Centrifugal (Ficticious) Force problem

[mst3kjunkie]

47. In an amusement park ride called the Roundup, passengers stand inside a 16m diameter rotating ring. After the ring has acquired suficient speed, it tilts into a vertical plane.

a. suppose the ring rotates once every 4.5 s. If a rider's mass is 55kg, with how much force does the ring pus on her at the top of the ride? At the bottom?

b. What is the longest rotation period of the wheel that will prevent the riders from falling off at the time?

I've calculated that the radius is 8m and the period T is equal to (1/4.5) or .22 revolutions per second. I'm completely stuck as to where to go from here. help?

 

[courtrigrad]

$$F = ma = m\frac{v^{2}}{r}$$

 

[andrevdh]

At the top of the ride both the weight, $W$, and the "push force" $F_P$ on a passenger is directed towards the center of the ring. The combined effect of these two forces gives us the needed centripetal force $F_C$ to make the passenger go along with the ride so

$$F_P + W = F_C$$