Two blocks, $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash ),$ are pushed across a horizontal surface by an external force as shown in the figure. The mass of block $\backslash ($ A $\backslash )$ is $3$ kg and the mass of block $\backslash ($ B $\backslash )$ is $4$ kg $.$ The coefficient of static friction between block A and block B is $\backslash (\backslash$mu$\_\{$s$\}=0\mathrm{.}5\backslash )$ and the coefficient of kinetic friction between block B and the horizontal surface is $\backslash (\backslash$mu$\_\{$k$\}=0\mathrm{.}22\backslash ).$ What is the minimum external force $($in N $)$ required such that block $\backslash ($ A $\backslash )$ does not slide down block B $?$

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