text: # Physics
  
  posted by .
  
  Rollercoaster has a dip that bottoms out in a vertical circle of radius r.
  
  Passenger feels seat of car pushing upward on her with a force twice her weight as she goes through the dip.
  
  If r = 20.0 m, how fast is rollercoaster going at bottom of the dip?
  
  • Physics -
  
  Potential energy at the topmost point = mg(2r)
  
  Kinetic energy at dip bottommost point= 1/2 m (v^2)
  
  so conservation of energy means
  
  mg 2r = 1/2 m(v^2)
  
  or 4rg= v^2
  or v = 2sqrt(rg)
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