The three ropes in$FIGUREEX6.2$are tied to a small, very light ring. Two of the ropes are anchored to walls at right angles, and the third rope pulls as shown. What are $T_1$and $T_2$, the magnitudes of the tension forces in the first two ropes?

The pulling force transferred axially by a string, cable, chain, or similar item, or by each end of a rod, truss member, or similar three-dimensional object is known as tension.

The figure depicts a light ring attached by three ropes, two of which are fixed to the walls at right angles.

Using Newton's second law for equilibrium condition in the horizontal direction,

$\sum _{}{F}_x=0$

Resolving the components of tension in the ropes in x-direction,

$-T_1+T_3\cos \theta =0$

The tension in the first rope =$T_1$

The tension in the third rope =$T_3$

The angle made by the third rope with the positive x-axis =$\theta$

Substitute $100N$for $T_3$and $30°$for $\theta$,

$$\begin{gathered} -T_1+\left(100N\right)\cos 30°=0 \\ {T}_1=\left(100N\right)\left(0.866\right) \\ =86.6N \end{gathered}$$

Hence, the magnitude of the tension$T_1$is$86.6N$.

The figure depicts a light ring attached by three ropes, two of which are fixed to the walls at right angles.

Using Newton's second law for equilibrium condition,

$\sum _{}{F}_y=0$

Resolving the components of tension in the ropes in y-direction,

$T_2-T_3\sin \theta =0$

Tension in the second rope =$T_2$.

Substitute $100N$for $T_3$and $30°$for $\theta$,

$$\begin{gathered} T_2-\left(100N\right)\sin 30°=0 \\ {T}_2=\left(100N\right)\left(0.5\right) \\ =50N \end{gathered}$$

Hence, magnitude of the tension$T_2$is$50N$.