I have a problem concerning forces. Here's the question.. please help me understand the solution. Thanks!    

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valentin68 | College Teacher | (Level 3) Associate Educator

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The figure is below.

To be in equilibrium the sum of all three forces (considered as vectors) from the springs need to be zero.

F1+ F2+ F3= 0

On the vertical axis one has

`F1_v =F2_v (= kx*sin(60))`  It results `F3_v =0 N`

On the horizontal axis

`F3_h =F1_h +F2_h = kx*cos(60) +kx*cos(60) =2kx*cos(60)`

If `l` is the extension of spring S3 the above equality is

`k*l =2kx*cos(60)`

`l =2x*cos(60) =2x*1/2 =x`

For equilibrium the extensions of all three springs (making with each other an angle of 120 degree) are the same (`= x)`

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