Answer
The mass of each block is 17.8 kg
Work Step by Step
We can find the speed of the pulse as:
$v = \frac{d}{t}$
$v = \frac{4.0~m}{24.0\times 10^{-3}~s}$
$v = 166.7~m/s$
Note that the mass of the middle part of the wire is 30.0 g. We can find the tension $T_m$ in the middle part of the wire.
$\sqrt{\frac{T_m}{\mu}} = v$
$T_m = v^2~\mu$
$T_m = v^2~(\frac{m}{L})$
$T_m = (166.7~m/s)^2~(\frac{0.0300~kg}{4.0~m})$
$T_m = 208.4~N$
This tension is equal to the horizontal component of the tension $T_x$ in the left section of the wire. We can find the vertical component $T_y$ of the tension in the left section of the wire.
$\frac{T_y}{T_x} = tan(40^{\circ})$
$T_y = T_x~tan(40^{\circ})$
$T_y = (208.4~N)~tan(40^{\circ})$
$T_y = 174.9~N$
The vertical component of the tension is equal to the weight of the block. We can find the mass of the block.
$mg = T_y$
$m = \frac{T_y}{g}$
$m = \frac{174.9~N}{9.80~m/s^2}$
$m = 17.8~kg$
The mass of each block is thus 17.8 kg.
