Pushing spring from both sides - Find the spring constant

[Pishard]

Homework Statement

A spring relaxed length is 0.5[m]. It is being pushed from both sides, and contracted to 0.4[m]. The force the spring is applying outwards is 3[N] on each side. What is the spring constant k?

Homework Equations

The Attempt at a Solution

I attempted drawing a force diagram, and then getting the equations out of it, but I got that the constant is 60 (6=0.1k - because total of force is 3+3=6[N]), although I know it is 30, but I can't get it right using the diagram and equations. What am I doing wrong?

Thanks!

 

[PeroK]

Homework Statement

A spring relaxed length is 0.5[m]. It is being pushed from both sides, and contracted to 0.4[m]. The force the spring is applying outwards is 3[N] on each side. What is the spring constant k?

Homework Equations

The Attempt at a Solution

I attempted drawing a force diagram, and then getting the equations out of it, but I got that the constant is 60 (6=0.1k - because total of force is 3+3=6[N]), although I know it is 30, but I can't get it right using the diagram and equations. What am I doing wrong?

Thanks!

Could you compress a spring by applying a force only on one side?

 

[Pishard]

Could you compress a spring by applying a force only on one side?

True, I have to apply force on both sides. So in the equation F=-kx, the x meaning the total change of spring length.
Thanks!

 

[PeroK]

True, I have to apply force on both sides. But I am still confused, how do I know that the change in length on one side isn't half of the total, in this case half of 0.1[m]? Why it's 3=k*(0.1), and not 3=k*(0.05)?

That's just the way a spring constant is defined. If you apply a force $F$ to both sides and it compresses by $x$, then the constant is defined to be $k = F/x$.

If you put one end of the spring against a wall and apply a force to the other end, then the wall will provide an equal and opposite force.

In any case, the spring constant is defined by the force at one end and the total compression (not by half the compression).

 

[Pishard]

Thank you! I got it now