Book edition 9th Edition

Author(s) Raymond A. Serway, John W. Jewett

Pages 1624 pages

ISBN 9781133947271

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Short Answer

Review. A solid sphere of brass (bulk modulus of $14 .0 \times 10^{10} \frac{N}{m^{2}}$ ) with a diameter of $3 .00 m$ is thrown into the ocean. By how much does the diameter of the sphere decrease as it sinks to a depth of $1 km$ ?

The decrease in diameter is $Δ D = 2.66 \times 10^{- 3} m$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Given Data:

The magnetic field, $B = 14.0 \times 10 {}^{10} \frac{N}{m^{2}}$

The depth of ocean, $h = 1 km = 1000 m$

The diameter of sphere, $D = 3.0 m$

The radius is,

\begin{array}{rcl} r & = & \frac{D}{2} \\ = & \frac{3.0 m}{2} \\ = & 1.5 m \end{array}

A concept:

The pressure $P$ in a fluid is the force per unit area exerted by the fluid on a surface:

$P = ρ g h$

In the SI system, pressure has units of Newton’s per square meter $\frac{N}{m^{2}}$ , and $1 \frac{N}{m^{2}} = 1 Pascal (Pa)$ .

Bulk modulus is given by,

role="math" localid="1663696968659" $B = \frac{P}{\frac{∆ v}{v}}$

Find the decrease in diameter:

Applying the formula of Bulk modulus here, you get

$B = \frac{P}{\frac{∆ v}{v}}$

While pressure is,

$P = ρ g h$

Combining both, you get

$Δ V = \frac{ρ g h \times V}{B} \frac{4}{3} π {(Δ r)}^{3} = \frac{ρ g h \times \frac{4}{3} π r^{3}}{B}$

$\begin{array}{rcl} {(Δ r)}^{3} & = & \frac{ρ g h \times r^{3}}{B} \\ = & \frac{1000 \times 10 \times 1000 \times {(1.5)}^{3}}{14.0 \times 10^{10}} \\ = & 2.4 \times 10^{- 4} \end{array}$

$\begin{array}{rcl} Δ r & = & \sqrt[3]{2.4 \times 10^{- 4}} \\ = & 0.062 m \end{array}$

Also diameter, $D = 2 r$

Therefore decrease in diameter is,

$\begin{array}{rcl} Δ D & = & 2 Δ r \\ = & 2 \times 0.062 m \\ = & 0.124 m \end{array}$

Hence, the decrease in diameter is $Δ D = 0.124 m$ .

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Physics For Scientists & Engineers

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Short Answer

Review. A solid sphere of brass (bulk modulus of $14 .0 \times 10^{10} \frac{N}{m^{2}}$ ) with a diameter of $3 .00 m$ is thrown into the ocean. By how much does the diameter of the sphere decrease as it sinks to a depth of $1 km$ ?

Step by Step Solution

Given Data:

A concept:

Find the decrease in diameter:

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Physics For Scientists & Engineers

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Short Answer

Review. A solid sphere of brass (bulk modulus of 14.0×1010 Nm2) with a diameter of 3.00 m is thrown into the ocean. By how much does the diameter of the sphere decrease as it sinks to a depth of 1 km?

Step by Step Solution

Given Data:

A concept:

Find the decrease in diameter:

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Review. A solid sphere of brass (bulk modulus of $14 .0 \times 10^{10} \frac{N}{m^{2}}$ ) with a diameter of $3 .00 m$ is thrown into the ocean. By how much does the diameter of the sphere decrease as it sinks to a depth of $1 km$ ?