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Chapter 10: Q.10 (page 256)

A 20 kg child is on a swing that hangs from 3.0-m-long chains. What is her maximum speed if she swings out to a 45掳 angle?

Short Answer

Expert verified

As a result, the child's maximum speed is4.15m/s.

Step by step solution

01

Introduction

The distance travelled by an object per unit time is known as its speed.

02

Explanation

Draw the child's and swing's free body diagrams.

Calculate the child's increased height.

Putting 3mfor ll, 0.7071for cos45掳in equation x=lcos45掳

x=(3m)(0.7071)

=2.12m

Putting 2.12mfor x, and 3mfor lin equation h=l-x

h=3m-2.12m

=0.88m

Calculate the child's maximum speed.

At the two positions depicted in the diagram, apply the law of conservation of energy.

KEi+PEi=KEf+PEf

12mvmax2+0=0+mgh

vmax=2gh

Putting 9.81m/s2for g, and 0.88mfor hby equation.

vmax=29.81m/s2(0.88m)

=17.26m2/s2

=4.15m/s

As a result, the child's maximum speed is 4.15m/s.

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