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## Homework Statement

If the resultant force acting on the bracket is required to be a minimum, determine the magnitude of F1. Set Φ=31°

## Homework Equations

F

_{x}=F(cos(θ))

F

_{y}=F(sin(θ))

## The Attempt at a Solution

First I tried to find ∑Fx and ∑Fy

ΣF

_{x}=0=200+cos(67.38)260+cos(59)F

_{1x}

ΣF

_{y}=0=sin(67.38)260+sin(59)F

_{1y}

Solving for F

_{1}, I got

x=-384.06

y=279.99

And then to find the magnitude, I found the root of the sum of their squares

√(-384.06² + 279.99²)=479.335N

which was wrong.

A few things: I know the x-component can't be negative, it makes no sense, but I don't know what to change to make it positive. I also don't know what is implied by "required to be a minimum."

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