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Physics Equilibrium - Single Triangle + Component Vectors

Physics Equilibrium - Single Triangle + Component Vectors
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2019-08-26 04:36
TriangleVectorGeometric Construction
This example demonstrates the relationship between a single triangle and component vectors in a state of physical equilibrium. Core math concepts include vectors, triangles, angles, length calculations, and orthogonal lines. It is constructed using GeoGebra commands and objects like Segment, Point, Line, Intersect, Vector, Translate, Angle, OrthogonalLine, Length, SelectedElement. Suitable for high school physics and mathematics teaching to understand force equilibrium and vector decomposition.

GeoGebra Commands & Parameters

  1. Segment(G, I) → j
  2. Point(j) → H
  3. Segment(G, H) → r
  4. Line(J, G) → l
  5. Line(P, l) → p
  6. Line(G, K) → m
  7. Line(P, m) → n
  8. Intersect(n, l) → O
  9. Vector(G, O) → v
  10. Intersect(p, m) → Q
  11. Vector(G, Q) → w
  12. Translate(R, v) → R'
  13. Translate(R', w) → R''
  14. Angle(R'', R', R) → η
  15. Vector(G, H) → u
  16. OrthogonalLine(G, u, xOyPlane) → k
  17. Intersect(n, k) → M
  18. Angle(O, G, M, xOyPlane) → γ
  19. Angle(R', R'', R) → ε
  20. Segment(A, B) → f
  21. Point(f) → C
  22. Point(f) → D
  23. Segment(C, E) → g
  24. Segment(E, D) → h
  25. Segment(E, F) → i
  26. Angle(f, g) → α
  27. Angle(f, h) → β
  28. Segment(P, G) → q
  29. Length(q) → a
  30. Length(r) → b
  31. Segment(J, O) → s
  32. Segment(Q, K) → t
  33. Intersect(p, k) → N
  34. Angle(Q, G, N, xOyPlane) → δ_1
  35. SelectedElement(L) → text8
  36. Vector(R, R') → c
  37. Vector(R', R'') → d
  38. Translate(R'', u) → R'''
  39. Vector(R'', R''') → e
  40. OrthogonalLine(R', e, xOyPlane) → f_1
  41. Segment(R'', R) → g_1
  42. Intersect(f_1, g_1) → S
  43. Angle(S, R', R, xOyPlane) → ε_1
  44. Angle(R'', R', S, xOyPlane) → ζ
  45. Angle(R', R, R'') → δ
  46. Segment(R', S) → h_1
  47. Segment(M, N) → i_1
  48. OrthogonalLine(O, i_1, xOyPlane) → j_1
  49. OrthogonalLine(Q, i_1, xOyPlane) → k_1
  50. Intersect(i_1, j_1) → T
  51. Intersect(k_1, i_1) → U
  52. Vector(G, T) → u_1
  53. Vector(T, O) → v_1
  54. Vector(G, U) → w_1
  55. Vector(U, Q) → a_1
  56. Segment(V, W) → l_1
  57. Segment(Z, A_1) → m_1
  58. Intersect(l_1, m_1) → B_1
  59. Vector(B_1, Z) → b_1
  60. Vector(B_1, W) → c_1
  61. Vector(B_1, A_1) → d_1
  62. Vector(B_1, V) → e_1
  63. Segment(C_1, D_1) → n_1
  64. Segment(E_1, F_1) → p_1