The brake pedal $\backslash ($ A B C D $\backslash )$ for an automobile has a torsional spring at pin $\backslash ($ C $\backslash ).$ The spring has $\backslash (4000\backslash$mathrm$\{$~N$\}\backslash$cdot $\backslash$mathrm$\{$~mm$\}/\backslash$mathrm$\{$rad$\}\backslash )$ stiffness and is prewound by $\backslash (1/2\backslash )$ of a turn so that contact is made at point $\backslash ($ E $\backslash )$ when $\backslash ($ P$=$Q$=0\backslash ).$ The pedal has negligible weight. Take the value of $\backslash ($ P $\backslash )$ to be $75$ N $.$

NOTE: This is a multi$-$part question. Once an answer is submitted, you will be unable to return to this part.

Problem $05\mathrm{.}065.$b $-$ Force on pedal to cause it to move and reaction at pin

Determine the value of $\backslash ($ Q $\backslash )$ that will cause the pedal to begin to move and the reactions at $\backslash ($ C $\backslash ).($Round the final answers to four decimal places.$)($Do not include a minus sign in your response.$)$

The value of $\backslash ($ Q $\backslash )$ that will cause the pedal to begin to move is

The horizontal component of the reaction force at $\backslash ($ C $\backslash )$ is

$\backslash [$

N $\backslash$leftarrow

$\backslash ]$

The vertical component of the reaction force at $\backslash ($ C $\backslash )$ is

$\backslash ($ N $\backslash$uparrow $\backslash )$