power-up transformer in the commercial area had a primary to secondary turns ratio of 1:1. The voltage transformer in the industrial area had a secondary to primary coil turns ratio of 1:1. The current transformer in the office area had a secondary to primary coil turns ratio of 3:1. The step-down transformer in the educational area had a secondary to",
  260.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. There was a weak magnetic field around the charged ball, which could potentially affect its motion, but was assumed to be insignificant. What are the currents passing through the primary and secondary coils of the transformer? The step-down transformer in the residential area has a primary to secondary coil turns ratio of $n_1$: 3:1. The specifications of the transformer were operating normally, but the charged ball was not. The weak magnetic field around the transformer was not affecting its motion, but was assumed to be insignificant. The transformer was used to power the bulbs, but the primary to secondary coil turns ratio of $n_1$: 3:1. The transformer was used to"
  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\". The toll station area had a very slight slope, but it was assumed to be a flat road in the analysis.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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\". The toll station area had a very slight slope, but it was assumed to be a flat road in the analysis. Find the magnitude of the displacement of A in the first 3 seconds, $x_{1}$ is the time of flight, and the time of flight is the time it takes for the drone to reach the velocity of the drone, and the drone to travel at the speed of the drone, and the drone to move at the velocity of the drone. The drone to fly at the speed of the aircraft, and the aircraft to travel at the velocity of the airplane, and the drone to move at the speed of the car, and the car to go at the velocity of the",
  277.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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\". The toll station area had a very slight slope, but it was assumed to be a flat road in the analysis. Find the maximum distance between A and B within the first 3 seconds. The first step is to determine the maximum distance between A and B, and the second step is to find the maximum distance between B and C. The third step is to determine the maximum distance between C and A, and the fourth step is to find the maximum distance between C and A. The fifth step is to determine the maximum distance between C and A, and the sixth step is to find the maximum distance between C and B. The seventh step is to determine the maximum distance",
  278.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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\". The toll station area had a very slight slope, but it was assumed to be a flat road in the analysis. To avoid collision, the condition for the acceleration $a_{0}$ when B starts to decelerate must satisfy: $a_{0} > a_{1}$ and $a_{1} > a_{2}$ and $b_{1} > a_{2}$ are all in the same direction. The drone, A, is, is flying in the same direction, and the drone, is, is moving at a velocity of $v_{1}$, and is not decelerating, and the drone, is not flying, and is not moving, and the velocity of A"
  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. The magnetic field around the coil had a small non - uniformity, but it was considered uniform for simplicity in this problem.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. The magnetic field around the coil had a small non - uniformity, but it was considered uniform for simplicity in this problem. Find the kinetic energy of the electron. The electron moves in a uniform motion, but the magnetic field is not. The mass of the electron is not considered. The charge of the electron is not given. The force of the electron is not considered. The velocity of the electron is not given. The potential of the electron is not considered. The kinetic energy of the electron is not given. The mass of the electron is not considered. The charge of the electron is not given. The gauge of the electron is not considered",
  295.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. The magnetic field around the coil had a small non - uniformity, but it was considered uniform for simplicity in this problem. Choosing the potential energy at an infinite distance from the nucleus as 0, the potential energy of the electron is $E_{p} = -\\frac{k e^2}{r}$. Find the energy of the hydrogen atom. The energy of the electron is $m_{e} = \\frac{m}{e}$. The energy of the nucleus is $k_{e} = \\frac{k}{e}$. The energy of the atom is $E_{p} = \\frac{P}{e}$. The energy of the proton is $E_{p} = \\frac{P}{e}$. The energy of the electron is $m_{e} = \\frac{m}{",
  296.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. The magnetic field around the coil had a small non - uniformity, but it was considered uniform for simplicity in this problem. Find the equivalent current $I$ formed by the motion of an electron around the nucleus. The electron is not in the center of the nucleus, but the motion of an electron is not the same as the motion of an electron. The motion of an electron is not the same as the motion of an electron, but the mass of the electron is not the same as the motion of an electron. The mass of the electron is not the same as the motion of an electron, but the charge of an electron is not the same as the motion of an electron. The charge"
  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 $2x$. The AC generator had a small amount of mechanical friction in its rotation, which was not considered in the power calculations.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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 $2x$. The AC generator had a small amount of mechanical friction in its rotation, which was not considered in the power calculations. Find the ratio of the amplitudes of the two oscillations. The AC motor has a small amount of mechanical friction in its rotation, which is not considered in the power calculations. The spring oscillator has a small amount of mechanical friction in its rotation, which is not considered in the final answer.\n## Step 1:  Determine the ratio of the amplitudes of the two oscillations.\nThe ratio of the amplitudes of the two oscillations is given by $\\frac{1}{x}$ and is equal to the power of the"
  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: The transmission line had a small capacitance effect, but it was ignored in the power transmission analysis.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). Student A starts from point $A$ at the center of the playground and walks $40\\mathrm{m}$ north to reach point $B$, taking 5 seconds. Then, they walk $30\\mathrm{m}$ west to reach point $C$, also taking 5 seconds. Find: The transmission line had a small capacitance effect, but it was ignored in the power transmission analysis. What is the average velocity of object A throughout the entire process? The average velocity of object A is the transmission of the final answer is the transmission of the final answer is the transmission of the final result is the transmission of the transmission of the transmission of the transmission of the transmission of the transmission of the transmission of the transmission of the transmission of the transmission of the transmission of the transmission of the transmission of the transmission of the transmission of the transmission of the transmission of the transmission of the transmission of the transmission of the transmission of the transmission of the transmission",
  327.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). Student A starts from point $A$ at the center of the playground and walks $40\\mathrm{m}$ north to reach point $B$, taking 5 seconds. Then, they walk $30\\mathrm{m}$ west to reach point $C$, also taking 5 seconds. Find: The transmission line had a small capacitance effect, but it was ignored in the power transmission analysis. What is the average speed of A throughout the entire process? The average speed of A is the transmission line, and the transmission line are the final answers with the points of view. The transmission line is a point of view, and the point of view is the transmission line. The transmission line is a point of view, and the point of view is the transmission line. The transmission line is a point of view, and the point of view is the transmission line. The transmission line is a point of view, and the point of view is",
  328.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). Student A starts from point $A$ at the center of the playground and walks $40\\mathrm{m}$ north to reach point $B$, taking 5 seconds. Then, they walk $30\\mathrm{m}$ west to reach point $C$, also taking 5 seconds. Find: The transmission line had a small capacitance effect, but it was ignored in the power transmission analysis. What is the average speed of person A moving from point $A$ to point $B$? [/begin{enumerate}\n## Step 1: Find the distance between the two points\nThe student A starts from point $A$ and walks to reach point $B$, taking 5 seconds. to walk $30\\mathrm{m}$ west to reach point $C$, and then take 5 seconds. to walk $40\\mathrm{m}$ north to reach point $D$, and then take 5 seconds. to walk $50\\mathrm{m}$ east",
  329.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). Student A starts from point $A$ at the center of the playground and walks $40\\mathrm{m}$ north to reach point $B$, taking 5 seconds. Then, they walk $30\\mathrm{m}$ west to reach point $C$, also taking 5 seconds. Find: The transmission line had a small capacitance effect, but it was ignored in the power transmission analysis. What is the average speed of A moving from point $B$ to point $C$? The transmission line was not a major contributor to the power transmission line. The transmission line was not a major contributor to the power transmission line. The transmission line was not a major contributor to the power transmission line. The transmission line was not a major contributor to the power transmission line. The transmission line was not a major contributor to the power transmission line. The transmission line was not a major contributor to the power transmission line. The transmission line was not a major contributor to the power transmission"
  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. The spring was slightly rusted, which might affect its elastic coefficient, but it was assumed to be negligible in the experiment.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). At 09:43 on June 23, 2020, at the Xichang Satellite Launch Center, the Long March 3B carrier rocket soared into the sky, successfully delivering the \"final star\" of the BeiDou-3 global system into its predetermined orbit. This marked the successful completion of the BeiDou global satellite navigation system, a project that took 26 years to accomplish. If the satellite orbits the Earth in a uniform circular motion at a height $h$ above the ground, with the Earth's radius being $R$, the gravitational acceleration at the Earth's surface being $g$, and the gravitational constant being $G$, the effect of the Earth's rotation can be ignored. The spring was slightly rusted, which might affect its elastic coefficient, but it was assumed to be negligible in the experiment. What is the mass of the Earth? The mass of the satellite is a large number of the Earth's mass, and the mass of the Earth's mass, and the mass of the Earth's mass, and the mass of the Earth's mass, and the mass of the Earth's mass, and the mass of the Earth's mass, and the mass of the Earth's mass, and the mass of the Earth's mass, and the mass of the Earth's mass, and the mass of the Earth's mass,",
  346.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). At 09:43 on June 23, 2020, at the Xichang Satellite Launch Center, the Long March 3B carrier rocket soared into the sky, successfully delivering the \"final star\" of the BeiDou-3 global system into its predetermined orbit. This marked the successful completion of the BeiDou global satellite navigation system, a project that took 26 years to accomplish. If the satellite orbits the Earth in a uniform circular motion at a height $h$ above the ground, with the Earth's radius being $R$, the gravitational acceleration at the Earth's surface being $g$, and the gravitational constant being $G$, the effect of the Earth's rotation can be ignored. The spring was slightly rusted, which might affect its elastic coefficient, but it was assumed to be negligible in the experiment. What is the centripetal acceleration of a satellite orbiting around the center of the Earth? The rocket's trajectory was a function of the launch velocity, which is a vector, and the velocity of the rocket was a scalar. The angular momentum of the rocket was a vector, and the velocity of the Earth was a tensor. The gravitational potential was a scalar, and the gravitational force was a vector. The gravitational potential was a tensor, and the potential flow was a vector. The rocket's trajectory was a function of the launch velocity, and the velocity of the Earth was",
  347.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). At 09:43 on June 23, 2020, at the Xichang Satellite Launch Center, the Long March 3B carrier rocket soared into the sky, successfully delivering the \"final star\" of the BeiDou-3 global system into its predetermined orbit. This marked the successful completion of the BeiDou global satellite navigation system, a project that took 26 years to accomplish. If the satellite orbits the Earth in a uniform circular motion at a height $h$ above the ground, with the Earth's radius being $R$, the gravitational acceleration at the Earth's surface being $g$, and the gravitational constant being $G$, the effect of the Earth's rotation can be ignored. The spring was slightly rusted, which might affect its elastic coefficient, but it was assumed to be negligible in the experiment. What is the orbital speed of a satellite as it revolves around the center of the Earth? The circular motion of a rocket as it travels through space, with the ground being left behind, and the satellite being in the front, with the center of the Earth, and the radius of the orbit being $R$, the velocity of the rocket being $V$ and the time of flight being $t$, the time of the rocket being $T$, the time of the rocket being $D$ and the velocity of the rocket being $V$, the orbital motion of the rocket"
  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 $2\\mathrm{m}/\\mathrm{s}^{2}$. There was a slight air resistance during the free - fall motion, although it was considered to have no significant impact on the result.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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 $2\\mathrm{m}/\\mathrm{s}^{2}$. There was a slight air resistance during the free - fall motion, although it was considered to have no significant impact on the result. The speed of the car after braking for 2 seconds. The pedestrian was not affected by the braking, but the driver was still at the intersection of the two roads. The car was not in the way of the driver, but the pedestrian was not in the way of the car. The speed of the car was not affected by the acceleration, but the driver was still on the road. The pedestrian was not under the acceleration, but the car was not in the way of the car. The speed of the car was not affected by the",
  364.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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 $2\\mathrm{m}/\\mathrm{s}^{2}$. There was a slight air resistance during the free - fall motion, although it was considered to have no significant impact on the result. The minimum distance for a car to stop before the zebra crossing when braking was made. The speed of a bus to pass through a pedestrian, but the driver was still in a good mood. The angle of the road to turn in a pedestrian, but the car was not in a position to make a left turn in a driver when he saw a car in a good condition, but he was unable to make a right turn in a vehicle with a speed limit, but he was unaware of the zema area, but he was in a busy mood,",
  365.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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 $2\\mathrm{m}/\\mathrm{s}^{2}$. There was a slight air resistance during the free - fall motion, although it was considered to have no significant impact on the result. The displacement of a car braking for 3 seconds. The acceleration of a pedestrian was not a problem, but a pedestrian was driving at a speed of $10\\mathrm{m}/\\mathrm{s}$ and the acceleration of a pedestrian was a problem, but a pedestrian was a driver. The car was driving at a speed of $15\\mathrm{m}/\\mathrm{s}$ and the displacement of a pedestrian was a problem, but the car was a vehicle.\n\nThe final answer is $\\boxed{1}$ and the final answer"
  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. The road surface where the cars were moving had a small coefficient of friction, but it was ignored in this problem.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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 road surface where the cars were moving had a small coefficient of friction, but it was ignored in this problem. The magnitude of the acceleration $\\mathbf{a}_1$ during the car's acceleration process. The area of the driver's reaction time had a small impact on the braking process. The mass of the road was not considered in this problem. The speed of the car was not affected by the braking process. The mass of the tire was not affected by the acceleration process. The radius of the tire was not affected by the braking process. The diameter of the wheel was not affected by the new car in the road. The area of the tire was not affected by the new car",
  380.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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 road surface where the cars were moving had a small coefficient of friction, but it was ignored in this problem. The magnitude of the acceleration $\\mathbf{a}_2$ during the braking process of the car. The value of the safety of the road. The value of the distance traveled by the car. The value of the time taken to the car. The final answer is the one that you are looking for. The car was moving at a constant speed of 30\\mathrm{m}/\\mathrm{s} and the acceleration of the car was a value of 30\\mathrm{m}/\\mathrm{s}. The braking process was a uniform acceleration of the car. The road was"
  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. During the particle collision, there was a very small amount of energy loss due to a brief magnetic field interference, which was not accounted for in the calculations.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. During the particle collision, there was a very small amount of energy loss due to a brief magnetic field interference, which was not accounted for in the calculations. What is the work $w$ done by the athlete on the basketball during the dribbling process? The kinetic energy of the ball is being transferred to the ground, and the rebounding ball is being kept in motion. The rebounded ball is in motion, and the kinetic energy of the basketball is being transferred to the athlete. The ground is being impacted by the ball, and the collision is being taken by the rebounding ball. The magnitude of the gravitational force is being considered, and the magnetic field is being factored into the calculations. The duration of the impact is being",
  395.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. During the particle collision, there was a very small amount of energy loss due to a brief magnetic field interference, which was not accounted for in the calculations. What is the magnitude of the force applied by the athlete on the basketball when dribbling? When the ball rebounds to the height of the ground, which was not accounted for in the calculations? Who is applying the force of the ground to the height of the rebound, which was not neglected? Which ball rebounds to the height of the ground, which was not impacted by the collision? Which ball rebounds to the height of the ground, which was not in motion? Which ball rebounds to the height of the ground, which was not in play?\n\n## Step 1: To"
  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 ($g=10\\mathrm{m}/\\mathrm{s}^{2}$). The lunar surface has a thin layer of dust, which might cause a small change in the gravitational field, but it was not considered in this model.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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 lunar surface has a thin layer of dust, which might cause a small change in the gravitational field, but it was not considered in this model. The magnitude of the acceleration of an object's motion. The mass of the object's motion. The speed of the object's velocity. The velocity of the object's kinetic energy. The kinetic energy of the object's potential. The potential of the object's kinetic potential. The kinetic potential of the object's specific velocity. The velocity of the object's specific marks. The answer to the object's velocity. The velocity of the object's kinetic energy. The kinetic energy of the object's potential velocity. The kinetic potential of the object's",
  412.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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 lunar surface has a thin layer of dust, which might cause a small change in the gravitational field, but it was not considered in this model. The displacement magnitude of the object after 5s is not equal to the displacement of the object, and the kinetic energy of the ground is not the same.\n\n## Step 1:  Determine the object\nThe object is placed on a horizontal surface, and the kinetic friction coefficient is 0.2. The displacement magnitude is 5. The kinetic energy of the ground is not the same, and the lunar surface is not considered.\n\n## Step 2:  Consider the object\nThe object is placed on a horizontal surface",
  413.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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 lunar surface has a thin layer of dust, which might cause a small change in the gravitational field, but it was not considered in this model. At the end of 5 seconds, the external force is removed. How much farther can the object move? The mass of the object is 0.5 kg, and the kinetic energy is 0.2 J, and the force is 15 N. The mass of the object is 0.2 kg, and the kinetic energy is 0.2 J, and the lunar surface is 0.2 m, and the force is 0.2 N, and the kinetic energy is 0.2 J, and the gravitational force is 0.2 m"
  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: There was a weak magnetic field around the charged ball, which could potentially affect its motion, but was assumed to be insignificant.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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: There was a weak magnetic field around the charged ball, which could potentially affect its motion, but was assumed to be insignificant. The time the small ball is in the air, which is the time the flight of the ball, which is the time the flight of the ball, which is the time the flight of the ball, which is the time the flight of the ball, which is the time the flight of the ball, which is the time the flight of the ball, which is the time the flight of the ball, which is the time the flight of the ball, which is the time the flight of the ball, which is the time the",
  430.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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: There was a weak magnetic field around the charged ball, which could potentially affect its motion, but was assumed to be insignificant. The speed and direction of the small ball when it hits the ground. The horizontal distance from the landing point to the ground is negligible. The velocity of the ball is not negligible. The mass of the ball is not affected by the velocity of the ground. The height of the ground is not affected by the mass of the height of the height of the height of the height of the height of the height of the height of the height of the height of the height of the height of the height of the height of the height of the height of the height",
  431.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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: There was a weak magnetic field around the charged ball, which could potentially affect its motion, but was assumed to be insignificant. The power of gravity during the ball's landing process is negligible. The final answer is a small ball with a mass of 1 kg is thrown horizontally with an initial velocity of 3 m/s. The distance between the ball and the ground is 1.2 m. The acceleration of the ball in the motion of the ball is negligible. The final answer is a ball with a mass of 1 kg is thrown horizontally with an initial velocity of $3 m/s$. The distance between the ball and the ground is $1"
  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 $\\mathbf{g}=10\\mathbf{m}/\\mathbf{s}^{2}$. The toll station area had a very slight slope, but it was assumed to be a flat road in the analysis.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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 $\\mathbf{g}=10\\mathbf{m}/\\mathbf{s}^{2}$. The toll station area had a very slight slope, but it was assumed to be a flat road in the analysis. Calculate the total time it takes for the ball to fall. The ball is in the air, and the ball is at the bottom of the list of the balls. The ball is at the bottom of the list of the ball. The ball is at rest, and the ball is at the bottom of the list of the ball. The ball is at rest, and the ball is at rest at the bottom of the list of the ball. The ball is at rest, and the ball is at rest at the bottom of the list of the",
  446.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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 $\\mathbf{g}=10\\mathbf{m}/\\mathbf{s}^{2}$. The toll station area had a very slight slope, but it was assumed to be a flat road in the analysis. Calculate the displacement of the ball during the final 2 seconds of its descent. The displacement of the ball is $\\mathbf{d}=\\frac{\\mathbf{a}}{3}$. The displacement of the ball is $\\mathbf{d}=\\mathbf{f}(x)=\\mathbf{A}(\\mathbf{r})$.\n## Step 1: Calculate the displacement of the ball.\nThe displacement of the ball as a function of position is $\\mathbf{d}=\\frac{\\mathbf{a}}{"
  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. The magnetic field around the coil had a small non - uniformity, but it was considered uniform for simplicity in this problem.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. The magnetic field around the coil had a small non - uniformity, but it was considered uniform for simplicity in this problem. What are the potential differences between AB, BC, and CA? \n## Step 1:  Find the difference in potential between point A and B.\nTo find the difference in potential between point B and C.\n## Step 2:  Find the difference in potential between point A and B.\nTo find the difference in potential between point C and B.\n## Step 3:  Find the difference in potential between point A and B.\nTo find the difference in potential between point C and B.\n## Step 4:  Find the",
  461.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. The magnetic field around the coil had a small non - uniformity, but it was considered uniform for simplicity in this problem. 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? What are the potential shapes of the charge at point B? What are the potential scales of the charge at point C? What are the potential charges of the charge at point D? What are the potential currents of the charge at point E? What are the potential reactions to the charge at point F? What are the potential comments of the charge at point G? What are the potential differences of the charge at point I? What are the potential equations of the charge at point J?"
  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. The AC generator had a small amount of mechanical friction in its rotation, which was not considered in the power calculations.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. The AC generator had a small amount of mechanical friction in its rotation, which was not considered in the power calculations. (a) Where should a pin be placed on the optical axis such that its image is formed at the same place? The optical axis of the convex lens is a thin concave, and the mirror is a flat surface. The AC generator has a small amount of light, which is reflected in the refractive index of the convex lens. The AC generator has a large amount of light, which is reflected in the refractive index of the convex mirror. The image of the convex lens is a thin concave, and the mirror is a flat surface. The optical axis of the AC lens is a",
  476.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). 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. The AC generator had a small amount of mechanical friction in its rotation, which was not considered in the power calculations. (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 AC generator has a small amount of mechanical friction in its rotation, which was not considered in the power calculations. The convex mirror has a large amount of mechanical friction in its rotation, which was not considered in the refractive index calculations. The pin has a small amount of mechanical friction in its rotation, which was not considered in the power calculations. The AC generator has a small amount of mechanical friction in its rotation, which was not considered in the refractive index calculations. to"
  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: The transmission line had a small capacitance effect, but it was ignored in the power transmission analysis.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). A small boat is crossing a river with a width of $d = 180 \\, \\mathsf{m}$. The speed of the river current is $v_{1} = 2.5 \\, \\mathrm{m}/\\mathrm{s}$. If the speed of the boat in still water is $v_{2} = 5 \\, \\mathsf{m}/\\mathsf{s}$, find: The transmission line had a small capacitance effect, but it was ignored in the power transmission analysis. 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? When is the speed of the river in the direction of the boat to cross the river, in which direction should the boat head? What is the transmission line? When is the displacement? When is the speed of the boat to cross the river, in which direction should the boat head? What is the time of the boat to cross the river, in which direction should the boat head? When is the time of the boat to cross the river, in which direction should the boat to",
  491.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). A small boat is crossing a river with a width of $d = 180 \\, \\mathsf{m}$. The speed of the river current is $v_{1} = 2.5 \\, \\mathrm{m}/\\mathrm{s}$. If the speed of the boat in still water is $v_{2} = 5 \\, \\mathsf{m}/\\mathsf{s}$, find: The transmission line had a small capacitance effect, but it was ignored in the power transmission analysis. 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 time of the day? What is the speed of the river? When will the boat be painted? When will the boat be launched? How will the boat be driven? When will the boat be pulled? What is the speed of the river? When will the boat be steered? How will the boat be propelled? What is the propulsion of the river? When will the boat be driven? How will the boat be pulled? What is the pull of the river"
  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. The spring was slightly rusted, which might affect its elastic coefficient, but it was assumed to be negligible in the experiment.",
  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.             "Please wrap the final answers with specific marks ([Answer] and [/Answer]). The turns ratio of the primary to secondary coils of an ideal transformer is $4:1$. If an AC voltage of $u=400^{\\sqrt{2}}\\mathrm{sin}\\ 100\\pi t\\ \\mathrm{v}$ is applied to the primary coil. The spring was slightly rusted, which might affect its elastic coefficient, but it was assumed to be negligible in the experiment. What is the voltage measured across the secondary coil using an AC voltmeter? The spring was not a function of the ideal transformer, but the voltage was not a function of the transformer. The turns ratio of the primary to secondary coils of the ideal transformer is $1:1$. The voltage was given by the secondary to the primary coil of the voltage. The spring was not a function of the transformer, but the voltage was given by the primary coil of the voltage. The turns ratio of the primary to secondary coils of the ideal transformer is $4:"
  504.         ]
  505.     }
  506. ]
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