(a)

Step 1:

Mass of the girl is 40 kg.

Diameter of Ferris wheel is 20 m .

Radius of the Ferris wheel is 10 m .

Angular velocity of the Ferris wheel is .

Find the girl’s centripetal acceleration ().

Where v is angular velocity,

              r is radius

1 revolution per minute =  meters per second.

4 revolution per minute = .

Linear velocity v = 4.188 m/s².

(b)

Step 1:

Mass of the girl is 40 kg.

Diameter of Ferris wheel is 20 m .

Radius of the Ferris wheel is 10 m .

Linear velocity v = 4.188 m/s.

Centripetal acceleration is 1.754 m/s².

At the top ( highest point),

The gravitational force acts towards Centre ( downwards).

Force exerted by the girl acts outside the Centre.

Consider the free body diagram.

Net force = .

At the top, the seat exerts a force of 321.8 N directed upward away from the centre. \ \

(c)

Step 1:

Mass of the girl is 40 kg.

Diameter of Ferris wheel is 20 m .

Radius of the Ferris wheel is 10 m .

Linear velocity v = 4.188 m/s.

Centripetal acceleration is 1.754 m/s².

At the halfway between the top and the bottom :

The gravitational force acts downwards..

Force exerted by the girl acts upwards away from the Centre.

Resultant force must be directed towards the centre.

Horizontal force .

Consider the free body diagram.

Net force = .

Direction : .

At the top, the seat exerts a force of 398.22 N and above the horizontal .