What mass M will cause this system accelerate e 0.75 m/s²?

Answer:
5.54 [kg].
Explanation:
1) if m₁=6; g=9.81; a=0.75 and m₂ - reqired mass, then
2) it is possible to write: m₁*a=m₁*g-m₂*g, and
3) [tex]m_2=\frac{m_1(g-a)}{g}; \ => \ m_2=\frac{6*(9.81-0.75)}{9.81}=5.54[kg].[/tex]