   Chapter 7, Problem 25P

Chapter
Section
Textbook Problem

A 50.0-kg child stands at the rim of a merry-go-round of radius 2.00 m, rotating with an angular speed of 3.00 rad/s. (a) What is the magnitude of the child’s centripetal acceleration? (b) What is the magnitude of the minimum force between her feet and the floor of the carousel that is required to keep her in the circular path? (c) What minimum coefficient of static friction is required? Is the answer you found reasonable? In other words, is she likely to stay on the merry-go-round?

(a)

To determine
The magnitude of child’s centripetal acceleration.

Explanation

Given Info: The radius of merry-go-round is 2.00m and an angular speed of the merry-go-round is 3.00rad/s .

Explanation:

The formula for the centripetal acceleration of the child is,

ac=rω2

• r is the radius of the merry-go-round.
• ω is angular speed of the merry-go-round.

Substitute 2.00m for r and 3.00rad/s for ω to find ac

(b)

To determine
The magnitude of minimum force between her feet and the floor of the carousel that is required to keep her in the circular path.

(c)

To determine
The minimum required coefficient of static friction for her to be stay on the merry-go-round.

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