#### Answer

$T_1 = 100 ~N$
$T_2 = 50 ~N$
$T_3 = 50 ~N$
$T_4 = 150 ~N$
$T_5 = 50 ~N$
$F = 50 ~N$

#### Work Step by Step

$T_1 = Mg$
$T_1 = (10.2~kg)(9.80~m/s^2)$
$T_1 = 100~N$
Note that $T_2 = T_3 = T_5$ and $T_2+T_3 = T_1$:
$T_2+T_3 = T_1$
$2T_2 = T_1$
$T_2 = \frac{T_1}{2}$
$T_2 = \frac{100~N}{2}$
$T_2 = 50~N$
Therefore, $T_3 = 50~N$ and $T_5 = 50~N$ since $T_2=T_3 = T_5$
$T_4 = T_2+T_3+T_5$
$T_4 = 50~N+50~N+50~N$
$T_4 = 150~N$
$F = T_5$
$F = 50~N$