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Elastic Collisions in One Dimension

Elastic Collisions in One Dimension
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2017-03-13 18:43
VectorFunctionCoordinate GeometryCalculusDerivative
In collections Physics Lab
This example demonstrates the motion trajectories and velocity changes of two objects in one-dimensional elastic collisions. Core math concepts include vectors, functions, derivatives, calculus, and momentum conservation. GeoGebra commands and objects used in construction are Point, Intersect, OrthogonalLine, If, Derivative, LaTeX, Circle, Vector, Translate, Textfield, Line. Suitable for high school physics and mathematics teaching to understand and visualize the elastic collision process.

GeoGebra Commands & Parameters

  1. Point(xAxis) → centermassB
  2. Point(xAxis) → centermassA
  3. Intersect(func1i, func2i, 1) → E
  4. OrthogonalLine(E, xAxis) → f
  5. Intersect(f, xAxis) → F
  6. If(condition01 ≤ 0, func2i, If[0 ≤ x ≤ x(F), func2i(x), func2f(x)]) → q
  7. Derivative(q) → q'
  8. If(condition01 ≤ 0, func1i, If[0 ≤ x ≤ x(F), func1i, func1f]) → p
  9. Derivative(p) → p'
  10. LaTeX(condition01, true, true) → text1
  11. LaTeX(e, true, true) → text2
  12. Circle(centermassA, m1 / 2) → c
  13. Circle(centermassB, m2 / 2) → d
  14. If((m1 > 6) ∨ (m2 > 6), -5.5, -3) → ground
  15. OrthogonalLine(A', z = 0) → i
  16. OrthogonalLine(B', z = 0) → j
  17. Vector((0, 0), Vec1 / 2) → VectorV1
  18. Vector((0, 0), Vec2 / 2) → VectorV2
  19. Translate(VectorV1, G) → u
  20. Translate(VectorV2, H) → v
  21. Translate(momentum1, G) → w
  22. Translate(momentum2, H) → b
  23. Textfield(m1) → InputBox1
  24. Textfield(m2) → InputBox2
  25. Textfield(v1i) → InputBox3
  26. Textfield(v2i) → InputBox4
  27. Vector((0, 0), Vec1) → g
  28. Vector((0, 0), Vec2) → m
  29. OrthogonalLine(L, xAxis) → r
  30. OrthogonalLine(J, xAxis) → s
  31. OrthogonalLine(K, xAxis) → t
  32. If((m1 ≤ 0.5) ∨ (m2 ≤ 0.5) ∨ (abs(v1i) < 0.5) ∨ (abs(v2i) < 0.5), 200, 25) → limtime
  33. Circle(A', A) → c_1
  34. Circle(B', B) → d_1
  35. Translate(VectorV1, M) → a_1
  36. Translate(momentum2, I) → w_1
  37. Translate(momentum1, M) → v_1
  38. Translate(VectorV2, I) → b_1
  39. LaTeX(limtime, true, true) → text4
  40. Line(centermassA, centermassB) → a

AI Drawing Prompt Reference

Draw a demonstration of one-dimensional elastic collisions showing the motion trajectories and velocity changes of two objects. Include the trajectories, velocity vectors, collision points, and momentum conservation vectors of the two objects. Start by plotting the initial positions and trajectories, then mark the collision point, followed by the velocity vectors after collision and momentum conservation vectors, and finally connect the centers of the two objects.
The prompt above was compiled from the original drawing commands and is for reference only.