Book edition 7th

Author(s) Douglas C. Giancoli

Pages 978 pages

ISBN 978-0321625922

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Short Answer

A child sitting 1.20 m from the center of a merry-go round moves with a speed of $1.10 m / s$ . Calculate (a) the centripetal acceleration of the child and (b) the net horizontal force exerted on the child $(mass = 22.5 kg)$ .

(a) The centripetal acceleration of the child is $1.01 m / s^{2}$ .

(b) The net horizontal force exerted on the child is $22.725 N$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Understanding the centripetal acceleration of the child

The child is rotating on the merry-go-round. The centripetal force acts on the child during the circular motion. The centripetal acceleration depends on the speed of the merry-go-round and the distance between the centre of the merry-go-round and the child.

Step 2. Identification of given data

The given data can be listed below as,

The distance between the centre of the merry-go-round and the child is, $r = 1.20 m$ .
The speed of the merry-go-round is, $v = 1.10 m / s$ .
The mass of the child is, $m = 22.5 kg$ .

Step 3. (a) Determination of the centripetal acceleration of the child

The centripetal acceleration can be expressed as,

$a_{c} = \frac{v^{2}}{r}$

Here, v is the speed of the merry-go-round, r is the distance between the centre of the merry-go-round and the child.

Substitute the values in the above equation.

$\begin{matrix} a_{c} = \frac{{(1.10 m / s)}^{2}}{1.20 m} \\ \approx 1.01 m / s^{2} \end{matrix}$

Thus, the centripetal acceleration of the child is $1.01 m / s^{2}$ .

Step 4. (b) Determination of the net horizontal force exerted on the child

The net horizontal force can be expressed as,

$F_{H} = m a_{c}$

Substitute the values in the above equation.

$\begin{matrix} F_{H} = 22.5 kg \times 1.01 m / s^{2} (\frac{1 N}{1 kg \cdot m / s^{2}}) \\ = 22.725 N \end{matrix}$

Thus, the net horizontal force acts on the child is $22.725 N$ .

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Physics Principles with Applications

Answers without the blur.

Short Answer

A child sitting 1.20 m from the center of a merry-go round moves with a speed of $1.10 m / s$ . Calculate (a) the centripetal acceleration of the child and (b) the net horizontal force exerted on the child $(mass = 22.5 kg)$ .

Step by Step Solution

Step 1. Understanding the centripetal acceleration of the child

Step 2. Identification of given data

Step 3. (a) Determination of the centripetal acceleration of the child

Step 4. (b) Determination of the net horizontal force exerted on the child

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Physics Principles with Applications

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Short Answer

A child sitting 1.20 m from the center of a merry-go round moves with a speed of 1.10m/s. Calculate (a) the centripetal acceleration of the child and (b) the net horizontal force exerted on the child mass=22.5kg.

Step by Step Solution

Step 1. Understanding the centripetal acceleration of the child

Step 2. Identification of given data

Step 3. (a) Determination of the centripetal acceleration of the child

Step 4. (b) Determination of the net horizontal force exerted on the child

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A child sitting 1.20 m from the center of a merry-go round moves with a speed of $1.10 m / s$ . Calculate (a) the centripetal acceleration of the child and (b) the net horizontal force exerted on the child $(mass = 22.5 kg)$ .