   Chapter 7, Problem 31P

Chapter
Section
Textbook Problem

A 40.0-kg child takes a ride on a Ferris wheel that rotates four times each minute and has a diameter of 18.0 m. (a) What is the centripetal acceleration of the child? (b) What force (magnitude and direction) does the seat exert on the child at the lowest point of the ride? (c) What force does the seat exert on the child at the highest point of the ride? (d) What force does the seat exert on the child when the child is halfway between the top and bottom?

(a)

To determine
The centripetal acceleration of the child.

Explanation

Given Info:

The mass of the child is 40.0kg .

The diameter of the Ferris wheel is 18.0m .

Explanation:

The Ferris wheel rotates four times in each minute.

Formula to calculate the centripetal acceleration is,

ac=rω2

• r is the radius of the Ferris wheel
• ω is the angular frequency

Substitute 9.0m for r and 4rev/min for ω to find the centripetal acceleration,

ac=(9

(b)

To determine
The magnitude and the direction of the force that the seat exerts on the child at the lowest point of the ride.

(c)

To determine
The force exerted on the child at the highest point by thy seat.

(d)

To determine
The force exerted on the child by the seat in the halfway between the top and the bottom.

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