Book edition 7th

Author(s) Douglas C. Giancoli

Pages 978 pages

ISBN 978-0321625922

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Short Answer

A 0.40-kg cord is stretched between two supports, 8.7 m apart. When one support is struck by a hammer, a transverse wave travels down the cord and reaches the other support in 0.85 s. What is the tension in the cord?

The tension in the cord is\(4.82\;{\rm{N}}\).

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Understanding about the tension

Whenever a specific length of wire/rod stretches with the help of an external force, then there would be a tension generated in the wire/rod. The value of tension force would be the same at each section of the wire/rod.

Identification of given data

The given data can be listed below as,

The mass of a cord is, \(m = 0.40\;{\rm{kg}}\).
The distance between two supports is, \(l = 8.7\;{\rm{m}}\).
The time taken by the transverse wave is, \(t = 0.85\;{\rm{s}}\).

Defining the expression of the speed of transverse wave

The speed of the transverse wave in the string can be expressed as,

\(\begin{aligned}{c}v &= \sqrt {\frac{T}{\mu }} \\ &= \sqrt {\frac{T}{{\left( {\frac{m}{l}} \right)}}} \\ &= \sqrt {\frac{{Tl}}{m}} \end{aligned}\)

Here, \(v\) is the speed of the transverse wave in the string, \(T\) is the tension in the cord, \(\mu \) is the mass per unit length and \(l\) is the length of the string.

Determining the tension in the cord

The expression of the velocity of transverse wave is given by,

\(\begin{aligned}{c}v &= \frac{l}{t}\\\sqrt {\frac{{Tl}}{m}} &= \frac{l}{t}\\T &= \frac{{ml}}{{{t^2}}}\end{aligned}\)

Here, \(t\) is the time taken by the pulse to travel from one support to other.

Substitute all the known values in the above equation.

\(\begin{aligned}{c}T &= \frac{{\left( {0.40\;{\rm{kg}}} \right)\left( {8.7\;{\rm{m}}} \right)}}{{{{\left( {0.85\;{\rm{s}}} \right)}^2}}}\\ &\approx 4.82\;{\rm{N}}\end{aligned}\)

Therefore, the tension in the cord is\(4.82\;{\rm{N}}\).

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Physics Principles with Applications

Answers without the blur.

Short Answer

A 0.40-kg cord is stretched between two supports, 8.7 m apart. When one support is struck by a hammer, a transverse wave travels down the cord and reaches the other support in 0.85 s. What is the tension in the cord?

Step by Step Solution

Understanding about the tension

Identification of given data

Defining the expression of the speed of transverse wave

Determining the tension in the cord

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Physics Principles with Applications

Answers without the blur.

Short Answer

A 0.40-kg cord is stretched between two supports, 8.7 m apart. When one support is struck by a hammer, a transverse wave travels down the cord and reaches the other support in 0.85 s. What is the tension in the cord?

Step by Step Solution

Understanding about the tension

Identification of given data

Defining the expression of the speed of transverse wave

Determining the tension in the cord

Most popular questions for Physics Textbooks

What is the area and its approximate uncertainty of a circle of the radius of \({\bf{3}}{\bf{.1}} \times {\bf{1}}{{\bf{0}}^{\bf{4}}}\;{\bf{cm}}\)?

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