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水平面上拉动物体：静摩擦与动摩擦的几何刻画

水平面上拉动物体：静摩擦与动摩擦的几何刻画
几何画板及绘图内容加载中，请稍等……
2020-09-16 19:00
角向量不等式几何作图滑块动画
该范例通过绳索在水平面上拉动物体的仿真，展示摩擦力在起动前后如何随牵引角与拉力变化而改变，从而影响盒子的加速度与速度变化。核心数学概念包括：静摩擦上限与动摩擦系数的分段判定（If），力的方向与夹角建模（Vector、Angle），法向力与摩擦力的几何表达（Segment、normal、fk），以及利用几何构型标注关键量（Textfield）。作图与构造要点可从“构造摘要”提炼为：使用 If 实现“未起动/起动”的条件分支；用 Polygon、Segment 与 Midpoint 构建盒体及力学受力示意；用 Vector 表示牵引力、摩擦力与速度等方向量；用 Angle 计算绳索方向与参考方向的夹角 θ；并通过 Textfield 动态显示参数与结果（如 μ_s、μ_k、fk、fsmax、vel、v0、t 等）。适合中学理科与数学建模课程用于力学建模、分段函数思想与几何—代数结合的探索，也可作为课堂演示与自学仿真活动的配套材料。

GeoGebra 命令及参数

  1. If((m * g) > (F * sin(θ)), (m * 9.8) - (F * sin(θ)), 0) → normal
  2. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  3. Segment(B, D) → e
  4. Segment((A1, B1), (A2, B2)) → C2
  5. Segment((A2, B2), (A3, B3)) → C3
  6. Segment((A3, B3), (A4, B4)) → C4
  7. Segment((A4, B4), (A5, B5)) → C5
  8. Segment((A5, B5), (A6, B6)) → C6
  9. Segment((A6, B6), (A7, B7)) → C7
  10. Segment((A7, B7), (A8, B8)) → C8
  11. Segment((A8, B8), (A9, B9)) → C9
  12. Segment((A9, B9), (A10, B10)) → C10
  13. Segment((A10, B10), (A11, B11)) → C11
  14. Segment((A11, B11), (A12, B12)) → C12
  15. Segment((A12, B12), (A13, B13)) → C13
  16. Segment((A13, B13), (A14, B14)) → C14
  17. Segment((A14, B14), (A15, B15)) → C15
  18. Segment((A15, B15), (A16, B16)) → C16
  19. Segment((A16, B16), (A17, B17)) → C17
  20. Segment((A17, B17), (A18, B18)) → C18
  21. Segment((A18, B18), (A19, B19)) → C19
  22. Segment((A19, B19), (A20, B20)) → C20
  23. Segment((A20, B20), (A21, B21)) → C21
  24. Segment((A21, B21), (A22, B22)) → C22
  25. Segment((A22, B22), (A23, B23)) → C23
  26. Segment((A23, B23), (A24, B24)) → C24
  27. Segment((A24, B24), (A25, B25)) → C25
  28. Segment((A25, B25), (A26, B26)) → C26
  29. Segment((A26, B26), (A27, B27)) → C27
  30. Segment((A27, B27), (A28, B28)) → C28
  31. Segment((A28, B28), (A29, B29)) → C29
  32. Segment((A29, B29), (A30, B30)) → C30
  33. Segment((A30, B30), (A31, B31)) → C31
  34. Segment((A31, B31), (A32, B32)) → C32
  35. Segment((A32, B32), (A33, B33)) → C33
  36. Segment((A33, B33), (A34, B34)) → C34
  37. Segment((A34, B34), (A35, B35)) → C35
  38. Segment((A35, B35), (A36, B36)) → C36
  39. Segment((A36, B36), (A37, B37)) → C37
  40. Segment((A37, B37), (A38, B38)) → C38
  41. Segment((A38, B38), (A39, B39)) → C39
  42. Segment((A39, B39), (A40, B40)) → C40
  43. Segment((A40, B40), (A41, B41)) → C41
  44. Segment((A41, B41), (A42, B42)) → C42
  45. Segment((A42, B42), (A43, B43)) → C43
  46. Segment((A43, B43), (A44, B44)) → C44
  47. Segment((A44, B44), (A45, B45)) → C45
  48. Segment((A45, B45), (A46, B46)) → C46
  49. Segment((A46, B46), (A47, B47)) → C47
  50. Segment((A47, B47), (A48, B48)) → C48
  51. Segment((A48, B48), (A49, B49)) → C49
  52. Segment((A49, B49), (A50, B50)) → C50
  53. Segment((A50, B50), (A51, B51)) → C51
  54. Segment((A51, B51), (A52, B52)) → C52
  55. Segment((A52, B52), (A53, B53)) → C53
  56. Segment((A53, B53), (A54, B54)) → C54
  57. Segment((A54, B54), (A55, B55)) → C55
  58. Segment((A55, B55), (A56, B56)) → C56
  59. Segment((A56, B56), (A57, B57)) → C57
  60. Segment((A57, B57), (A58, B58)) → C58
  61. Segment((A58, B58), (A59, B59)) → C59
  62. Segment((A59, B59), (A60, B60)) → C60
  63. Segment((A60, B60), (A61, B61)) → C61
  64. Segment((A61, B61), (A62, B62)) → C62
  65. Segment((A62, B62), (A63, B63)) → C63
  66. Segment((A63, B63), (A64, B64)) → C64
  67. Segment((A64, B64), (A65, B65)) → C65
  68. Segment((A65, B65), (A66, B66)) → C66
  69. Segment((A66, B66), (A67, B67)) → C67
  70. Segment((A67, B67), (A68, B68)) → C68
  71. Segment((A68, B68), (A69, B69)) → C69
  72. Segment((A69, B69), (A70, B70)) → C70
  73. Segment((A70, B70), (A71, B71)) → C71
  74. Segment((A71, B71), (A72, B72)) → C72
  75. Segment((A72, B72), (A73, B73)) → C73
  76. Segment((A73, B73), (A74, B74)) → C74
  77. Segment((A74, B74), (A75, B75)) → C75
  78. Segment((A75, B75), (A76, B76)) → C76
  79. Segment((A76, B76), (A77, B77)) → C77
  80. Segment((A77, B77), (A78, B78)) → C78
  81. Segment((A78, B78), (A79, B79)) → C79
  82. Segment((A79, B79), (A80, B80)) → C80
  83. Segment((A80, B80), (A81, B81)) → C81
  84. Segment((A81, B81), (A82, B82)) → C82
  85. Segment((A82, B82), (A83, B83)) → C83
  86. Segment((A83, B83), (A84, B84)) → C84
  87. Segment((A84, B84), (A85, B85)) → C85
  88. Segment((A85, B85), (A86, B86)) → C86
  89. Segment((A86, B86), (A87, B87)) → C87
  90. Segment((A87, B87), (A88, B88)) → C88
  91. Segment((A88, B88), (A89, B89)) → C89
  92. Segment((A89, B89), (A90, B90)) → C90
  93. Segment((A90, B90), (A91, B91)) → C91
  94. Segment((A91, B91), (A92, B92)) → C92
  95. Segment((A92, B92), (A93, B93)) → C93
  96. Segment((A93, B93), (A94, B94)) → C94
  97. Segment((A94, B94), (A95, B95)) → C95
  98. Segment((A95, B95), (A96, B96)) → C96
  99. Segment((A96, B96), (A97, B97)) → C97
  100. Segment((A97, B97), (A98, B98)) → C98
  101. Segment((A98, B98), (A99, B99)) → C99
  102. Segment((A99, B99), (A100, B100)) → C100
  103. Segment((A100, B100), (A101, B101)) → C101
  104. Midpoint(e) → E
  105. Vector(E, H) → v
  106. If(F > ((μ_s * m) * g), fk, fsmax) → f
  107. Vector(E, (x(E) + (F * cos(θ) / 20), y(E))) → T_x
  108. Vector((x(E) + 0.02, y(E)), (x(E) + 0.02, y(E) + (F * sin(θ) / 20))) → T_y
  109. Vector(E, (x(E) + (F * cos(θ) / 20), y(E) + (F * sin(θ) / 20))) → T
  110. Vector(E, (x(E), y(E) - (m * 9.8 / 20))) → mg
  111. Vector((x(E) - 0.02, y(E)), (x(E) - 0.02, y(E) + Length[mg] - Length[T_y])) → n
  112. Vector(E, H2) → u
  113. If(vel > 0, ((F * cos(θ)) - fk) / m, If[fsmax > (F * cos(θ)), 0, ((F * cos(θ)) - fk) / m]) → acc
  114. If((F * sin(θ)) ≥ (m * g), true, false) → up
  115. Angle(T_x, T) → α
  116. Textfield(F) → inputBox1
  117. Textfield(m) → inputBox2
  118. Textfield(θ) → inputBox3
  119. Textfield(μ_s) → inputBox4
  120. Textfield(μ_k) → inputBox5

AI 绘图提示语参考

绘制一个模拟箱子在水平面上被拉动的图形。图形包含一个水平表面、一个箱子、一个绳子连接箱子与固定点，以及一个力图示展示静摩擦和动摩擦。构造顺序：先画出水平表面，再放置箱子，然后绘制绳子，最后添加力图示以显示摩擦力方向和大小变化。图形应体现静摩擦与动摩擦的区别，以及绳子拉力如何影响运动状态。
以上提示语为根据原始绘图命令整理而来，仅供参考。