Question

Static EquilibriumA weight of $2000$pounds is suspended from two cables, as shown in the figure. What are the tensions in each cable?

Short answer

The tension in the cable is approximately equal to $1843.21lb$and $1630.41lb$.

Step-by-step solution

Step 1. Given information 

We are given a figure,

Step 2. Finding the tension

Under the equilibrium conditions, the vertical components of the tension in the cables will balance the weight of chandelier, and horizontal component will balance each other, so

For vertical direction,

$$\begin{gathered} T_1\sin {40}^{\circ }+T_2\sin {30}^{\circ }=2000 \\ 0.643T_1+\frac{1}{2}{T}_2=2000 \end{gathered}$$

For horizontal direction,

$$\begin{gathered} T_1\cos {40}^{\circ }=T_2\cos {30}^{\circ } \\ {T}_1=1.13T_2 \end{gathered}$$

Step 3. Finding the tension 

Substituting the value of $T_1$in first equation, we get

localid="1647059749047" $$\begin{gathered} 0.643\left(1.13T_2\right)+\frac{1}{2}{T}_2=2000 \\ {T}_2=1630.41lb \end{gathered}$$

So,

localid="1647059921184" $$\begin{gathered} T_1=1.13(1630.54) \\ =1843.21lb \end{gathered}$$

The tension in the cable is localid="1647059931398" $1843.21lb$and localid="1647059756761" $1630.41lb$.