Years ago I had a boyfriend who was really into the sciences, and we went on a bike ride. At a certain point we got to the top of a hill and started coasting down. He got way ahead of me. At the bottom I surmised that this was because he outweighed me by, like, 100 pounds. He took offense–not because I was calling him fat (I wasn’t, I was a skinny girl) and blamed it on my bicycle. So we pedaled back up to the top of the hill and changed bikes, and then started from a dead stop, because he really wanted me to believe in physics.
Once again, he took an early lead and sailed right along and I was behind him.
We went back up the hill again, adjusting for other variables. I had long hair, but I had it in a braid, he had short hair and was almost bald. Other than that we were both wearing bike shorts and windbreakers, with the additional variable being that I probably had shaved my legs and he hadn’t (being a guy). No matter what we did, he beat me down the hill every time. It drove him nuts. He finally blamed it on my hair.
However, it did bring out that the founding father of the issues in this thread is Guilliame Amontons, who’s name I am embarrassed to say I never knew.
“Amonton’s paradox” became a focus there, but rather than x-post, I ask here: what is it, particularly in the context of this homely OP? WAG: the influence of deformation and energy transfer of the runners/skids on the sleds?
All of physics consists in a set of approximations, and expertise in physics largely consists in knowing which approximations are good enough in a particular situation. Friction between two given surfaces is often approximated as proportional to the normal force between those surfaces, and independent of all other variables. This is often a good enough approximation, but not always. One situation where it is not a good approximation, as mentioned in this thread, is when one of the surfaces is snow. Another situation where it is not a good approximation is when the surfaces deform significantly, as they can with rubber tires, and this appears to have been the subject of Amonton’s work.
Thanks, sort of (/wow is that misplaced not real snark.) So at least my A can still produce decent G’s.
But:
Is this discussed in Amontons’ 1699 paper “On the resistance caused in machines, both by the rubbing of the parts that compose them and by the stiffness of the cords that one uses in them, & the way of calculating both [underline added]”–with reference here to my query to the underlined words?
If so, what’s the paradox? Even if termed as such as such in later physics, due to limiting factors, whence that term? The paradox of the twins falls out naturally from Einstein’s physics; similarly, I believe, with different ontological suppositions, does Maxwell’s demon. But here?
Not a nitpick because I’m so fucking smug and proud of myself: “Amontons” not “Amonton,” also directed to myself in part. Let the royal us be charitable: I, like Chronos and Homer, just nodded off there in my bumping-post. [Watch, someone will point out he changed he spelling of his name later…]
I will issue another WAG and suppose that a ‘limiting factor,’ as I put it, not discussed by Amontons but the focus of this OP, is “non-dry friction.” (Easier to let fly a WAG than simply reading the thing … )
Nontheless, my bump-query still stands.
Is “wet-friction” really the normal term in physics for what we are talking about?
I wouldn’t use “wet friction” as a term. Dry friction is a thing: Whenever we speak of dry friction, we mean something that behaves according to the same mathematical relationship. Non-dry friction consists of everything that deviates from that relationship, and there are many possible ways one could deviate. Giving all non-dry friction the same term (like “wet”) would incorrectly suggest that all of those sorts of friction are in some way similar.
The reason the apparent paradox rises, is that Amonton’s work considered the apparent contact area and not the actual contact area.
No surface is perfectly smooth, and so it will have smaller regions that actually touch or interact with another surface (atoms don’t actually touch).
If you run an experiment like Amonton did, where you increase the area while keeping the force the same that increase area with less pressure per unit of area will appear to have a similar coefficient of friction. But if you could look close enough you would see that the real contact surface decreases, as smaller irregularities that did interact with more pressure per area no longer do when you increase the surface area.
It ends up that if you can calculate the actual contact surface area it is linier as was documented in the other thread.
The reason this doesn’t work for tires is because they are balloons, which get flattened across a the section of their contact patch.
As they were rotating, then are increasingly deformed from their round shape then bounce back they act like bristles on a broom.
Because they are under different stress loads, those different areas of the patch will yield at different points, because they are under varying stress. In the case of braking, the rear part of the contact patch will break free first, and if there aren’t enough other “bristles” to take up the remainder of that force it will start slipping.
Depending on your needed level of accuracy this applies in almost all cases just at a lower scale. But companies who do need to care about this like the companies that make ABS systems and Traction Control systems do. The unfortunate part of this is that it is very expensive in time and resources to accurately calculate and there is lots of active work trying to find simpler models as they cannot rely on the classical equivalence.
As Chronos pointed out, physics uses models that make predictions within an acceptable amount of accuracy. But unfortunately, due to concerns like a desire to keep students interested and concerns about teaching more modern models there is a hard line in most physics education between classical and modern physics.
These classical models are important andy typically useful, but may or may not still be laws in a modern context or in all applications. In some cases, like this one our understanding actually superseded this theory, and people need to avoid making derivative theories from it’s assumptions. In other cases like Newton’s first law there are better models but for the most part you can still derive new ideas from it.
Amontons’ 2nd law is a short cut, if you use it while remember that you need to check that the shortcut is still valid you will be OK.
The problem arises when you approach complex problems with the assumption that it is a fundamental truth.
While everyone talks in absolutes from time to time, you will notice that most professional physicist will be very careful about qualifying statements. But for K-12/undergrad physics, which tend to focus on classical theories it would be hard to teach a 14 year old saying (well this is kinda true…except) on these topics.
It is a bit more complex then that, but people forget this and thus with topics with friction and tides in particular this means that almost all “expert” explanations are wrong.
Just avoid absolute statements and most of these problems go away
(/wow is that misplaced not real snark.) So at least my A can still produce decent G’s.
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