
Coefficient of friction
Body A lies on a rough horizontal table and is connected to freely hanging bodies B and C by light inextensible strings passing over smooth pulleys.
A is 5kg B is 3kg and C is 2kg. When the system is released from rest, the body B descends with an acceleration of 0.28. Find the coefficient of friction between body A and the table.
Any help is much appreciated thanks

Let $\displaystyle T_1$ = tension between mass A and B
$\displaystyle T_2$ = tension between mass B and C
forces acting on mass A ...
$\displaystyle F_{net} = m_A a$
$\displaystyle T_1  f_k = m_A a$
*** $\displaystyle T_1  \mu m_A g = m_A a$
forces acting on mass B ...
$\displaystyle F_{net} = m_B a$
*** $\displaystyle T_2 + m_B g  T_1 = m_B a$
forces acting on mass C ...
$\displaystyle F_{net} = m_C a$
*** $\displaystyle m_C g  T_2 = m_C a$
solve the system of equations (***) for $\displaystyle \mu$