Is the normal force just kinetic energy?

[Hallucinogen]

Possibly useful viewing (based on Chabay & Sherwood's Matter and Interactions)

Thanks Rob! That's helped me understand russ_watters's point that there's only 4 fundamental forces and that normal/macroscopic forces aren't anything separate.

It depends on the force, but generally it is a matter of magnitude of a force-causing property and distance. For magnetism, that would be charge and distance. For gravity, it is mass and distance.
Consider a book sitting on a table, for example. No energy exchange there and two fundamental forces are at play. Can you name them and do you understand how to calculate their magnitudes?

I think the force pulling the book down is gravitational, simply mg, and the static force is electromagnetic, but I don't know how to calculate its magnitude (back when I did my physics A level I'd probably know how), but it's probably Hooke's law?

I may be reading more into your thought process than is there, but I'm getting the impression you might be putting some fundamental importance on "energy" and considering force as secondary. You have it backwards, if that is the case. "Energy" is just a convenient bookkeeping quantity. It is useful, but it is not a fundamental property in and of itself.

I think one source of my confusion is that I didn't think of electromagnetism in terms of Newtons, as we do for everyday macroscopic forces - I think of electromagnetism in terms of amperes, volts, coulombs, teslas, Webers... I was forgetting that Qd produces force in electromagnetism.

Force is defined as the gradient of the potential energy field.
...but somehow you can't comprehend the origin of the force when things bump into one another?

Thanks Zz, that helps me understand better. And yes, I had a problem there, but Robphy's video cleared that up for me.

Again: energy can be related to force in certain cases, but that is not true for every case and that doesn't make force a manifestation of energy in general.

The force is $\partial L/\partial h=-mg$. This is regardless of $T$, so there is no conversion of kinetic energy involved. This force is also present if $V$ is not changing over time during the evolution of the system.

Energy isn't responsible for force in all cases, understood, and the lagrangian shows that $T$ can be excluded in those cases. I'll probably have to go away and study partial derivatives to really understand this (the stuff about coordinates and constraints), though.

FYI, the reason that I am going on about the Lagrangian is that is the formalism with the closest general connection between energy and force, which seems to be the connection you wish to explore

What I am now not understanding is how energy, or at least momentum (I know of the impulse equation), is contributing towards force between two objects in the cases where it is at least a contributory factor. E.g. why the force would be larger if a molecular orbital hit another faster (kinetic energy), or why a molecular motor, electrostatically bound to another molecule, might be able to pull that molecule through a greater distance if it absorbs more heat (chemical energy).

 

[Dale]

What I am now not understanding is how energy, or at least momentum (I know of the impulse equation), is contributing towards force between two objects in the cases where it is at least a contributory factor. E.g. why the force would be larger if a molecular orbital hit another faster (kinetic energy),

What I just showed you above is that force has nothing to do with kinetic energy. Think of shooting a BB into a steel plate vs a rubber sheet. The KE is the same, but the force is different. The force is higher for the system where $\partial L/\partial x$ is greatest. $T$ is not a factor.

The only time that $T$ increases force is indirectly when it allows the system to reach a state with a large $\partial L/\partial x$ that it couldn't otherwise reach. Again, consider two BBs hitting a rubber sheet, one fast one slow. The force is indirectly higher for the fast one because the system gets to a greater displacement where the coordinate derivative of the Lagrangian is greater.

 

[Hallucinogen]

What I just showed you above is that force has nothing to do with kinetic energy.

I thought that example was of the force on a mass moving vertically in a uniform gravitational field, not molecules hitting or pushing on each other.

The KE is the same, but the force is different. The force is higher for the system where $\partial L/\partial x$ is greatest.

I would normally have thought that the force is the same, but the rubber sheet bends because its intermolecular forces are weaker than that of steel, and rubber has a lower force threshold for deformation. But if that's not the case then it leads me on to my next question.

The force is indirectly higher for the fast one because the system gets to a greater displacement where the coordinate derivative of the Lagrangian is greater.

Okay, so if it's not because of the greater kinetic energy that the faster one delivers more force, then why does a greater displacement (that means distance moved through, right?) and a higher $\partial L$ cause greater force?

 

[Dale]

I thought that example was of the force on a mass moving vertically in a uniform gravitational field, not molecules hitting or pushing on each other

Yes, it is the simplest example I could think of. Collisions use the same framework, but the formulas are more complicated.

I would normally have thought that the force is the same

No, the forces are definitely different.

Okay, so if it's not because of the greater kinetic energy that the faster one delivers more force, then why does a greater displacement (that means distance moved through, right?) and a higher ∂L cause greater force?

I don't have an easy answer for this one. The proof is well known and is featured in many textbooks on classical mechanics, but it is not trivial. Here are a couple of the "gentler" versions that I could find.

http://www.people.fas.harvard.edu/~djmorin/chap6.pdf
https://ocw.mit.edu/courses/aeronau...fall-2009/lecture-notes/MIT16_07F09_Lec20.pdf