The masses $m_A=20kg$ and $m_B=40$ kg $,$ and the coefficients of friction between all of the surfaces are ${}_s=0\mathrm{.}42$ and ${}_k=0\mathrm{.}38.$ The blocks are stationary when the constant force $F$ is applied. Determine the resulting acceleration of block $B$ if $($a$)F=200N,($b$)F=400N.$