Chapter 7 - Newton's Third Law - Exercises and Problems - Page 179: 37

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

$T_1 = Mg$ $T_1 = (10.2~kg)(9.80~m/s^2)$ $T_1 = 100~N$ 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 $T_2=T_3 = T_5$ $T_4 = T_2+T_3+T_5$ $T_4 = 50~N+50~N+50~N$ $T_4 = 150~N$ $F = T_5$ $F = 50~N$