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Assignment $1$D $($CHAPTER $5)-$ Attempt $1$

Problem $5\mathrm{.}24$

$2$ of $4$

Review

Introduction

The relay shown in $($Figure $1)$ regulates voltage and current. The spring CD

has a stiffness of k

$=150$ N$/$m

$.$ Assume that the angle of $10$

in case $($a$)$ is small enough to consider the spring to be vertical.

Figure$1$ of $1$

A relay is shown in two cases, labeled $\text{'}$a$\text{'}$ and b$.$ In both cases, a straight armature $\text{'}$A$\text{'}$ C is attached with its right end C to a vertical spring C D of stiffness k that is located below the armature. Also, the armature is pin connected to a support at point B that is between ends $\text{'}$A$\text{'}$ and C of the armature. In case $\text{'}$a$\text{'},$ the armature extends upward and to the left making an angle of $10$ degrees with the horizontal. The left end of the armature labeled as $\text{'}$A$\text{'}$ is in contact with a battery. In case b$,$ the armature $\text{'}$A$\text{'}$ C is oriented horizontally and touches a coil at point E$.$ Point E is $50$ millimeters to the right of the left end of the armature labeled as $\text{'}$A$\text{'}$ and $50$ millimeters to the left of point B$.$ Point B is $30$ millimeters to the left of the right end of the armature labeled as C$.$

Part A

Determine the force in the spring CD

$,$ so that it will allow the armature to make contact at A

in figure $($a$)$ with a vertical force of $0\mathrm{.}4$ N

$.$

Express your answer to three significant figures and include the appropriate units.

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Fs

$=$

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Part B Complete previous part$($s$)$

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