Hi there!
We can begin by doing a summation of forces for each block.
Block A:
This block has the force of tension (in direction of acceleration +) and static friction (opposite direction -) acting on it. Thus:
[tex]\Sigma F_A = T - F_s\\\\m_Aa = T - \mu m_Ag[/tex]
Block B:
This block has the force of tension (opposite of acc. -) and gravity (in direction of acc +), working on it.
[tex]\Sigma F_B = m_Bg - T\\\\ m_Ba = m_Bg - T[/tex]
Add both of the expressions and solve for the maximum mass of Block B.
[tex]\Sigma F = m_Bg - T + T - \mu m_Ag\\\\a(m_A + m_B) = m_Bg - \mu m_Ag[/tex]
To find the minimum value, we can set a = 0, so:
[tex]0 = m_Bg - \mu m_Ag\\\\\mu m_Ag = m_B g\\\\0.8(20)(9.8) = m_B (9.8)\\\\m_B = \frac{0.8(20)(9.8)}{9.8)} = \boxed{16 kg}[/tex]
The block must weigh > 16 kg for block A to move.
