# Thread: Forces in Equilibrium (Vectors)

1. ## Forces in Equilibrium (Vectors)

Hey guys, I am stuck on this question. Can anyone give me some hints? I know the sum of the x and y components have to equal zero but I don't know how to find "the minimum". Here is the problem

Thanks!

2. Consider the following relations:
$F_{2}\sin(30)=F_{3}\sin(\alpha)$
and
$F_{2}\cos(30)+F_{3}\cos(\alpha)=F_{1}$

3. Yea I know how to get that far, but I don't know how to do the next parts. Finding F1 and alpha so F3 is a minimum.

4. Originally Posted by Oblivionwarrior
Hey guys, I am stuck on this question. Can anyone give me some hints? I know the sum of the x and y components have to equal zero but I don't know how to find "the minimum". Here is the problem

Thanks!
Even just by looking at the diagram, the minimum F3 should be such thast F3 does not contribute to the F1. Meaning, F3 should have no horizontal component that would be pulled by F1.
So minimum F3 has zero horizontal component,
(F3)cos(alpha) = 0 -----(i)

For Eq.(i) to be true, if F3 is not zero, the cos(alpha) should be zero, so,
cos(alpha) = 0
alpha = arccos(0) = 90 degrees, for minimum F3 ---------answer.
And, minimum F3 = 137sin(30deg) = 68.5 newtons ------answer.

5. Thank you so much.