Part A

The block shown in $($Figure $1)$ has a mass of $\backslash ($ m$=75\backslash$mathrm$\{$~kg$\}\backslash ),$ a height $\backslash ($ H$=1\mathrm{.}3\backslash$mathrm$\{$~m$\}\backslash ),$ and width $\backslash ($ L$=1\mathrm{.}7\backslash$mathrm$\{$~m$\}\backslash ).$ It is resting on a ramp that makes an angle $\backslash (\backslash$theta$=31^\{\backslash$circ$\}\backslash )$ with the horizontal. A force $\backslash (\backslash$mathbf$\{$P$\}\backslash )$ is applied parallel to the surface of the ramp at the top of the block. What is the maximum force that can be applied without causing the block to move? The coefficient of static friction is $\backslash (\backslash$mu$\_\{$s$\}=0\mathrm{.}4\backslash ),$ and the center of mass of the block is at the center of the rectangle.

Figure

Part C

Part B

There are two ways the block can move: by slipping up the ramp or by tipping over. First consider the block slipping up the ramp. What is the magnitude of the normal force between the block and the ramp?

Express your answer to three significant figures with appropriate units.

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What is the maximum magnitude of $\backslash (\backslash$mathbf$\{$P$\}\backslash )$ that can be applied before slipping would occur, assuming the block does not tip?

Express your answer to three significant figures with appropriate units.

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Now consider the case of impending tipping. Where do the normal force and friction force act in this case?