If we fix one end of a spring and apply some force on the free end

[davon806]

Homework Statement

If we fix one end of a spring and apply some force on the free end,the spring will elongate.If we remove the force,the spring will return to its original length(assume that Hooke's law is obeyed).
Metals are usually ductile due to their metallic bonds.In metallic bonds valence shell electrons are delocalized and shared between many atoms. The delocalized electrons allow metal atoms to slide past one another without being subjected to strong repulsive forces that would cause other materials to shatter.
So,my question is:
1)Why the spring is not ductile,consider a spring which is made of gold,
even if you pull it with a small force,it will deform and it will not return its initial structure.
Is it because the spring is not made by pure metal?Is it made by some alloys or
any other substances?
2)Why does a spring return to its original structure when the force is removed?
What's happened between the inter-atomic bondings?

Thx a lot :)

Homework Equations

The Attempt at a Solution

 

[Simon Bridge]

1)Why the spring is not ductile,consider a spring which is made of gold,
even if you pull it with a small force,it will deform and it will not return its initial structure.
Is it because the spring is not made by pure metal?Is it made by some alloys or
any other substances?

If the substance is not ductile, then small forces will rearrange it's constituents.
Something like rubber consists of strands of polymer which slide against each other when you pull on it. There are other effects, like pulling on the "spring" heats it up which can help constituents change configuration. You should be able to extrapolate this for soft metals like gold even where there are no impurities present (so there is only one type of atom present).

2)Why does a spring return to its original structure when the force is removed?
What's happened between the inter-atomic bondings?

When a good spring is pulled, the inter-atomic bonds stretch. When you release the spring, the inter-atomic bonds return to their previous mean length. This is an electromagnetic interaction: the atoms have a preferred configuration that minimizes the energy - they will stay close to that configuration unless forced to do something else - remove the force and back they go.

 

[CWatters]

I think quite a lot of things can effect the yield point or Elastic limit of a material. Heat treatment for example (so can't be all down to atomic scale effects?). Not really my field.

 

[Simon Bridge]

My understanding is that it is, indeed, not all down to atomic-scale effects.

eg. a car door is pretty springy and made of metal but you can also put a dent in it.
The mechanism that gets the dent is not as straight forward as the simple model that OP is contemplating would suggest ... the dent is a macroscopic effect but there is also an atomic-level deformation around the edges of the dent which you'll see even after the dent has been "popped" out. Here the metal is no longer as nice-a crystal as before.
(And I am over-simplifying as usual...)

It's actually quite a big subject. Beginning descriptions for how classroom springs work tend to sound like what the question is talking about so the atomic/molecular-scale effects provide a common starting point for understanding these things.

Hopefully I'll get a better idea of where OP is coming from with more conversation.
Merry Xmas :)

 

[Nickie]

I would like to clarify some misconceptions in the given content. First, the statement "the spring will elongate" is not entirely accurate. The spring will experience a change in length, either elongation or compression, depending on the direction of the applied force. This is because the spring is a mechanical element that follows Hooke's law, which states that the force applied to the spring is directly proportional to the change in length of the spring.

Now, to address the questions raised in the content.

1) The reason why a spring is not ductile, even if it is made of a metal like gold, is because of its specific design and construction. A spring is usually made of a single wire or multiple wires tightly wound in a helical shape, which creates a series of turns that are closely packed together. This structure limits the movement of the atoms within the metal, making it less ductile compared to a solid piece of metal. Additionally, the specific alloy used in making the spring also plays a role in its ductility. Some alloys may be more brittle than others, making the spring more prone to deformation.

2) When the force is removed from the spring, it returns to its original structure because of the elastic properties of the metal it is made of. The atoms in the metal are held together by interatomic bonds, which can be stretched or compressed when an external force is applied. When the force is removed, the atoms return to their original positions due to the restoring force of these bonds. This is why a spring is able to return to its original length, as long as the force applied does not exceed its elastic limit.

In conclusion, the ductility of a material depends on its structure, composition, and external factors like temperature and pressure. The design and construction of a spring make it less ductile compared to a solid piece of metal, but its elastic properties allow it to return to its original shape when the force is removed.