Chapter 9, Problem 60RE

To determine

To find: The tensions in each cable.

Answer to Problem 60RE

The tensions in each cable are $1842.51\text{pounds}$ and $1630.54\text{pounds}$ .

Explanation of Solution

Given information:

The weight is $W=2000\text{pounds}$ .

The angles are $40°$ and $30°$ .

Calculation:

Balance the force in the vertical direction.

  $\begin{array}{c}{T}_1\sin 40°+T_2\sin 30°=2000\\ 0.643T_1+\frac{1}{2}{T}_2=2000\end{array}$ …. (1)

Balance the force in the horizontal direction.

  $\begin{array}{c}{T}_1\cos 40°+T_2\cos 30°=2000\\ T_1=1.13T_2\end{array}$ … (2)

Substitute the value in the first equation.

  $\begin{array}{c}0.643\left(1.13T_2\right)+\frac{1}{2}{T}_2=2000\\ T_2=1630.54\text{pounds}\end{array}$

Substitute the value in second equation.

  $\begin{array}{c}{T}_1=1.13\left(1630.54\text{pounds}\right)\\ =1842.51\text{pounds}\end{array}$

Therefore, the tensions in each cable are $1842.51\text{pounds}$ and $1630.54\text{pounds}$ .