Answer
$M=1413N$
Work Step by Step
There are 3 forces that produce torques affecting the rotation of the arm:
- $M$ produces a clockwise (negative) torque. The lever arm is $0.069m\times\sin29=0.033m$
- The arm's weight $W$ produces a clockwise (negative) torque. The lever arm is $0.28m$
- The tension in the rope $T$ produces a counterclockwise (positive) torque. The lever arm is $0.61m$
Because the arm is in equilibrium, $$\sum\tau=-0.033M-0.28W+0.61T=0$$ $$M=\frac{0.61T-0.28W}{0.033}$$
We have $W=47N$. $T$ has to balance out the stationary's weight, because the stationary is in equilibrium, too, so $T=98N$
$$M=1413N$$
