The 30-kg pipe is supported at A by a system of five cords. Determine the force in each cord for equilibrium.

#### Solution:

Show me the final answers↓

Let us draw a free body diagram focusing on ring A.

Now, we will write an equation of equilibrium for y-axis forces.

T_{AB}\text{sin}\,(60^0)\,-\,294.3\,=\,0 N

Solve for T_{AB}:

T_{AB}\,=\,339.8 N

Now, we will write an equation equilibrium for x-axis forces.

T_{AE}\,-\,339.8\text{cos}\,(60^0)\,=\,0

(Remember we just found T_{AB}\,=\,339.8 N)

Solve for T_{AE}:

T_{AE}\,=\,169.9 N

We can now focus on ring B and draw a free body diagram.

Again, we will write an equation of equilibrium for y-axis forces.

T_{BD}\dfrac{3}{5}\,-\,339.8\text{sin}\,(60^0)\,=\,0

Solve for T_{BD}:

T_{BD}\,=\,490.4 N

Now, we will write an equation of equilibrium for x-axis forces.

490.4\left(\dfrac{4}{5}\right)\,+\,339.8\text{cos}\,(60^0)\,-\,T_{BC}\,=\,0

(Remember, we found T_{BD}\,=\,490.4 N)

Solve for T_{BC}:

T_{BC}\,=\,562.2 N

#### Final Answers:

T_{AE}\,=\,169.9 N

T_{BD}\,=\,490.4 N

T_{BC}\,=\,562.2 N