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

1 Answer

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valentin68 | College Teacher | (Level 3) Associate Educator

Posted on

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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