How does the force get cancel out?

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The discussion revolves around understanding how forces cancel out in a physics problem. The user questions why a specific force, F1, is not included in the calculations while a similar force, F4, is. There is mention of horizontal and vertical vectors potentially canceling each other, leading to confusion about the calculations involved. The user ultimately indicates they have solved the problem, suggesting they gained clarity on the force cancellation concept. The conversation highlights the importance of vector components in analyzing force interactions.
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Homework Statement



How does the force get cancel out?

Homework Equations





The Attempt at a Solution



Please see the picture.
I don't understand why is F1 not included in the system ?
F1 just looks the same as F4, but F4 is included in the calculation.
Someone told me the horizontal vector and vertical vector somehow cancel out each other but i don't quite get it..
 

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What exactly does the calculation involve?
 
solved the problem!
 
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