← Paul Test
doc399 121b1088-410e-492f-a9b0-ca9f21c2d300_1783086558_Copy_of_Bridge_Challenge.pdf
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figure (5)
formula (13)
heading (7)
list (4)
list_item (19)
text (21)
title (1)
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Page 1 JSON
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"text": "Bridge Building Challenge",
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"text": "Goal: Design and build a model bridge that spans a given distance and holds the maximum load possible using the provided materials. Your bridge must be strong, stable, and efficient!",
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"text": "• Popsicle sticks",
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"id": "p1.6.2",
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"text": "• Wood glue",
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"text": "• String or tape",
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"text": "• Cardboard base (supports)",
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"text": "• Small weights (for testing)",
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"text": "Constraints:",
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"text": "• The bridge must span 30 cm between the supports.",
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"text": "• Only the provided materials may be used.",
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"text": "• The bridge must be no wider than 10 cm.",
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"text": "• Build time: 60 minutes.",
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"text": "• Testing will be done by placing weights at the center of the bridge until it fails.",
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"text": "Think Like an Engineer!",
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"text": "A bridge must resist different types of forces and distribute the load to the supports.",
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"text": "Common Bridge Shapes",
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"text": "→ strong and stable",
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"text": "→ good for heavy loads",
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"text": "Arch Bridge\n→ compression only",
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"text": "Load and Strength (Algebra)",
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"text": "Load (L) is the total weight the bridge holds. If the bridge holds 5 weights and each weight is 20 g:",
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"type": "formula",
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"text": "where w = weight of one mass\nL = 5(20) = 100 g",
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"text": "Your goal is to MAXIMIZE L (the load) before failure!",
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"type": "heading",
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"text": "Example Calculation:",
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"type": "text",
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"b": 158.1318
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"text": "If your bridge holds 8 weights (20 g each) and the span is 30 cm:",
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},
{
"id": "p1.28",
"order": 42,
"type": "formula",
"bbox": {
"l": 45.1064,
"t": 156.2122,
"r": 165.31,
"b": 140.375
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"text": "L = 8(20) = 160g",
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},
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"text": "Convert to Newtons (1 g[p1.29.1] 0.0098 N)",
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"text": "≈",
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"text_span": 9,
"bbox_estimated": true,
"alt": "is approximately",
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{
"id": "p1.30",
"order": 45,
"type": "formula",
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"l": 18.2345,
"t": 119.7387,
"r": 192.9017,
"b": 102.2218
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"text": "P = 160g × 0.0098 ≈ 1.57N",
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"latex": "P=160g\\times0.0098\\approx1.57N",
"alt": "P equals 160 g times 0.0098 is approximately 1.57 N",
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"type": "formula",
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"t": 94.3032,
"r": 218.334,
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"text": "M = 7.5P = 7.5(1.57) ≈ 11.78N · cm",
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"id": "p1.32",
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"type": "text",
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"text": "Stress ([p1.32.1]) is the force on a material",
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{
"id": "p1.32.1",
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"type": "formula",
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"text": "σ",
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"latex": "\\sigma",
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"text_span": 9,
"bbox_estimated": true,
"alt": "sigma",
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"children": []
}
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},
{
"id": "p1.33",
"order": 49,
"type": "text",
"bbox": {
"l": 277.5961,
"t": 372.1737,
"r": 491.3715,
"b": 355.6167
},
"text": "divided by the area (A) of the material.",
"children": []
},
{
"id": "p1.34",
"order": 50,
"type": "formula",
"bbox": {
"l": 306.6273,
"t": 350.0976,
"r": 369.0085,
"b": 317.4635
},
"text": "σ = F/A",
"attrs": {
"block_label": "display_formula",
"latex": "\\sigma = \\frac{F}{A}",
"alt": "sigma equals F over A",
"mathml": "<math aria-label=\"sigma equals F over A\" xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mrow><mi>σ</mi><mo>=</mo><mfrac><mrow><mi>F</mi></mrow><mrow><mi>A</mi></mrow></mfrac></mrow></math>"
},
"children": []
},
{
"id": "p1.35",
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"type": "text",
"bbox": {
"l": 383.1642,
"t": 352.4972,
"r": 593.5806,
"b": 325.862
},
"text": "If a stick has a cross-sectional area of[p1.35.1] and the force on it is 12 N:",
"children": [
{
"id": "p1.35.1",
"order": 52,
"type": "formula",
"bbox": {
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"t": 352.4972,
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"text": "0.2 cm²",
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"text_offset": 40,
"text_span": 9,
"bbox_estimated": true,
"alt": "0.2, cm squared",
"mathml": "<math aria-label=\"0.2, cm squared\" xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mrow><mn>0.2</mn><mspace width=\"0.167em\" /><mi>c</mi><msup><mi>m</mi><mrow><mn>2</mn></mrow></msup></mrow></math>"
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},
{
"id": "p1.36",
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"type": "formula",
"bbox": {
"l": 394.4408,
"t": 324.6622,
"r": 541.7562,
"b": 299.4667
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"text": "σ = 12/0.2 = 60N/cm²",
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"block_label": "display_formula",
"latex": "\\sigma=\\frac{12}{0.2}=60N/c m^{2}",
"alt": "sigma equals 12 over 0.2 equals 60 N over cm squared",
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"type": "text",
"bbox": {
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"t": 295.1474,
"r": 492.5711,
"b": 267.0724
},
"text": "Stronger designs spread the load across more members, reducing stress.",
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},
{
"id": "p1.38",
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"type": "text",
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"t": 263.2331,
"r": 496.8898,
"b": 233.7184
},
"text": "Bending Moment (M) at the center of a simply supported beam with a center load:",
"children": []
},
{
"id": "p1.39",
"order": 56,
"type": "formula",
"bbox": {
"l": 289.3525,
"t": 226.9996,
"r": 347.8948,
"b": 197.0049
},
"text": "M = PL/4",
"attrs": {
"block_label": "display_formula",
"latex": "M=\\frac{P L}{4}",
"alt": "M equals PL over 4",
"mathml": "<math aria-label=\"M equals PL over 4\" xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mrow><mi>M</mi><mo>=</mo><mfrac><mrow><mi>P</mi><mi>L</mi></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></math>"
},
"children": []
},
{
"id": "p1.40",
"order": 57,
"type": "text",
"bbox": {
"l": 391.5616,
"t": 232.9985,
"r": 477.6956,
"b": 219.5609
},
"text": "where P = load",
"children": []
},
{
"id": "p1.41",
"order": 58,
"type": "formula",
"bbox": {
"l": 427.3108,
"t": 219.8009,
"r": 513.4448,
"b": 205.1635
},
"text": "L = spanlength",
"attrs": {
"block_label": "display_formula",
"latex": "L=s p a n l e n g t h",
"alt": "L equals spanlength",
"mathml": "<math aria-label=\"L equals spanlength\" xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mrow><mi>L</mi><mo>=</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>l</mi><mi>e</mi><mi>n</mi><mi>g</mi><mi>t</mi><mi>h</mi></mrow></math>"
},
"children": []
},
{
"id": "p1.42",
"order": 59,
"type": "text",
"bbox": {
"l": 377.4059,
"t": 203.9637,
"r": 542.716,
"b": 187.8865
},
"text": "For our bridge, [p1.42.1]",
"children": [
{
"id": "p1.42.1",
"order": 60,
"type": "formula",
"bbox": {
"l": 377.4059,
"t": 203.9637,
"r": 542.716,
"b": 187.8865
},
"text": "L = 30 cm",
"attrs": {
"latex": "L = 30 \\, cm",
"inline": true,
"text_offset": 16,
"text_span": 9,
"bbox_estimated": true,
"alt": "L equals 30, cm",
"mathml": "<math aria-label=\"L equals 30, cm\" xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mrow><mi>L</mi><mo>=</mo><mn>30</mn><mspace width=\"0.167em\" /><mi>c</mi><mi>m</mi></mrow></math>"
},
"children": []
}
]
},
{
"id": "p1.43",
"order": 61,
"type": "formula",
"bbox": {
"l": 376.6861,
"t": 185.247,
"r": 571.0274,
"b": 161.2513
},
"text": "S₀,M = P(30)/4 = 7.5P(N · cm)",
"attrs": {
"block_label": "display_formula",
"latex": "S_{0},M=\\frac{P(30)}{4}=7.5P(N\\cdot c m)",
"alt": "S sub 0, M equals P of 30 over 4 equals 7.5 P of N times cm",
"mathml": "<math aria-label=\"S sub 0, M equals P of 30 over 4 equals 7.5 P of N times cm\" xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><mrow><msub><mi>S</mi><mrow><mn>0</mn></mrow></msub><mo>,</mo><mi>M</mi><mo>=</mo><mfrac><mrow><mi>P</mi><mo stretchy=\"false\">(</mo><mn>30</mn><mo stretchy=\"false\">)</mo></mrow><mrow><mn>4</mn></mrow></mfrac><mo>=</mo><mn>7.5</mn><mi>P</mi><mo stretchy=\"false\">(</mo><mi>N</mi><mo>·</mo><mi>c</mi><mi>m</mi><mo stretchy=\"false\">)</mo></mrow></math>"
},
"children": []
},
{
"id": "p1.44",
"order": 62,
"type": "text",
"bbox": {
"l": 252.8836,
"t": 165.3306,
"r": 314.5449,
"b": 57.1098
},
"text": "Good design\n=\nBalance of Strength, Stability, and Efficiency!",
"children": []
},
{
"id": "p1.45",
"order": 63,
"type": "heading",
"bbox": {
"l": 347.6549,
"t": 151.413,
"r": 448.9043,
"b": 134.1361
},
"text": "Testing Procedure:",
"children": []
},
{
"id": "p1.46",
"order": 64,
"type": "list",
"bbox": {
"l": 348.6146,
"t": 131.26,
"r": 591.1813,
"b": 59.51
},
"text": "",
"attrs": {
"item_count": 5
},
"children": [
{
"id": "p1.46.1",
"order": 65,
"type": "list_item",
"bbox": {
"l": 349.5743,
"t": 131.26,
"r": 550.8735,
"b": 116.38
},
"text": "1. Place the bridge on the supports.",
"attrs": {
"bbox_estimated": true
},
"children": []
},
{
"id": "p1.46.2",
"order": 66,
"type": "list_item",
"bbox": {
"l": 349.3344,
"t": 116.38,
"r": 591.1813,
"b": 101.98
},
"text": "2. Add one weight at a time to the center.",
"attrs": {
"bbox_estimated": true
},
"children": []
},
{
"id": "p1.46.3",
"order": 67,
"type": "list_item",
"bbox": {
"l": 349.5743,
"t": 102.46,
"r": 495.9301,
"b": 89.02
},
"text": "3. Record the total load.",
"attrs": {
"bbox_estimated": true
},
"children": []
},
{
"id": "p1.46.4",
"order": 68,
"type": "list_item",
"bbox": {
"l": 349.0945,
"t": 89.26,
"r": 547.2746,
"b": 75.35
},
"text": "4. Continue until the bridge fails.",
"attrs": {
"bbox_estimated": true
},
"children": []
},
{
"id": "p1.46.5",
"order": 69,
"type": "list_item",
"bbox": {
"l": 348.6146,
"t": 75.35,
"r": 580.3846,
"b": 59.51
},
"text": "5. The team with the highest load wins!",
"attrs": {
"bbox_estimated": true
},
"children": []
}
]
},
{
"id": "p1.47",
"order": 70,
"type": "text",
"bbox": {
"l": 49.4251,
"t": 41.9925,
"r": 511.2855,
"b": 16.797
},
"text": "☆ Plan carefully. Build strong. Test fairly. Improve together! ☆",
"children": []
}
],
"ai_page_review": {
"model": "claude-opus-4-8",
"applied": true,
"changed": true,
"reviewed_at": "2026-08-21T10:01:29+00:00"
}
}