If FB = 560 N and FC = 700 N determine 3

If F_B = 560 N and F_C = 700 N, determine the magnitude and coordinate direction angles of the resultant force acting on the flag pole.

If FB = 560 N and FC = 700 N

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


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We will first write the locations of points A, B and C are in Cartesian vector form.

If FB = 560 N and FC = 700 N

Looking at the diagram, we can write the following:





We can now find the position vectors from A to B and A to C.


r_{AB}\,=\,\left\{2i-3j-6k\right\} m



r_{AC}\,=\,\left\{3i+2j-6k\right\} m


We now need to find the magnitude of each position vector so that we can use it to find the unit vector in the next step.

Magnitude of r_{AB}\,=\,\sqrt{(2^2)+(-3)^2+(-6)^2}

Magnitude of r_{AB}\,=\,7 m


Magnitude of r_{AC}\,=\,\sqrt{(3^2)+(2)^2+(-6)^2}

Magnitude of r_{AC}\,=\,7 m


Let us now find the unit vector for each force. Remember, this is found by dividing each component of the position vector by it’s magnitude.




We can now write force F_B and F_C in Cartesian form.


F_B\,=\,\left\{160i\,-\,240j\,-\,480k\right\} N



F_C\,=\,\left\{300i\,+\,200j\,-\,600k\right\} N

(Here we multiplied each individual component by the force. In other words, expand the brackets using FOIL)


We can find the resultant force by adding both forces together like so:



F_R\,=\,\left\{460i-40j-1080k\right\} N


To figure out the coordinate direction angles, we need to find the magnitude of the resultant force we just found.

magnitude of F_R\,=\,\sqrt{(460^2)+(-40)^2+(-1080)^2}

magnitude of F_R\,=\,1174.56 N


Coordinate direction angles can be found taking the cosine inverse of each component of the resultant divided by the magnitude:





Final Answers:

magnitude of F_R\,=\,1174.56 N





This question can be found in Engineering Mechanics: Statics (SI edition), 13th edition, chapter 2, question 2-92.

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3 thoughts on “If FB = 560 N and FC = 700 N determine

    • questionsolutions Post author

      I assume you mean lengths of each of the ropes? All you need to do is write a position vector from A to B, and then find the magnitude of it. That will give you the length. The same goes for rope AC, so you write a position vector from A to C, and then find the magnitude.