High School How Does Gravity Affect Spring Stretching in Einstein's Theory?

[Dr_Mike_J]

TL;DR

Gravity and Force

A thought occurred to me.
According to Einsteins general theory of relativity gravity is not a force.
How then does it cause a spring to stretch?

 

[Dale]

Summary:: Gravity and Force

According to Einsteins general theory of relativity gravity is not a force.
How then does it cause a spring to stretch?

It doesn’t. The spring is stretched by the contact force at the top. If you remove the contact force then it will stop stretching.

 

[Dr_Mike_J]

It doesn’t. The spring is stretched by the contact force at the top. If you remove the contact force then it will stop stretching.

What is the origin of the contact force?

 

[sophiecentaur]

It doesn’t. The spring is stretched by the contact force at the top. If you remove the contact force then it will stop stretching.

The OP has to realize that your answer will need reading and re-reading, followed by a lot more reading round this topic. GR is actually VERY HARD and it can be quite a struggle to relate it to our experience. So was Newton's Physics in his time.

 

[Dale]

What is the origin of the contact force?

I don’t know. You didn’t describe the scenario completely. It could be a person’s hand or it could be glue or a screw or a weld. It doesn’t matter what the origin is.

 

[etotheipi]

Imagine you lay the massive spring horizontally on a smooth ice rink, and pull one end with a constant force. The spring stretches!

 

[sophiecentaur]

@Dr_Mike_J See what I mean! I foresee some brain ache on the horizon.

 

[Dr_Mike_J]

I don’t know. You didn’t describe the scenario completely. It could be a person’s hand or it could be glue or a screw or a weld. It doesn’t matter what the origin is.

OK, more detail.
Spring hanging from a hook on a ceiling.
A 1kg mass on the end of the spring held by a human hand such that the spring is at its natural length unstretched.
You let go of the mass slowly avoiding any adiabatic changes so that the spring smoothly attains its new equilibrium configuration so there is now a force acting through the whole spring F=kx.
My question is what is the origin of this force within the spring which is the sum of all the interatomic attractions within the metal of the spring caused by the displacement of the constituent atoms from their equilibrium positions.

 

[Dale]

My question is what is the origin of this force within the spring which is the sum of all the interatomic attractions within the metal of the spring caused by the displacement of the constituent atoms from their equilibrium positions.

The contact force from the hook on the top.

 

[sophiecentaur]

Give him a break!

 

[Dale]

What? That is the GR answer. In GR that is the only external force acting on the spring/mass system.

Edit: hmm I just realized he may not have intended the mass to be part of the spring, but rather separate. In which case it would be the pair of contact forces from the mass and the hook.

 

[sophiecentaur]

I told him there would be some brain ache.

 

[Dr_Mike_J]

My question is quite genuine. I think there is a real conceptual problem here.
Springs stretch because an external force pulls the constituent atoms away from each other.
If gravity is not a force how does the spring get deformed by a hanging mass.
GR says that it's the warp of space-time causing the mass to try to move along the new geodesic generated by the presence of the Earth. Electrostatic intermolecular theory says that the spring stretches when the constituent atoms are caused by an external force to increase their average separation against the force generated by their intermolecular potential. So where does this force originate if the gravity that balances it is not a force?

 

[Dale]

My question is quite genuine

Yes, I assume you are being genuine in your question, as am I in my answer.

If gravity is not a force how does the spring get deformed by a hanging mass.

Even in Newtonian mechanics gravity doesn’t deform a spring. It is always the contact forces which deform the spring. This is not unique to GR, although it may be that GR challenges you to think about it correctly by not labeling gravity as a force.

So where does this force originate if the gravity that balances it is not a force?

The contact force(s) on the spring.

Think about more scenarios (use Newtonian mechanics), some with gravity and some without, some at rest some accelerating, some with contact forces and some without. Identify which scenarios have the spring in tension and which do not. You will see that you can have a spring in tension with or without gravity, but that you must have the contact forces. Therefore the origin of the tension is the contact forces not gravity.

 

[Nugatory]

14 posts in and no one has linked @A.T.'s video yet?
Watch this video, imagine that the apple is connected to the branch by a spring... the spring will stretch until it is exerting a force sufficient to pull the apple back onto the "hang" worldline.

 

[ZapperZ]

We get this type of question A LOT, and we need to go back several paces here.

Just because something can be viewed another way, it doesn't mean that the first or original way of looking at it isn't valid anymore. Let's look at the concept of classical force in general. Notice I didn't say WHAT type of force, just a generic force.

If you look at classical mechanics, a force F can also be looked at as nothing more than a gradient of the potential energy field V, i.e.

F = - dV/dx

where I've restricted this to 1D for simplicity since I don't know if the grad operator is understood here.

Then, by the same logic, does it mean that ALL forces don't really exist, but instead it is simply a gradient in the potential field? How did you pull on the spring then?

So the question here is that, are you aware of this, and if you do, why aren't you asking the same question about all forces, be it gravity or electrostatic, etc.?

Zz.

 

[Ibix]

Actually, @etotheipi's comment about a mass and spring lying horizontally on ice is a nice example. The spring stretches if you pull one end, even though gravity is completely irrelevant here.

The point is that in GR, the curvature of spacetime is such that the unaccelerated path of the mass is to fall to the floor, just as the (horizontally) unaccelerated path of the mass on the ice is to just sit there. In either case you need to apply a force to get it to follow an accelerated path, and that force comes from whatever's holding the spring at the other end. It's this force that stretches the spring.

 

[DrStupid]

Springs stretch because an external force pulls the constituent atoms away from each other.
If gravity is not a force how does the spring get deformed by a hanging mass.

There is a similar effect in classical mechanics: Just take a spring with two masses at the ends and let it rotate around the common center of mass. If centrifugal force is not a force (in fact it isn't) how does the spring gets deformed by the rotating masses?

 

[Dr_Mike_J]

OK Before the mass is put on the end of the spring the spring is unstretched. When the mass is put on the end of the spring what causes the spring to stretch?

 

[DrStupid]

When the mass is put on the end of the spring what causes the spring to stretch?

The electromagnetic force between mass and spring.

 

[A.T.]

OK Before the mass is put on the end of the spring the spring is unstretched. When the mass is put on the end of the spring what causes the spring to stretch?

Note that causation is not relevant to force analysis.

 

[Ibix]

OK Before the mass is put on the end of the spring the spring is unstretched. When the mass is put on the end of the spring what causes the spring to stretch?

The spring starts pulling the mass out of its freefall trajectory with a proper acceleration of 1g. Just like the mass-on-ice example, the force at one end of the spring and the resistance to acceleration of the mass lead to the spring stretching.

 

[A.T.]

Even in Newtonian mechanics gravity doesn’t deform a spring. It is always the contact forces which deform the spring. This is not unique to GR, although it may be that GR challenges you to think about it correctly by not labeling gravity as a force.

I think the above is key here. A local uniform gravitational field cannot deform anything. Neither in Newtonian gravity nor in GR. If the gravity is not uniform, it will deform the spring, even without anything attached to it.

 

[pervect]

Let's try a different question. Suppose you are on an accelerating elevator, and you have the same hanging spring.

How would you describe the origin of the springs stretch in this case? What are the real forces on the hanging spring in the accelerating elevator?

Spoiler

The only real force on the spring is the force making applied to make it accelerate. Other forces are fictitious forces.

 

[Dr_Mike_J]

Going back to the spring hanging from the ceiling...
When the mass is on the point of being hung on the end of the spring, that is the surface of the material of the hook of the mass is in contact with the surface of the material of the spring there are balanced electrostatic repulsions and attractions between their constituent positive and negative charges - the spring is in equilibrium.
As the mass is allowed to hang from the spring what is the reason for the spring's loss of equilibrium?

 

[A.T.]

When the mass is on the point of being hung on the end of the spring, that is the surface of the material of the hook of the mass is in contact with the surface of the material of the spring there are balanced electrostatic repulsions and attractions between their constituent positive and negative charges - the spring is in equilibrium.

Sounds like you are confusing Newtons 3rd Law (equal but opposite forces between mass and spring) with Newtons 2nd Law (force equilibrium on the spring).

 

[DrStupid]

As the mass is allowed to hang from the spring what is the reason for the spring's loss of equilibrium?

The spring starts excerting a force on the mass, pulling it ouf of its geodesic. The corresponding counter force (together with the force from the ceiling that keeps the top of the spring in place) stretchs the spring. There are no other forces involved.

 

[Sagittarius A-Star]

Summary:: Gravity and Force
How then does it cause a spring to stretch?

You need a force to accelerate a mass, in an inertial frame. The hook is accelerating with 9.81 m/s² upwards, relative to the local inertial system in a nearby free falling elevator cabin. If you force the mass to get the same acceleration, a contact force is needed. You can regard the spring as an acceleratometer.

But be aware: If the spring stretches, you store mechanical energy in it. According to E=mc², it gets more mass by the stretching and the needed force is even greater. -:)

 

[Dale]

OK Before the mass is put on the end of the spring the spring is unstretched. When the mass is put on the end of the spring what causes the spring to stretch?

The contact force from the mass.

Did you go through the exercise I suggested? What scenarios did you consider and what did you find?

As the mass is allowed to hang from the spring what is the reason for the spring's loss of equilibrium?

The contact forces on the ends of the spring. They were zero before stretching and nonzero after stretching.

This is getting a little repetitive.

 

[Dale]

To break the repetitiveness let me try a different approach. I will propose many different scenarios including if the spring is stretched or unstretched. You identify the forces acting on the spring itself, and assume that the spring itself has mass. We are only interested in forces along the direction of the spring, not transverse forces.

1) spring is stretched horizontally attached to two walls, supported by a frictionless table to keep it straight

2) spring is unattached and unstretched as it free falls vertically

3) spring is attached to the ceiling and is stretched slightly under its own weight

4) spring is stretched between my hand and a mass while accelerating horizontally across a frictionless table

5) spring is unstretched lying on a table

6) spring is stretched between two masses in horizontal uniform circular motion on a frictionless table