Answer
The tension in the lower chain is $w$.
The tension in the upper chain is $w$.
$F = \frac{w}{2}$
Work Step by Step
Since the system is moving at a constant speed, the acceleration is zero.
The tension $T_1$ in the lower chain is equal in magnitude to the weight $w$. That is, $T_1 = w$.
We can find the tension $T_2$ in the rope.
$2~T_2 = T_1$
$T_2 = \frac{T_1}{2} = \frac{w}{2}$
Since $F=T_2$ (the tension in the rope), we know that $F = \frac{w}{2}$
We can find the tension $T_3$ in the upper chain.
$T_3 = 2~T_2 = 2~\frac{w}{2} = w$
The tension in the upper chain is $w$.
