$8.[0/3$ Points$]$

SERCP$127.$XP$\mathrm{.}026.$

A small block of mass $\backslash ($ m$=0\mathrm{.}500\backslash$mathrm$\{$~kg$\}\backslash )$ is fired with an initial speed of $\backslash ($ v$\_\{0\}=4\mathrm{.}50\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ along a horizontal section of frictionless track, as shown in the top portion of the figure below. The block then moves along the frictionless, semicircular, vertical tracks of radius $\backslash ($ R$=1\mathrm{.}40\backslash$mathrm$\{$~m$\}\backslash ).$

$($a$)$ Determine the force exerted by the track on the block at points $\backslash (\{\}^\{($A$)\}\backslash )$ and $($B$).$

track force at $\backslash (\{\}^\{(4)\}\backslash )$

Your response differs from the correct answer by more than $\backslash (10\backslash \%\backslash ).$ Double check your calculations. N

track force at $\backslash (\{\}^\{($B$)\}\backslash )$

Your response differs from the correct answer by more than $\backslash (10\backslash \%\backslash ).$ Double check your calculations. N

$($b$)$ The bottom of the track consists of a section $\backslash (($L$=0\mathrm{.}422\backslash$mathrm$\{$~m$\})\backslash )$ with friction. Determine the coefficient of kinetic friction between the block and that portion of the bottom track if the block just makes it to point $\backslash (\backslash$mathbb$\{$C$\}\backslash )$ on the first trip. Hint: If the block just makes it to point $\backslash (\backslash$mathbb$\{$C$\}\backslash ),$ the force of contact exerted by the track on the block at that point is zero.

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