If the resultant force of the two tugboats


If the resultant force of the two tugboats is 3 kN, directed along the x positive axis, determine the required magnitude of force F_B and its direction θ.

If the resultant force of the two tugboats

Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.

Solution:

Let us first draw the vector components like so.

If the resultant force of the two tugboats

Now let’s draw the vectors tail to tail as follows.

If the resultant force of the two tugboats

From this, we can figure out FB by using the law of cosines. (Forgot the law of cosines?)

(F_B)^2=2^2+3^2-2(2)(3)\cos 30^0

F_B=\sqrt{2^2+3^2-2(2)(3)\cos 30^0}

F_B=1.615 kN

 

To figure out θ we can use the law of sines. (Forgot the law of sines?)

\dfrac{\sin \theta}{2}=\dfrac{\sin 30^0}{1.615}

\theta=38.3^0

 

This question can be found in Engineering Mechanics: Statics (SI edition), 13th edition, chapter 2, question 2-28.

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