Chapter 6.3, Problem 87E

To determine

The tension in the low lines when they each make 18^o angle with the axis of the barge.

Answer to Problem 87E

The tension in the each toe line is 3154.4 lb.

Explanation of Solution

Given:

Two tugboats are towing the loaded barge and the magnitude of the resultant is 6000 pounds.

The diagram is given as:

  

Referring to the given figure, the resultant force is the sum of the individual tension by the each tug boats:

  $\begin{array}{l}F=T\cos \theta +T\cos \theta \\ =2T\cos \theta \\ \text{Since,}\\ F=6000\\ \theta ={18}^o\end{array}$

Now, solving the equation of the resultant force:

  $\begin{array}{l}6000=2T\cos {18}^o\\ T=3154.4\end{array}$

Therefore, the tension in the each toe line is 3154.4 lb.