Learning Goal:

The crate shown is held against wedge $\backslash ($ B $\backslash )$ by a spring. The spring is $\backslash (93\mathrm{.}5\backslash \%\backslash )$ of its original uncompressed length $\backslash ($ l$=2\mathrm{.}00\backslash$mathrm$\{$~m$\}\backslash ),$ and the spring constant is given as $\backslash ($ k$=1250\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash ).$ The coefficient of static friction at all contacting surfaces is $\backslash (\backslash$mu$\_\{$s$\}=0\mathrm{.}130\backslash ).$ The mass of the crate is $\backslash ($ m$=22\mathrm{.}0\backslash$mathrm$\{$~kg$\}\backslash ).$ The angle is $\backslash (\backslash$theta$=11\mathrm{.}0^\{\backslash$circ$\}\backslash ).$ Neglect the mass of the wedge. Assume the crate only moves in the $\backslash ($ y $\backslash )$ direction and that wedge $\backslash ($ A $\backslash )$ cannot move.$($Figure $1)$

Figure

Part A $-$ Determining the normal force exerted by the crate on the wedge

Determine the normal force $\backslash ($ N$\_\{$C$\}\backslash )$ that the crate exerts on the wedge when the system is at rest.

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

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Part B $-$ Finding the smallest horizontal force $\backslash (\backslash$mathbf$\{$P$\}\backslash )$ to move the crate upward

Determine the magnitude of the smallest horizontal force $\backslash ($ P $\backslash )$ that is necessary to begin moving the crate upward.

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

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