posted by Jenn .
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?
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)