The force applied by B on A is________                     

$50-\text{N}-{\text{f}}_1=10\text{a}$

$\underset{\_}{{\text{N}}_1-{\text{f}}_{\text{2}}=5\text{a}}$

$50-\left({\mu }_1\text{N}+{\mu }_2\text{N}\right)=15\text{a}$

$\text{50-}\left(0.1\times 100+0.2\times 50\right)=15\text{a}$

$\text{50}-\text{20}=\text{15a}$

$\text{15a}=\text{30}$

$\text{a}=\text{2}{\text{m/s}}^2$

${\text{N}}_{\text{1}}=5\text{a}+{\text{f}}_{\text{2}}$

$=10+10=20\text{N}$