Physics Help??

Question

A 40.0-kg girl rides on a Ferris wheel of diameter of 20.0 m that rotates four times each minute.

a.   What is the girl’s centripetal acceleration?

b.   What force (magnitude and direction) does the seat exert on the girl at the top of the ride?

c.   What force (magnitude and direction) does the seat exert on the girl when she is halfway between the top and the bottom?

Answer 1

(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/s.

Solution :

Girl’s centripetal acceleration is 1.754 m/s².

Answer 2

(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.

Solution :

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

Answer 3

(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 : .

The seat exerts a force of 398.22 N and above the horizontal .

Solution :

The seat exerts a force of 398.22 N and above the horizontal .