8.16.
Model:
Visualize:
Model the roller coaster car as a particle undergoing uniform circular motion along a loop.
Notice that the r-axis points downward, toward the center of the circle.
Solve: In this problem the normal force is equal to the gravitational force: n = FG = mg . We have
∑F
r
= n + FG =
mv 2
= mg + mg ⇒ v = 2rg = 2 ( 20 m ) ( 9.8 m/s 2 ) = 19.8 m/s
r