ANSWER:
92.09 kg.
STEP-BY-STEP EXPLANATION:
Mass board (M) = 65 kg
Length board (L) = 6.2 m
Left edge wooden (l) = -2 m
Tension (T) = 800 N
There are a total of 3 forces acting on the board, they are the following:
[tex]\begin{gathered} W_{board}=M\cdot g=65\cdot9.8=637\text{ N} \\ \\ W_{wooden}=mg=m(9.8)=9.8m\text{ N} \\ \\ T_y=T\cdot\sin\theta=800\cdot\sin45\degree=565.7\text{ N} \end{gathered}[/tex]
Since the board is balanced, the net torque acting up will be equal to the net torque acting down.
So we can establish the following balance:
[tex]\begin{gathered} \tau_{tension}=\tau_{board}+\tau_{wooden} \\ \\ T_y\cdot d=W_{board}\cdot\frac{L}{2}+W_{wooden}\cdot l \\ \\ \text{ We replacing:} \\ \\ 565.7\cdot0.3=637\cdot\frac{6.2}{2}+9.8m\cdot-2 \\ \\ 169.71=1974.7-19.6m \\ \\ m=\frac{1974.7-169.71}{19.6} \\ \\ m=92.09\text{ kg} \end{gathered}[/tex]
The mass of the wooden crate is 92.09 kg.
