Vertical Dip
October 4th, 2009
Vertical Dip
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physics-how fast is the roller coaster traveling at the bottom of the dip?
A roller coaster at an amusement park has a dip that bottoms out in a vertical circle of radius r. A passenger feels the seat of the car pushing upward on her with a force equal to four times her weight as she goes through the dip. If r = 17.5 m, how fast is the roller coaster traveling at the bottom of the dip?
Centripetal acceleration = velocity squared / radius
a_c = v^2/r
a_c = 4*g
r = 17.5 m
g = 9.8 m/s^2
Solve for velocity
v = sqrt (a_c * r)
v = sqrt (4*g*r) = 26.2 m/s
which is about 58.6 mph, pretty typical for a modern rollercoaster