The bolt is subjected to the force F


The bolt is subjected to the force F, which has components acting along the x, y, z axes as shown. If the magnitude of F is 80 N, and α=60° and γ=45°, determine the magnitudes of its components.

The bolt 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 solve this question, we will have to use the following equation.

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

 

We will now isolate for \text{cos}\beta.

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

 

As stated in the question, we will now substitute the values given to us.

\text{cos}\beta =\sqrt{1-\text{cos}^{2}60^0-\text{cos}^{2}45^0}

 

Solve for \beta.

\beta=120^0

 

The next step is to figure out the magnitudes of F’s components knowing that the magnitude of F is 80 N as stated in the question.

F_x=\mid80\text{cos}60^0\mid= 40N

F_y=\mid80\text{cos}120^0\mid= 40N

F_z=\mid80\text{cos}45^0\mid= 56.6N

This question can be found in Engineering Mechanics: Statics (SI edition), 13th edition, chapter 2, question 2-63.

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