• VPhysics程式設計

自由落體追撞

• 講義

• 兩自由落體球間的彈性碰撞

  • 程式碼

  Web VPython 3.2
  # 匯入視覺化套件
  from vpython import *
  
  # 1. 參數設定
  # 重力加速度
  g = -9.8
  # 時間間隔
  dt = 0.0001
  # 經過時間
  t=0
  
  # 2. 畫面設定
  # 畫布
  scene = canvas(width=600, height=600, background=vector(0.5,0.6,0.5), center=vector(0,2,0))
  # 地板
  floor = box(pos=vector(0,-0.2,0), length=5, height=0.1, width=5, texture=textures.wood)
  # 兩球高度時間圖
  gd = graph(title='y vs t', xtitle='t', ytitle='y', ymax=13, xmax=10, background=vector(0.3,0.3,0.3))
  yt1 = gcurve(graph=gd, color=color.cyan)
  yt2 = gcurve(graph=gd, color=color.red)
  
  # 3. 球的設定
  ball1 = sphere(radius=0.05, color=color.white, v=0, m=0.2)
  ball2 = sphere(radius=0.1,  color=color.white, v=0, m=0.6)
  ball2.pos = vector(0,2,0)
  ball1.pos=vector(0,2+ball1.radius+ball2.radius+0.05,0)
  
  # 4. 函數定義
  def collide(v1,v2,m1,m2):
      v1f = v1*(m1-m2)/(m1+m2) + v2*2*m2/(m1+m2)
      v2f = v1*2*m1/(m2+m1) + v2*(m2-m1)/(m2+m1)
      return v1f, v2f
  
  # 5. 運動部分
  while t<=10:
      rate(2000)
      t = t + dt
      ball1.v = ball1.v + g * dt
      ball1.pos.y = ball1.pos.y + ball1.v * dt
      if ball1.pos.y <= 0:
          ball1.v = -ball1.v
      yt1.plot( pos = (t, ball1.pos.y))
  
      ball2.v = ball2.v + g * dt
      ball2.pos.y = ball2.pos.y + ball2.v * dt
      if ball2.pos.y <= 0:
          ball2.v = -ball2.v
      yt2.plot( pos = (t, ball2.pos.y))
  
      # 兩球碰撞
      if mag(ball1.pos-ball2.pos) <= ball1.radius + ball2.radius :
          ball1.v, ball2.v = collide(m1=ball1.m, v1=ball1.v, v2=ball2.v, m2=ball2.m)

  【作業】

  三顆球從高空自由落下互相追撞。

  【參考影片】