$8.\backslash ((6/102)\backslash )$ Shown in the figure is the design of a band$-$type oil$-$filter wrench. If the coefficient of friction between the band and the fixed filter is $0\mathrm{.}25,$ determine the minimum value of $\backslash ($ h $\backslash )$ which ensures that the wrench will not slip on the filter, regardless of the magnitude of the force $\backslash ($ P $\backslash ).$ Neglect the mass of the wrench and assume that the effect of the small part $\backslash ($ A $\backslash )$ is equivalent to that of a band wrap which begins at the three$-$o'clock position and runs clockwise. That is$,$ the vertical force at A is equal to the tension in the band that connects to A$.$

$($ANS $\backslash (\backslash$mathrm$\{$h$\}=27\mathrm{.}8\backslash$mathrm$\{$~mm$\}\backslash ))$

$9.(6/106)$ If the effective coefficient of friction at the railing is $\backslash (\backslash$mu$=0\mathrm{.}20\backslash ).($a$)$ determine the tension $\backslash ($ T $\backslash )$ which the shipworkers must develop in the cable to lower the $100-$kg crate at a slow steady speed. $($b$)$ What would be the value of $\backslash ($ T $\backslash )$ in order to raise the crate? $($c$)$ Are these reasonable forces for two workers to apply? Provide evidence to support your argument.

$($ANS $\backslash (\backslash$mathrm$\{$T$\}=717\backslash$mathrm$\{$~N$\}\backslash$mathrm$\{$~T$\}=1340\backslash$mathrm$\{$~N$\}\backslash ))$