Consider a force $F$ pulling the rope as in the Figure. The rope is massless and the pulley is frictionless. The coefficient of friction between each box and the surface is $\mu_k = 0.05$, $m_A = 2 \text{ kg}$ and $m_B= 2 \text{ kg}$. Given that the two boxes move with an acceleration of magnitude $a = 1 \space \text {ms}^{-2}$
How do we find the tensions $T_1$ and $T_2$ in the two ropes? So, I don't know what equations we need. Moreover, this question seems a bit hard to me.
Extend to you my warmest regards!
Hint: The tensile force for the box $B$ is equal to the force $F$ that is externally applied. Set up the free body diagrams for both boxes and use Newtons $2^{\text{nd}}$ law of motion:
$$m_Ba=F-T_2-\mu_km_Bg$$ $$m_Aa=T_2-\mu_km_Ag.$$
By adding both equations you can determine $F$ and then use one of the equations to determine the tensile force on the rope between $A$ and $B$ which I labelled as $T_2$.