7. (15 points) The structure consists of two weightless rods $AB$ and $CD$, a weightless pulley, and a load of mass $m=3$ kg, which is suspended at point $G$. All threads are weightless and inextensible. At point $A$, the rod is attached to a hinge that allows the rod to rotate in the plane of the diagram. Here, $CG=\frac{1}{4} CD$, $AE=\frac{1}{4} AB$, and point $F$ is the midpoint of rod $AB$. The acceleration due to gravity is $g=10 \mathrm{~m} / \mathrm{c}^{2}$. Determine the tension force $T_{0}$ in the thread attached to rod $AB$ at point $E$.

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Answer: $T_{0}=15 \mathrm{H}$

Solution. The moment rule for rod $C D$ about point $C$: $m g \cdot \frac{1}{4} C D=T_{2} \cdot C D$

Tension force in thread $B D: T_{2}=\frac{1}{4} m g=7.5 \mathrm{H}$.

Therefore, the tension force in thread $C F: T_{1}=\frac{3}{4} m g=22.5 \mathrm{H}$.

The moment rule for rod $A B$ about point $A$:

$T_{0} \cdot \frac{1}{4} A B+T_{2} \cdot A B=T_{1} \cdot \frac{1}{2} A B$.

As a result, we get $T_{0}=15 \mathrm{H}$.