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.
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