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{
"id": "p1.1",
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"type": "title",
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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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{
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"text": "Materials:",
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"bbox": {
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"b": 669.48
},
"text": "• Popsicle sticks",
"attrs": {
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},
"children": []
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{
"id": "p1.6.2",
"order": 8,
"type": "list_item",
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"text": "• Wood glue",
"attrs": {
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{
"id": "p1.6.3",
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"type": "list_item",
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"text": "• String or tape",
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{
"id": "p1.6.4",
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"type": "list_item",
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"text": "• Cardboard base (supports)",
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"bbox_estimated": true
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"children": []
},
{
"id": "p1.6.5",
"order": 11,
"type": "list_item",
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"text": "• Small weights (for testing)",
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"bbox_estimated": true
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"children": []
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},
{
"id": "p1.7",
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"type": "heading",
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"b": 687.7175
},
"text": "Constraints:",
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{
"id": "p1.8",
"order": 13,
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"b": 582.14
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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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"bbox_estimated": true
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{
"id": "p1.8.3",
"order": 16,
"type": "list_item",
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"text": "• The bridge must be no wider than 10 cm.",
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{
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"text": "• Build time: 60 minutes.",
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"type": "list_item",
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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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{
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"type": "heading",
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"b": 546.3827
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"text": "Think Like an Engineer!",
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},
{
"id": "p1.10",
"order": 20,
"type": "text",
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"text": "A bridge must resist different types of forces and distribute the load to the supports.",
"children": []
},
{
"id": "p1.11",
"order": 21,
"type": "list",
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"b": 407.2075
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"text": "• Compression: squishing force",
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"type": "list_item",
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"text": "• Tension: pulling force",
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"text": "• Shear: forces sliding across each other",
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},
{
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"text": "• Bending: caused by the load pushing down on the bridge",
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}
]
},
{
"id": "p1.12",
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"type": "heading",
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"b": 546.6226
},
"text": "Common Bridge Shapes",
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},
{
"id": "p1.13",
"order": 27,
"type": "figure",
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"b": 509.1893
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},
{
"id": "p1.14",
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"text": "Triangular Truss",
"children": []
},
{
"id": "p1.15",
"order": 29,
"type": "text",
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"r": 538.1573,
"b": 503.4303
},
"text": "→ strong and stable",
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},
{
"id": "p1.16",
"order": 30,
"type": "figure",
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"r": 391.8016,
"b": 466.9568
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"text": "",
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"children": []
},
{
"id": "p1.17",
"order": 31,
"type": "text",
"bbox": {
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"r": 473.3769,
"b": 478.7147
},
"text": "Howe Truss",
"children": []
},
{
"id": "p1.18",
"order": 32,
"type": "text",
"bbox": {
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"t": 477.9949,
"r": 548.7141,
"b": 459.0382
},
"text": "→ good for heavy loads",
"children": []
},
{
"id": "p1.19",
"order": 33,
"type": "figure",
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"t": 457.5985,
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"b": 418.7254
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"text": "",
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"block_label": "image"
},
"children": []
},
{
"id": "p1.20",
"order": 34,
"type": "text",
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"t": 446.8004,
"r": 534.3185,
"b": 413.4464
},
"text": "Arch Bridge\n→ compression only",
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},
{
"id": "p1.21",
"order": 35,
"type": "heading",
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"b": 371.6938
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"text": "Load and Strength (Algebra)",
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"block_label": "paragraph_title"
},
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},
{
"id": "p1.22",
"order": 36,
"type": "text",
"bbox": {
"l": 23.273,
"t": 366.8947,
"r": 264.4001,
"b": 319.3831
},
"text": "Load (L) is the total weight the bridge holds. If the bridge holds 5 weights and each weight is 20 g:",
"children": []
},
{
"id": "p1.23",
"order": 37,
"type": "formula",
"bbox": {
"l": 56.6229,
"t": 317.2235,
"r": 103.8886,
"b": 304.5058
},
"text": "L = 5w",
"attrs": {
"block_label": "display_formula",
"latex": "L=5w",
"alt": "L equals 5 w",
"mathml": ""
},
"children": []
},
{
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"order": 38,
"type": "text",
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"l": 23.033,
"t": 303.066,
"r": 202.0189,
"b": 270.4318
},
"text": "where w = weight of one mass\nL = 5(20) = 100 g",
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},
{
"id": "p1.25",
"order": 39,
"type": "text",
"bbox": {
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"t": 263.4731,
"r": 204.8981,
"b": 227.9594
},
"text": "Your goal is to MAXIMIZE L (the load) before failure!",
"children": []
},
{
"id": "p1.26",
"order": 40,
"type": "heading",
"bbox": {
"l": 19.1942,
"t": 209.7226,
"r": 134.3594,
"b": 192.2058
},
"text": "Example Calculation:",
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},
{
"id": "p1.27",
"order": 41,
"type": "text",
"bbox": {
"l": 18.2345,
"t": 187.1667,
"r": 243.5264,
"b": 158.1318
},
"text": "If your bridge holds 8 weights (20 g each) and the span is 30 cm:",
"children": []
},
{
"id": "p1.28",
"order": 42,
"type": "formula",
"bbox": {
"l": 45.1064,
"t": 156.2122,
"r": 165.31,
"b": 140.375
},
"text": "L = 8(20) = 160g",
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"latex": "L=8(20)=160g",
"alt": "L equals 8 times 20 equals 160 g",
"mathml": ""
},
"children": []
},
{
"id": "p1.29",
"order": 43,
"type": "text",
"bbox": {
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"t": 138.4553,
"r": 218.0941,
"b": 121.1784
},
"text": "Convert to Newtons (1 g[p1.29.1] 0.0098 N)",
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{
"id": "p1.29.1",
"order": 44,
"type": "formula",
"bbox": {
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"t": 138.4553,
"r": 218.0941,
"b": 121.1784
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"text": "≈",
"attrs": {
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"text_offset": 23,
"text_span": 9,
"bbox_estimated": true,
"alt": "is approximately",
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"id": "p1.30",
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"type": "formula",
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"t": 119.7387,
"r": 192.9017,
"b": 102.2218
},
"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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{
"id": "p1.31",
"order": 46,
"type": "formula",
"bbox": {
"l": 17.7546,
"t": 94.3032,
"r": 218.334,
"b": 76.3064
},
"text": "M = 7.5P = 7.5(1.57) ≈ 11.78N · cm",
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"latex": "M=7.5P=7.5(1.57)\\approx11.78N\\cdot c m",
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{
"id": "p1.32",
"order": 47,
"type": "text",
"bbox": {
"l": 275.6767,
"t": 389.2107,
"r": 464.9795,
"b": 374.0934
},
"text": "Stress ([p1.32.1]) is the force on a material",
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{
"id": "p1.32.1",
"order": 48,
"type": "formula",
"bbox": {
"l": 275.6767,
"t": 389.2107,
"r": 464.9795,
"b": 374.0934
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"text": "σ",
"attrs": {
"latex": "\\sigma",
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"text_offset": 8,
"text_span": 9,
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"alt": "sigma",
"mathml": ""
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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": ""
},
"children": []
},
{
"id": "p1.35",
"order": 51,
"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": {
"l": 383.1642,
"t": 352.4972,
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"text": "0.2 cm²",
"attrs": {
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"text_offset": 40,
"text_span": 9,
"bbox_estimated": true,
"alt": "0.2, cm squared",
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},
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}
]
},
{
"id": "p1.36",
"order": 53,
"type": "formula",
"bbox": {
"l": 394.4408,
"t": 324.6622,
"r": 541.7562,
"b": 299.4667
},
"text": "σ = 12/0.2 = 60N/cm²",
"attrs": {
"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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},
"children": []
},
{
"id": "p1.37",
"order": 54,
"type": "text",
"bbox": {
"l": 276.3965,
"t": 295.1474,
"r": 492.5711,
"b": 267.0724
},
"text": "Stronger designs spread the load across more members, reducing stress.",
"children": []
},
{
"id": "p1.38",
"order": 55,
"type": "text",
"bbox": {
"l": 276.3965,
"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": ""
},
"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": ""
},
"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": ""
},
"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",
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},
"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": []
},
{
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"order": 63,
"type": "heading",
"bbox": {
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"t": 151.413,
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"b": 134.1361
},
"text": "Testing Procedure:",
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"text": "1. Place the bridge on the supports.",
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"text": "2. Add one weight at a time to the center.",
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"text": "3. Record the total load.",
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"text": "4. Continue until the bridge fails.",
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"text": "5. The team with the highest load wins!",
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"text": "☆ Plan carefully. Build strong. Test fairly. Improve together! ☆",
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