Question

Driving in your car with a constant speed of 12 m/s, you encounter a bump in the road that has a circular cross section, as indicated in the figure. If the radius of curvature of the bump is r = 29 m, find the apparent weight of a 66-kg person in your car as you pass over the top of the bump.

Answer 1

Since it's circular motion your weight minus the normal force will be equal to the centripetal force:
\[mg-F_n=m\frac{v^2}{r}\]Rearranging things a bit:
\[F_n=mg-m\frac{v^2}{r}\]Simplifying:\[F_n=m(g-\frac{v^2}{r})=319kg\]This will be your apparent weight.

BTW: a bump with a radius of 29m? Wow!