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at_rest_newbatch/10/annotation.txt

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+Environment: g=-9.81, F_drag=0.0

at_rest_newbatch/10/formula_info.json

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+{
+  "correct_letter": "B",
+  "correct_formula": "ΣF_ext = 0",
+  "annotation": "Environment: g=-9.81, F_drag=0.0",
+  "choices": [
+    "ΣF = m·Δv / (Δt·cosθ)",
+    "ΣF_ext = 0",
+    "W = ΔE_k = (1/2)·m·v_t² - (1/2)·m·v_0²",
+    "U = -G·m_1·m_2 / r"
+  ],
+  "correct_index": 1,
+  "physics_type": "AtRest",
+  "seed": "AtRest|benchmark/at_rest_newbatch/10"
+}

at_rest_newbatch/10/initial_state/instance_segmentation_mapping_0000.json

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+{"1": "INVALID", "2": "/World/Ground", "4": "/World/OakCylinder", "5": "/World/CherryCube", "3": "/World/WalnutCube"}

at_rest_newbatch/10/instantaneous_velocity/velocity.json

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+{
+  "time_seconds": 1.0,
+  "labels": [
+    {
+      "prim_path": "/World/OakCylinder",
+      "speed": 0.0,
+      "label_str": "$v=0.00$",
+      "label_x": 708,
+      "label_y": 305,
+      "label_w": 99,
+      "label_h": 31,
+      "center_2d": [
+        639.5,
+        321.46762462302644
+      ],
+      "velocity": [
+        0.0,
+        0.0,
+        0.0
+      ]
+    },
+    {
+      "prim_path": "/World/CherryCube",
+      "speed": 0.0,
+      "label_str": "$v=0.00$",
+      "label_x": 706,
+      "label_y": 214,
+      "label_w": 99,
+      "label_h": 31,
+      "center_2d": [
+        639.5,
+        230.42070030895982
+      ],
+      "velocity": [
+        0.0,
+        0.0,
+        0.0
+      ]
+    },
+    {
+      "prim_path": "/World/WalnutCube",
+      "speed": 0.0,
+      "label_str": "$v=0.00$",
+      "label_x": 688,
+      "label_y": 151,
+      "label_w": 99,
+      "label_h": 31,
+      "center_2d": [
+        639.5,
+        167.1080937167199
+      ],
+      "velocity": [
+        0.0,
+        0.0,
+        0.0
+      ]
+    }
+  ]
+}

at_rest_newbatch/10/physics_duration.txt

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+10.0

at_rest_newbatch/12/annotation.txt

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+Environment: g=-9.81, F_drag=0.0

at_rest_newbatch/12/formula_info.json

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+{
+  "correct_letter": "C",
+  "correct_formula": "ΣM_ext = 0",
+  "annotation": "Environment: g=-9.81, F_drag=0.0",
+  "choices": [
+    "G = m·g",
+    "ΔS = Q_rev / T",
+    "ΣM_ext = 0",
+    "ΣM_ext = F·r·cos²θ / (1 + sinθ)"
+  ],
+  "correct_index": 2,
+  "physics_type": "AtRest",
+  "seed": "AtRest|benchmark/at_rest_newbatch/12"
+}

at_rest_newbatch/12/initial_state/instance_segmentation_mapping_0000.json

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+{"1": "INVALID", "2": "/World/Ground", "5": "/World/OakCube", "6": "/World/AshPlanksCube", "4": "/World/CherryCube", "3": "/World/WalnutCube"}

at_rest_newbatch/12/instantaneous_velocity/velocity.json

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+{
+  "time_seconds": 1.0,
+  "labels": [
+    {
+      "prim_path": "/World/OakCube",
+      "speed": 0.0,
+      "label_str": "$v=0.00$",
+      "label_x": 736,
+      "label_y": 304,
+      "label_w": 99,
+      "label_h": 31,
+      "center_2d": [
+        665.4470619729622,
+        320.07509034935083
+      ],
+      "velocity": [
+        0.0,
+        0.0,
+        0.0
+      ]
+    },
+    {
+      "prim_path": "/World/CherryCube",
+      "speed": 0.0,
+      "label_str": "$v=0.00$",
+      "label_x": 717,
+      "label_y": 234,
+      "label_w": 99,
+      "label_h": 31,
+      "center_2d": [
+        656.7818851016162,
+        249.79132661225796
+      ],
+      "velocity": [
+        0.0,
+        0.0,
+        0.0
+      ]
+    },
+    {
+      "prim_path": "/World/WalnutCube",
+      "speed": 0.0,
+      "label_str": "$v=0.00$",
+      "label_x": 707,
+      "label_y": 173,
+      "label_w": 99,
+      "label_h": 31,
+      "center_2d": [
+        657.0067432567432,
+        189.06893106893108
+      ],
+      "velocity": [
+        0.0,
+        0.0,
+        0.0
+      ]
+    },
+    {
+      "prim_path": "/World/AshPlanksCube",
+      "speed": 0.0,
+      "label_str": "$v=0.00$",
+      "label_x": 648,
+      "label_y": 330,
+      "label_w": 99,
+      "label_h": 31,
+      "center_2d": [
+        585.6124213836478,
+        346.0847746331237
+      ],
+      "velocity": [
+        0.0,
+        0.0,
+        0.0
+      ]
+    }
+  ]
+}

at_rest_newbatch/12/physics_duration.txt

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+10.0

at_rest_newbatch/14/annotation.txt

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+Environment: g=-9.81, F_drag=0.0

at_rest_newbatch/14/formula_info.json

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+{
+  "correct_letter": "D",
+  "correct_formula": "ΣM_ext = 0",
+  "annotation": "Environment: g=-9.81, F_drag=0.0",
+  "choices": [
+    "ΣM_ext = F·r·cos²θ / (1 + sinθ)",
+    "ΔS = Q_rev / T",
+    "W = ΔE_k = (1/2)·m·v_t² - (1/2)·m·v_0²",
+    "ΣM_ext = 0"
+  ],
+  "correct_index": 3,
+  "physics_type": "AtRest",
+  "seed": "AtRest|benchmark/at_rest_newbatch/14"
+}

at_rest_newbatch/14/initial_state/instance_segmentation_mapping_0000.json

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+{"1": "INVALID", "4": "/World/Ground", "3": "/World/OakCube", "5": "/World/CherryCube", "2": "/World/WalnutCube", "6": "/World/AshPlanksSphere"}

at_rest_newbatch/14/instantaneous_velocity/velocity.json

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+{
+  "time_seconds": 1.0,
+  "labels": [
+    {
+      "prim_path": "/World/OakCube",
+      "speed": 0.0,
+      "label_str": "$v=0.00$",
+      "label_x": 735,
+      "label_y": 300,
+      "label_w": 99,
+      "label_h": 31,
+      "center_2d": [
+        639.5,
+        316.35316346361475
+      ],
+      "velocity": [
+        0.0,
+        0.0,
+        0.0
+      ]
+    },
+    {
+      "prim_path": "/World/CherryCube",
+      "speed": 0.0,
+      "label_str": "$v=0.00$",
+      "label_x": 714,
+      "label_y": 202,
+      "label_w": 99,
+      "label_h": 31,
+      "center_2d": [
+        639.5,
+        218.04393879952923
+      ],
+      "velocity": [
+        0.0,
+        0.0,
+        0.0
+      ]
+    },
+    {
+      "prim_path": "/World/WalnutCube",
+      "speed": 0.0,
+      "label_str": "$v=0.00$",
+      "label_x": 698,
+      "label_y": 126,
+      "label_w": 99,
+      "label_h": 31,
+      "center_2d": [
+        639.5,
+        142.18252100840337
+      ],
+      "velocity": [
+        0.0,
+        0.0,
+        0.0
+      ]
+    },
+    {
+      "prim_path": "/World/AshPlanksSphere",
+      "speed": 0.0,
+      "label_str": "$v=0.00$",
+      "label_x": 671,
+      "label_y": 77,
+      "label_w": 99,
+      "label_h": 31,
+      "center_2d": [
+        639.5,
+        92.65904365904366
+      ],
+      "velocity": [
+        0.0,
+        0.0,
+        0.0
+      ]
+    }
+  ]
+}

at_rest_newbatch/14/physics_duration.txt

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+10.0

circular_newbatch/11/annotation.txt

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+Environment: g=-9.81, F_drag=0.0
+Ground: mu_s=0.0, mu_k=0.0
+TireSphere: d = 1.0, e = 0.6, theta_start = 360°, v_0 = -3.0
+Track_0: R = 2.0, e = 0.3, theta_min = 270°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0

circular_newbatch/11/formula_info.json

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+{
+  "correct_letter": "D",
+  "correct_formula": "(1/2)·m·v_0² + m·g·R·(1-cosθ_start) = (1/2)·m·v² + m·g·R·(1-cosθ)",
+  "annotation": "Environment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nTireSphere: d = 1.0, e = 0.6, theta_start = 360°, v_0 = -3.0\nTrack_0: R = 2.0, e = 0.3, theta_min = 270°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0",
+  "choices": [
+    "F_drag =(1/2)·C_d·ρ·A·v²",
+    "E_total = m·g·R·(3/2 - cosθ)²",
+    "ΔS = Q_rev / T",
+    "(1/2)·m·v_0² + m·g·R·(1-cosθ_start) = (1/2)·m·v² + m·g·R·(1-cosθ)"
+  ],
+  "correct_index": 3,
+  "physics_type": "Circular",
+  "seed": "Circular|benchmark/circular_newbatch/11"
+}

circular_newbatch/11/initial_state/instance_segmentation_mapping_0000.json

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+{"1": "INVALID", "2": "/World/Ground", "3": "/World/CircularTrack_0", "4": "/World/TireSphere"}

circular_newbatch/11/instantaneous_velocity/velocity.json

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+{
+  "time_seconds": 0.5,
+  "labels": [
+    {
+      "prim_path": "/World/TireSphere",
+      "speed": 0.9386701437420369,
+      "label_str": "$v=0.94$",
+      "label_x": 921,
+      "label_y": 144,
+      "label_w": 99,
+      "label_h": 31,
+      "center_2d": [
+        850.2816381987577,
+        179.03319099378882
+      ],
+      "velocity": [
+        0.0,
+        -0.6767805814743042,
+        0.6504380702972412
+      ],
+      "arrow_start": [
+        850.2816381987577,
+        179.03319099378882
+      ],
+      "arrow_end": [
+        921.9148080424079,
+        109.25719957732267
+      ]
+    }
+  ]
+}

circular_newbatch/11/physics_duration.txt

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+3.5

circular_newbatch/12/annotation.txt

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+Environment: g=-3.71, F_drag=0.0
+Ground: mu_s=0.7, mu_k=0.5
+TireSphere: d = 1.0, e = 0.6, theta_start = 90°, v_0 = 6.0
+Track_0: R = 2.5, e = 0.3, theta_min = 90°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0

circular_newbatch/12/formula_info.json

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+{
+  "correct_letter": "A",
+  "correct_formula": "F_N - m·g·cosθ = m·v²/R",
+  "annotation": "Environment: g=-3.71, F_drag=0.0\nGround: mu_s=0.7, mu_k=0.5\nTireSphere: d = 1.0, e = 0.6, theta_start = 90°, v_0 = 6.0\nTrack_0: R = 2.5, e = 0.3, theta_min = 90°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0",
+  "choices": [
+    "F_N - m·g·cosθ = m·v²/R",
+    "E_total = m·g·R·(3/2 - cosθ)²",
+    "e = (v_2f - v_1f) / (v_1i - v_2i)",
+    "B = μ_0·n·I"
+  ],
+  "correct_index": 0,
+  "physics_type": "Circular",
+  "seed": "Circular|benchmark/circular_newbatch/12"
+}

circular_newbatch/12/initial_state/instance_segmentation_mapping_0000.json

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+{"1": "INVALID", "3": "/World/Ground", "4": "/World/CircularTrack_0", "2": "/World/TireSphere"}