How do dual-length springs with different tensions behave under external forces?

[NickTheFill]

Hi all,
If two springs with the same stiffness rate but different lengths are connected together one inside the other so that at equilibrium one is in tension and the other is in compression how will the whole system behave if an external force is applied?

 

[scottdave]

Take an example set of springs and see what happens. Draw some free body diagrams to see what the force of each spring is, taking note of the magnitude and direction. Since it is in equilibrium after you connect them, what will they do with an external force? What will they do when the force is removed. Try a spring 1 meter long and 1.2 meters long. With the same spring constants, what is the equilibrium position? If you stretch it to 1.15 m, what are the forces? How about 1.2 m? If you compressed to 1.05 m what are the forces? What about 1.0 meter?

 

[berkeman]

Hi all,
If two springs with the same stiffness rate but different lengths are connected together one inside the other so that at equilibrium one is in tension and the other is in compression how will the whole system behave if an external force is applied?

Fun problem.

Is this from your homework assignment? Where did you find the problem? What equations would you use to start exploring how to figure this out?

 

[NickTheFill]

Hi
Problem has come from me simplifying a basic bolted joint analysis. In this case, the joint is the one compressed spring (so there cannot be any joint separation). The bolt is the tense spring. An FBD and F=-Kx is the stuff I’m using.
Question...if the compressed ‘joint’ spring is constrained at one end and a tensile force is applied to the other. Is it’s spring constant negative until it reaches its free length?

 

[sophiecentaur]

Is it’s spring constant negative

Nope; k is always positive. It's the displacement from the spring's unloaded length that counts. That can be positive or negative - to give you the sign of the force.
If you write down the force equation for the two spring combination, using their respective spring constants, you will get to an answer. (Start with no applied load) You have to get in there and do some Maths or it will always be arm waving. 'Believe' that the answer is in there. If you re-arrange the initial equation, you will be able to get an overall Force and an overall Displacement. That is what you are after, I think.
Come back with some equations and 'we' can help you further. (A diagram, however sparse, would also help us to be on the same lines as you are.)

 

[scottdave]

I have doubts that they have the same spring constant. The bolt and joint might be the same material, but they have different geometric shapes.

You would need to determine an estimate of k from either experiment or datasheet. The datasheet may tell you Young's Modulus or elastic modulus. This relates stress and strain rather than force and displacement, but you may be able to work with that. These links may be some help, if you are unfamiliar with stress and strain.
http://hyperphysics.phy-astr.gsu.edu/hbase/permot3.html

https://en.m.wikipedia.org/wiki/Elastic_modulus

 

[sophiecentaur]

I have doubts that they have the same spring constant. The bolt and joint might be the same material, but they have different geometric shapes.

You would need to determine an estimate of k from either experiment or datasheet. The datasheet may tell you Young's Modulus or elastic modulus. This relates stress and strain rather than force and displacement, but you may be able to work with that. These links may be some help, if you are unfamiliar with stress and strain.
http://hyperphysics.phy-astr.gsu.edu/hbase/permot3.html

https://en.m.wikipedia.org/wiki/Elastic_modulus

The OP would definitely have to reply on some experimental measurements - not very hard if the springs are to hand. One reasonable prediction would be that the two springs would act together as an equivalent single spring with a constant k over a range that doesn't stretch one of them beyond its elastic limit or compress one so that the coils touch each other.