MathPlotAI Logo MathPlotAI

Elastic Collisions Simulation

Elastic Collisions Simulation
Loading the math board and drawing, please wait…
2017-07-10 08:31
VectorCoordinate GeometryOptimizationGeometric Construction
In collections Physics Lab
This example demonstrates the elastic collision of two objects in a 2D plane. It involves core mathematical concepts like vector operations, conservation of momentum and energy, and coordinate geometry. Construction highlights include using GeoGebra commands and objects such as If, Vector, Circle, Translate, Textfield, Ray, and Intersect for position, velocity vector calculations, and collision detection. Suitable for high school physics and mathematics courses to understand collision principles and mathematical modeling.

GeoGebra Commands & Parameters

  1. If(abs((d * sin(γxy - γv))) ≤ m1 / 2 + m2 / 2, true, false) → condition
  2. If(condition ≟ true, asin((d * sin(γxy - γv) / (m1 / 2 + m2 / 2))), 10) → α
  3. If(a ≟ a, a, 10) → a'
  4. Vector(C) → u1
  5. Vector(C') → u2
  6. Vector(D) → v1
  7. Vector(D') → v2
  8. Circle(AM, m1 / 2) → c1
  9. Circle(BM, m2 / 2) → c2
  10. If(Distance[AM, BM] > m1 / 2 + m2 / 2, false, true) → collision
  11. If(collision ≟ true, u2, u1) → auxv1
  12. If(collision ≟ true, v2, v1) → auxv2
  13. Circle(E, m1 / 2) → d1
  14. Circle(F, m2 / 2) → d2
  15. If(time2 ≟ time2, abs(time2), 30) → auxtime
  16. Vector(A, I) → u
  17. Vector(B, J) → v
  18. Translate(u1, AM) → u3
  19. Translate(v1, BM) → v3
  20. Translate(u2, E) → u4
  21. Translate(v2, F) → v4
  22. Translate(A, u3) → A'
  23. Translate(B, v3) → B'
  24. Translate(mt1i, AM) → c1i
  25. Translate(mt1f, E) → c1f
  26. Translate(mt2i, BM) → d1i
  27. Translate(mt2f, F) → d1f
  28. If(t > auxtime, Pxf, Pxi) → Px
  29. If(t > auxtime, Pyf, Pyi) → Py
  30. If(t > auxtime, PPxf, PPxi) → PPx
  31. If(t > auxtime, PPyf, PPyi) → PPy
  32. Textfield(step) → InputBox1
  33. Textfield(vx1) → InputBox2
  34. Textfield(vy1) → InputBox3
  35. Textfield(vx2) → InputBox4
  36. Textfield(vy2) → InputBox5
  37. Textfield(m1) → InputBox6
  38. Textfield(m2) → InputBox7
  39. Circle(A, abs(u1)) → circle1
  40. Ray(A, u1) → LineA
  41. Circle(B, abs(v1)) → circle2
  42. Ray(B, v1) → LineB
  43. Intersect(circle1, LineA) → InterA,
  44. Intersect(circle2, LineB) → InterB,

AI Drawing Prompt Reference

Create a simulation of elastic collisions between two objects in a 2D plane. Start by defining the initial positions and velocity vectors of the objects, then use vectors and circles to represent the objects. Next, use collision detection to determine if a collision occurs, and adjust the velocity vectors if a collision happens. Finally, update the positions of the objects based on time changes and display input fields for velocity and mass before and after the collision.
The prompt above was compiled from the original drawing commands and is for reference only.