Answer
$T=426N$
Work Step by Step
Let's take the axis of rotation to be at point A, shown in the figure below, and examine the torques. Because $N$ and $f_k$ pass through A, they have no torques.
$W$ and $T$ produce torques, with lever arm $l_W$ and $l_T$ respectively. The figure below also shows how to find $l_W$ and $l_T$
- $l_W=L\cos(25+\theta)$. $L$ is half the diagonal of the crate, so $L=0.5\sqrt{0.9^2+0.4^2}=0.49m$. $\theta$ is the angle the diagonal makes with the long side, so $\theta=\tan^{-1}\frac{0.4}{0.9}=24^o$.
Therefore, $$l_W=0.49\times\cos49=0.32m$$
- $l_T=0.9\times\sin36=0.53m$
The net torque is zero, so the torques produced by $W$ and $T$ balance each other: $$0.32W=0.53T$$ $$T=\frac{0.32W}{0.53}$$
We have $W=72kg\times9.8m/s^2=705.6N$
Therefore, $T=426N$
