Calculating Resultant Force of F3 in 3D Space

[Bluestribute]

Homework Statement

If the coordinate direction angles for F3 = 650lb are α = 110∘, β = 25∘ and γ = 76∘, determine the magnitude of the resultant force acting on the eyebolt.

FIGURE:

Homework Equations

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The Attempt at a Solution

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New semester, and so happy to start with a statics instructor I can't understand or follow . . . I seriously don't even know where to begin and neither does anyone else (we've tried lots, multiple times). I know there's some formulas like cos^2α + cos^2β + cos^2γ = 1 or something, but I don't even know where I would start.

 

[STEMucator]

The direction angles are related to the resultant force and axial components by the relationships:

$cos(\alpha) = \frac{F_{3_x}}{F_3}$
$cos(\beta) = \frac{F_{3_y}}{F_3}$
$cos(\gamma) = \frac{F_{3_z}}{F_3}$

 

[Bluestribute]

Ah, learning more here than so far in class. Love it. Using those relationships, I got the vector components of F3, and using trig, got the vector components of F1 and F2, added the components together, and took the magnitude. Done √.

And the rest of the problem is just asking for alpha, beta, and gamma, which I now know! Thanks! I'll probably be back with a new thread in a bit unless the next problem uses the same relationships . . .

 

[clueless54]

How did you get the vector components of F1?

 

[clueless54]

To find F1
700cos(30)= 606 i
700sin(30)= 350 j
700cos(90)= 0 k