CIRCULAR MOTION relakjkjasldfj help please?

Question

A 40.0 kg child takes a ride on a Ferris wheel that rotates four times each minute and has a diameter of 21.0 m.

1. What force does the seat exert on the child at the lowest point of the ride?... magnitude and direction

2. What force does the seat exert on the child at the highest point of the ride?... magnitude and direction

3. What force does the seat exert on the child when the child is halfway between the top and bottom?... magnitude and direction

i found the centripel acceleration to be 1.84 m/s2 and the angular velocity to be 0.418879 rad/s. i have no idea what to do next :( please help. thanks

Answer 1

At all times, the centripetal acceleration has magnitude v^2 / r and is always directed towards the center of the Ferris Wheel. This acceleration is provided by some combination of the normal force from the seat and from g, the local accelation of gravity.

1. The two forces on the child are N (up) and mg (down).
The centripetal acceleration is directed up.

F = N - mg = m v^2 / r

2. The two forces on the child are again N (up) and mg (down). The centripetal acceleration is down, so

F = mg - N = m v^2 / r

3. At the halfway point, the centripetal acceleration is horizontal and must be provided by the horizontal component of the contact force with the seat. So the seat provides a contact force with components mg (up) and m v^2 / r (sideways).