The pole is subjected to the force F which


The pole is subjected to the force F which has components F_x= 1.5 kN and F_z= 1.25 kN. If β =75°, determine the magnitudes of F and F_y.

The pole is subjected to the force F

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

Solution:

To do this question, we have to remember the following equation:

\text{cos}^2\alpha +\text{cos}^2\beta +\text{cos}^2\gamma =1

 

Looking at the diagram and the values given to us in the question, we can write \text{cos}\,\alpha as \frac{1.5}{F}.

 

We also know from the question that \beta=75^0.

 

Similar to before, we can write \text{cos}\,\gamma as \frac{1.25}{F}.

 

Let us substitute these values into our equation like so:

(\frac{1.5}{F})^2\,+\,\text{cos}^{2}(75^0)\,+\,(\frac{1.25}{F})^2=1

 

Solving for F gives us:

F= 2.02 kN

 

F_y can be found by multiplying the force by the value of \text{cos}75^0. Thus, F_y is:

F_y=2.02\text{cos}\,75^0=0.523 kN

This question can be found in Engineering Mechanics: Statics (SI edition), 13th edition, chapter 2, question 2-85.

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