Chapter 6.1, Problem 48E

Solution

To calculate: The required force $w$ .

  $47.95\text{ lb}$

Given:

Juana pulling force $=23\text{ lb}$

Diego pulling force $=27\text{ lb}$

Explanation:

The force applied by Juana $=〈23\cos 18,27\sin 18〉$

And the force applied by Diego $=〈27\cos \left(-15\right),27\sin \left(-15\right)〉$

So, the combined force is,

  $\begin{array}{l}=〈23\cos 18+27\cos \left(-15\right),27\sin 18+27\sin \left(-15\right)〉\\ =〈21.87+26.08,7.11-6.99〉\\ =〈47.95,0.12〉\end{array}$

The force should be equal but the opposite is direction. So,

The magnitude of the pulling force is,

  $\begin{array}{c}\left|F\right|=\sqrt{{\left(-47.95\right)}^2+{\left(-0.12\right)}^2}\\ =47.95\text{ lb}\end{array}$

Conclusion:

The magnitude of required force is $47.95\text{ lb}$ .