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January 5

Can neutron star heat and/or rotation affect the maximum mass before either collapse or black hole formation by more than 0.1 solar masses?

I was editing Degenerate matter#Neutron degeneracy, but was unable to find academic references to settle the question of whether or not neutron star heat and/or rotation affect the maximum mass before either collapse or black hole formation by a significant amount, say more than 0.1 solar masses? If anyone is able to find a reference to a freely available full-text or sufficiently worthy abstract or summary much more modern than Oppenheimer and Volkoff, 1939 on the topic of the significance of heat & rotation on neutron star mass limits, then please post it here. It's well-known that the radius of a rotating black hole is different to that of a non-rotating black hole of the same mass. It therefore stands to reason (to me at least) that the rotation speed of a neutron star would influence the size beyond which it would no longer be considered a neutron star and would instead be considered to be a black hole, yet I can't find a supporting reference. Oppenheimer and Volkoff discounted the influence of heat, stating in reference to work by Landau (1932), 'even [at] 10⁷ degrees… the pressure is determined essentially by the density only and not by the temperature' - yet it has been estimated that temperatures can reach up to approximately >10⁹ K during formation of a neutron star, mergers and binary accretion. Another source of heat and therefore collapse-resisting pressure in neutron stars is 'viscous friction in the presence of differential rotation.' Kaminker Et Al. 'Thermal emission of neutron stars with internal heaters', Royal Astronomical Society, 2014. MathewMunro (talk) 07:14, 5 January 2024 (UTC)[reply]

earliest appearance of Hg in history

Our articles Timeline of chemical element discoveries and Mercury (element) simply make a matter-of-fact mention that Hg was found in Egyptian tombs from 1500 BC. The cited source makes an equally matter-of-fact mention. So: does anyone have any more details about this? Double sharp (talk) 08:49, 5 January 2024 (UTC)[reply]

See cinnebar which was used as a cosmetic long before even the Egyptians and from which mercury can be got quite easily. NadVolum (talk) 09:10, 5 January 2024 (UTC)[reply]

True. I should thus clarify my question: what's the earliest documentary proof that elemental Hg was known?

(Note that heating cinnabar results in decomposition to mercury vapour, because of the temperatures involved. So I guess this amounts to asking who first had the bright idea to come up with a condenser.) Double sharp (talk) 09:20, 5 January 2024 (UTC)[reply]

In this book on "Mercury in the Environment: Pattern and Process" in the chapter "Industrial Use of Mercury in the Ancient World" William Brooks states "Archaeologist have shown that cinnabar was mined and mercury produced more than 8000 years ago in Turkey." Mikenorton (talk) 10:15, 5 January 2024 (UTC)[reply]

Interesting. This put me on a good lead: this document starts by saying Cinnabar is believed to have been mined in Turkey 8,000 years ago for use as "paint," and archaeological evidence indicates that mercury metal was recovered from the sulfide ore near Konya in Roman times or possibly even hundreds of years earlier by the Greeks (Barnes and others, 1972). Thus it may be that both cinnabar mining and mercury production first originated in Turkey. Unfortunately I cannot find their original source (Barnes, J. W., & Bailey, E. H. (1972). Turkey’s Major Mercury Mine Today and How It Was Mined 8000 Years Ago. World Mining, 25, 49-55.) Double sharp (talk) 14:40, 5 January 2024 (UTC)[reply]

Something that I'm sure that I should have been aware of is that mercury occurs in its native form in small amounts associated with cinnabar deposits, including those worked in ancient Turkey - see the USGS report that you linked to.Mikenorton (talk) 12:57, 6 January 2024 (UTC)[reply]

Thanks for pointing that out! I think this is a very plausible answer to the question "when was metallic Hg first seen by humans", then. Double sharp (talk) 09:17, 7 January 2024 (UTC)[reply]

Elements

Is it possible to add the first 12 terms of (sequence A249874 in the OEIS)? i.e. add the order of date of discovery of carbon (6), sulfur (16), iron (26), copper (29), zinc (30), arsenic (33), silver (47), tin (50), antimony (51), gold (79), mercury (80), lead (82). 223.141.52.225 (talk) 12:17, 5 January 2024 (UTC)[reply]

It's not clear to me what you're asking. I've given this its own section as it doesn't seem to be a response to the Hg question.Mikenorton (talk) 13:09, 5 January 2024 (UTC)[reply]

No one really knows exactly when these were discovered, so the question is unanswerable. It seems likely to me that carbon was the first of all pure elements to be discovered by humans, but even that's just speculation. In Timeline of chemical element discoveries we mostly only have limits for the earliest elements. The limits probably don't reflect the actual order: considering the technology required to extract them, surely Au must have been discovered before Pb. I think the order suggested at the Sodium Lamp blog makes chemical sense (C, S, Au, Cu, Ag, Pb, Sn, Fe, Sb, Hg, Zn, Pt, As, Bi, then P and the recorded discoveries), but (1) not RS and (2) there's not iron-clad proof and perhaps the actual order was not the chemically expected one. (In the modern era, I still find it surprising that Te was discovered before Se. And in the f-block, Eu was discovered very late, despite having a prominent unusual oxidation state for a lanthanoid that would've helped separate it out.)

P.S. platinum (78) belongs with the unrecorded discoveries. It was known to pre-Columbian South Americans, though it was not recognised in the Old World before the 18th century. Also, bismuth (83) is technically also unrecorded, but was recognised as distinct c. 1500, far later than the thirteen before it. Double sharp (talk) 14:18, 5 January 2024 (UTC)[reply]

P.P.S. Mary Elvira Weeks wrote in Discovery of the Elements (p. 116): It really is strange that phosphorus was discovered so early in the history of chemistry, for the reactions involved in Brand's method are rather complex, and even today this element is not isolated with ease. So, one should certainly not assume that the prehistoric elements were necessarily discovered in the chemically expected order. :) Double sharp (talk) 08:36, 8 January 2024 (UTC)[reply]

Forces on a rod

Hi, this ought to be simple but I can't figure it out. As depicted in the diagram at https://imgur.com/e2GfOZg, a rod is suspended at an angle by vertical strings fixed at each end. Now, if the strings could slide along the rod, e.g. the rod was slung in loops of string, with no friction, then clearly the rod would slide down in the direction of the arrow A. So, given that the strings are in fact fixed to the rod, and the rod in fact cannot slide, there must be forces B at either end to stop it sliding. Yet a vertical string can only impart force to the rod directly upwards, and not in the direction of B, can't it? So what is the explanation?

This is a question that I thought of myself. It is not homework. 2A00:23C8:7B09:FA01:D49A:B7CA:A452:8DE6 (talk) 20:18, 5 January 2024 (UTC)[reply]

There are two forces acting on the rod - the force of gravity pointing down, and the tension on the strings, acting up. At equilibrium, those forces are equal. (If the tension was higher, the rod would move up. If gravity were higher, the strings would stretch.)

However, you can decompose the gravitational force into two perpendicular components - one pointing perpendicular to the rod, and one pointed parallel to it. You can also do this with the tension force, and at equilibrium, they will again all balance.

But in the sliding case, the opposing force in the parallel direction ISN'T string tension - it's just friction against the loop. That friction force is determined by the coefficient of friction between the loop and the rod. It is also proportional to the normal (perpendicular to the rod) component of the gravitational force.

So if the coefficient of friction is low, the frictional force won't be enough to counteract the parallel component of the gravitational force, and the rod will slide. If the coefficient of friction is high, then the frictional force will balance the gravitational force, and the rod won't move.

Similarly, since the frictional force is proportional to the normal force, changing the angle of the rod also has an effect. The steeper the angle, the smaller the normal component of the gravitational force, and thus, the smaller the frictional force. The extreme case is a rod in a loop hung vertically. There is no normal component of the gravitational force, so no friction, and the rod just falls out. PianoDan (talk) 21:39, 5 January 2024 (UTC)[reply]

@PianoDan: Thanks for your reply. In the case that friction between the string and the rod prevents the rod from slipping, must there not still be some force (tension) to stop the string simply being dragged in the direction of A with the rod? I mean, friction alone cannot prevent something from moving, can it? There has to be some opposing force applied to whatever is providing the friction, doesn't there, to prevent the two things simply moving together? 2A00:23C8:7B09:FA01:D49A:B7CA:A452:8DE6 (talk) 22:13, 5 January 2024 (UTC)[reply]

Friction alone absolutely can stop something from moving. Put sandpaper on an shallow ramp, and put a block on the ramp. The ONLY reason the block doesn't slide down is because of friction.

In the case of the rod on the ropes, remember that both the gravitational AND opposing forces can be decomposed.

In the perpendicular to the rod direction, you have a component of the gravitational force pointing one way, and the opposing component of the tension force. Those are always going to balance, by the same argument as why they balanced in the fixed rope case. If they don't, the rope will either compress or stretch until they do.

In the parallel to the rod direction, you have the other component of the gravitational force, balanced by the frictional force. If they are balanced, there's no motion. If they aren't, the rod moves PianoDan (talk) 23:29, 5 January 2024 (UTC)[reply]

Thanks. If you have time, I wonder whether you might be able to look at my "Another scenario" post, below in this thread, and give any view on (1) Whether the stoppers in that scenario exert a force on the uprights; (2) Whether the uprights exert an opposite force against the stoppers; (3) Whether in the original "suspended by strings" case, a corresponding force, that I have labelled B in the diagram that I linked to, needs to be applied to the rod; (4) If so, how does the string apply this when it can only pull vertically upwards (e.g. consider that any non-vertical force on a plumb bob will cause the string to deviate from the vertical); or (5) If not, why not? I mean, what is the essential difference between the "rod suspended by strings" case (please ignore friction per se and assume that the strings are fixed or "welded" to the rod) and the "rod resting on uprights" case? Thanks for your help with this. 2A00:23C8:7B09:FA01:ECF0:2E16:36C5:3807 (talk) 00:00, 7 January 2024 (UTC)[reply]

Actually, thinking about this some more, I wonder whether the key to this conundrum may be that the direct-gravity-opposing force applied by the string is not vertical, but that together with the slippage-opposing force it resolves to vertical. Could that be correct? (Or perhaps that that is essentially what you were saying anyway?) 2A00:23C8:7B09:FA01:6841:2BD3:1F38:7DA2 (talk) 01:38, 7 January 2024 (UTC)[reply]

The force directly opposing gravity IS vertical, because it is opposing gravity. And specifically, that force is the tension force in the string. The fact that you can decompose a force into orthogonal components is a convenience, but it doesn't change the direction of the original force.

When we talk about the "perpendicular" or "parallel" component of a force here, they are still just that - components. There is no NET horizontal force, and as such, no horizontal deflection. The decomposition is purely a convenience for ease of analysis.

There's really no essential difference between "Strings with high enough friction to stop the rod from moving" and "Support uprights with stoppers." In both cases there's one force of gravity, which can be broken into a component along the rod, and one parallel to it.

Opposing that there is a vertical force from the support structure. That force can be also broken into two parts.

Perpendicular to the rod, the force is simply equal and opposite that of the perpendicular component of gravity. If it were not, the support would deform.

Parallel to the rod, you have the opposite component of the force from the support. Friction in the original case, and the parallel component of the force from support in the fixed case. Again - if those components are equal, nothing will move, and if they are NOT the system will adjust until they are. (unequal forces here meaning that you've exceeded the structural strength of your uprights or your stoppers.)

I think what's tripping you up is that you may be thinking of the forces from your supports as a fixed value. Instead, think of them as whatever force is required to exactly balance the force of gravity. The structure will NEVER exert MORE force than the gravitational force unless you put energy into it from outside. On the other hand, there is a MAXIMUM amount of gravitational force any structure can balance, and once you hit that, it will deform and/or break.

So there's just two possibilities here - everything is exactly balanced, or else you're going to break something. PianoDan (talk) 17:16, 8 January 2024 (UTC)[reply]

I have seen this puzzle before but instead of loops of string, the rod sits on a pair of frictionless rollers and one of the rollers is slightly higher than the other. To stop the rod from accelerating “downhill” on the rollers it is restrained by a force pointing slightly “uphill”. If this restraining force disappears the rod rolls downhill off the rollers.

A characteristic property of all frictionless rollers (and unbraked wheels) is that when they are in contact with a solid surface such that a contact force exists, its line of action is a line through both the point of contact and the center of the roller (or wheel.) A frictionless loop of string will have this same property, as a roller with a very small diameter.

When the two rollers are at different heights the lines of action of the contact forces are tilted slightly away from the vertical by the same angle as the rod is away from the horizontal. It is the horizontal components of these two contact forces, added to the downwards force of gravity on the rod, that causes the rod to accelerate downhill along the rollers.

In the case of the strings fixed to the rod, the strings behave like a wheel with the brakes locked on - the line of action of the contact force does NOT act through the center of the wheel. Instead, the contact force includes a component of sliding friction that causes the line of action to point somewhere other than through the center of the wheel. This means the forces on the rod, provided by the strings, are vertically upwards - there is no horizontal component and so no tendency for the rod to accelerate downhill. Consequently there is no horizontal force on the rod to stop it accelerating because there is no horizontal component of force exerted by the strings. Dolphin (t) 22:19, 5 January 2024 (UTC)[reply]

[Edit conflict] Another scenario to consider is a rod resting at an angle on two rigid uprights, one at either end. In the absence of friction, the rod would slip down in the same direction, A. However, if stoppers were fixed to the rod then these would push against the uprights and prevent it slipping, and presumably the uprights would provide equal and opposite forces to the stoppers. So, in the "suspended by fixed strings" case, what happens to those forces? 2A00:23C8:7B09:FA01:D49A:B7CA:A452:8DE6 (talk) 22:21, 5 January 2024 (UTC)[reply]

Climate questions

These questions are not homework. These came to my mind shortly before.

Why the Köppen climate type Dfa (hot-summer humid continental) is rarer in Europe than North America?
Is there any places in Southern Hemisphere with a group D climate that has all months' average low temperature over 10 °C?
Why Australia does not have cold winters?

--40bus (talk) 20:30, 5 January 2024 (UTC)[reply]

3 Australia is surrounded by a vast blob of liquid water, and is situated almost exactly on the tropic of whichever. So the northern half roughly is tropical in tendency. Greglocock (talk) 00:16, 6 January 2024 (UTC)[reply]

#3. OP, your premise is flawed. But then, "cold" is a relative term. Are Australian winters as cold as those in Canada, Russia or Scandinavia? Not at all. What is your yardstick? -- Jack of Oz ^{[pleasantries]} 02:30, 6 January 2024 (UTC)[reply]

OP's userpage states "I'm from Finland". So, presumably Scandinavia. Double sharp (talk) 04:42, 6 January 2024 (UTC)[reply]

It's often convenient to omit higher latitudes of the southern hemisphere on world maps. Maybe not seeing the full yardstick makes it appear you should be colder? fiveby(zero) 04:20, 6 January 2024 (UTC)[reply]

The record low temperature of Florida is minus nineteen Celsius only slightly inland and near sea level. I bet the same 30.45 degree latitude of Australia doesn't get that cold at that altitude. It has snowed in the port city of Miami at the latitude of 26 and altitude of "count meters on one hand". Minus three C and the cold weakens a lot past the thicker "testicle/pubis" landmass of Florida's "penis". Miami's right on a warm current from equatorial Atlantic! And downwind of ocean no matter which way the wind blows unless it's from a specific few tens of degrees. The very bottom of Texas 2.49 degrees from the tropics has reached minus eleven C at 10 meters from sea level and had snow. The lack of huge landmass above 40 really enmildens the Australian cold. Sagittarian Milky Way (talk) 23:00, 7 January 2024 (UTC)[reply]

1: The parts of Europe close enough to the equator to get hot summers, are either too close to the Mediterranean or Black Sea to get a continental climate or too high in the mountains to get hot summers. There's a lot of sea and mountain in southern Europe. At the same latitudes in North America (central to northern US), there's a lot of open plain, far from the ocean. PiusImpavidus (talk) 11:15, 6 January 2024 (UTC)[reply]

40bus, bear in mind that Australia is a large country; per List of extreme points of Australia, we cover almost 33° of latitude (northernmost point 10°41'S, southernmost point 43°38'S), even if you ignore little islands farther out. This means that you really can't generalise about winter temperatures. Most of the country doesn't have cold winters — even here in Melbourne, near the southern tip of the mainland, it virtually never snows — but there's a reason that part of the Great Dividing Range is called the Snowy Mountains, and farther south, the Central Highlands (Tasmania) are typically quite cold in the winter. Nyttend (talk) 00:45, 12 January 2024 (UTC)[reply]