I How a rigid body causes a reaction force?

[jbriggs444]

Yeah, I know that the contact force is actually Electromagnetic force between the constituent molecules.

But I think at the time of Newton this fact was quite unknown. So, is there any explanation why Newton’s Third Law occurs/exists purely on the basis of macroscopic level?

If you are digging for some underlying principle by which Newton's Third Law could be deduced from the physics and mathematics known to Newton, I would answer "there is none". It was a testable hypothesis consistent with the available physical evidence. Assuming its truth allowed for additional testable conclusions to be reached. That is pretty much all that one can ask of a physical principle.

It is in the nature of things that first principles cannot be deduced from nothing. They have to be guessed at based on experimental results. That's how science works.

 

[SammyS]

It's interesting to note that apparently O.P. has a hangup about a reaction force only being possible when there is a deformation. Below is one of several posts @Adesh made to the following tread in the Homework Help forum. https://www.physicsforums.com/threads/trouble-with-the-concept-of-tension.985741/

Tension will be caused only when there is a stretch, in my opinion.

 

[vanhees71]

But that's correct. There's no rigid body in nature. It's only an (non-relativistic) approximation for very stiff (elastic) bodies, and indeed the reaction force comes from deformations of the body from its equilibrium state, when no external forces are acting. As stated some times before, the reaction force is electromagnetic and a consequence of the Pauli exclusion principle.

 

[sophiecentaur]

How the second body exerted force on the first body (if it cannot be deformed)?

I have just dipped into the thread (far too many posts to stagger through them all) and this post demonstrates the problem. There is no such object that cannot be deformed - just give it as high a modulus as you like and you are back in the real world and there is nothing paradoxical at work. Every step function that occurs in scientific theory is a nonsense until we acknowledge that it's a justifiable approximation.

My Grandad, who was in no way a Scientist (I did love him), used to ask the old question "What happens when an unstoppable force meets an immovable object?" It made him feel smart that a teenager couldn't put him straight on the flawed philosophy behind the question. But, again, he had a problem understanding why we couldn't actually hear the Satelloon going overhead in the early 1960s; it "had to have an engine".

 

[anorlunda]

There is no such object that cannot be deformed

If you read the earlier posts, you would see discussions of free electrons, and other subatomic particles. AFAIK, we can't deform those, yet they obey the 3rd law.

Only late in the thread did the OP clarify that he meant only bulk objects in contact. Obviously, the 3rd law is valid for cases other than that one.

 

[vanhees71]

Hm, subatomic particles are described by quantum mechanics rather than classical mechanics. It's a good question, in which sense (other than momentum conservation) the 3rd law is valid in QM, but that's another story...

 

[Adesh]

I have just dipped into the thread (far too many posts to stagger through them all) and this post demonstrates the problem. There is no such object that cannot be deformed - just give it as high a modulus as you like and you are back in the real world and there is nothing paradoxical at work. Every step function that occurs in scientific theory is a nonsense until we acknowledge that it's a justifiable approximation.

My Grandad, who was in no way a Scientist (I did love him), used to ask the old question "What happens when an unstoppable force meets an immovable object?" It made him feel smart that a teenager couldn't put him straight on the flawed philosophy behind the question. But, again, he had a problem understanding why we couldn't actually hear the Satelloon going overhead in the early 1960s; it "had to have an engine".

Really enjoyed your reply.

 

[sophiecentaur]

If you read the earlier posts, you would see discussions of free electrons, and other subatomic particles. AFAIK, we can't deform those, yet they obey the 3rd law.

I think what we have seen in this thread is a typical PF treatment of a topic. I read the first post and it was very clear to me that the OP was asking about macroscopic structures being 'explained' with a mechanical version of microscopic structures and a possible problem with a too simple model. It's very easy for contributors to introduce ' what they know' about exceptions to an elementary / classical treatment and that can take a thread way off course from where it started. There are always lines of demarkation between mechanical, mathematical and quantum and I really feel it's up to contributors to try to avoid crossing over them unless absolutely necessary. Imo, the OP introduced or implied, perhaps the possibility of a problem in reconciling the mechanical with the mathematical. Once the gloves are off, we could end up talking about the mechanics of inside black holes / degenerate states - you name it. Would that help? It would definitely have given me a problem at A level.
All good fun though.

Let's face it, once we are dealing with fundamental particles, we mostly stick to the conservation laws and don't get too mechanical.

 

[vanhees71]

I disagree. One has to clearly state that classical models have their limitations though in some aspects (particularly concerning linear-response theory of electromagnetic interactions, i.e., the usual macroscopic classical elctrodynamics taught in the intro-E&M lecture) they are quite accurate, though sometimes only qualitatively but as effective theories with phenomenological constitutive relations very valuable also quantitatively.

In this case, as usual as soon as properties of matter are concerned, you cannot answer the question without referring to QT. In this case it's also very easy to argue with relativity that there are no strictly rigid bodies in nature though it's a very useful and even quantitatively working non-relativistic model (with the tensor of inertia the "phenomenological constitutive parameters").

As Einstein said: "Make things as simple as possible, but not simpler!"

 

[sophiecentaur]

I disagree.

Which bit are you disagreeing with? Can you be disagreeing that an appropriate depth of treatment should always be used in education?This thread is surely about early steps in the understanding of the mechanical world and not doing the whole lot in one go. That would be too much for almost anybody.
Quoting Einstein (ad hominem) in a vacuum is not really helpful because there would have been a very relevant context to his remark.

 

[vanhees71]

I'm diagreeing with the idea, not to answer a question according to the known facts. Of course, when learning about classical mechanics in the very first semesters you cannot explain relativity and quantum mechanics in all detail, but you can tell the students already then, in a qualitative way, as I tried in my answers above, that you need more advanced physics to answer the question. After all, we teach classical mechanics not so much for its own sake but as the preparation for the more advanced and up-to-date topics of modern physics.

For me the main justification to teach the fascinating subject of rigid bodies and spinning tops is to introduce the rotation group as a Lie group and use Lie-algebra arguments to derive the equations of motion using Hamilton's principle (at my university it's usualy taught in the 2nd semester in the 2nd theory-course lecture, where analiytical mechanics is treated). It's a great opportunity to introduce these quite advanced topics at the example of a non-trivial but fascinating phenomenon.

 

[sophiecentaur]

(at my university it's usualy taught in the 2nd semester in the 2nd theory-course lecture,

I have to agree that the Thread Header is I so it is probably appropriate. However, the question about an infinitely strong rope doesn't fit in with that and I was suggesting that the point couldn't be appropriately answered by just digging deeper.