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Geography, geology, geometry and geodesy

What’s the difference between geometry, geology, geography and geodesy?

Geometry

the branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids.

and of course geometry has many practical uses in many careers, such as building gears, drills bits, laying out camera lenses, and so much more.

 

Geology

the science that deals with the earth’s physical structure and substance, its history, and the processes that act on it.

Moho discontinuity

Which includes the study of minerals, crystals and rocks.

Geography

the spatial study of Earth’s landscapes, peoples, places and environments. This includes cartography (map-making.)

There are many types of maps used in geography.

Geodesy

Geodesy combines applied mathematics and earth sciences to measure and represent the Earth (or any planet.)

what is Geodesy

NOAA National Geodetic Survey, from a PPT by Hawaii Geographic Information Coordinating Council

.

Geodesy reasons

from the  National Oceanic and Atmospheric Administration Ocean Service Education page on Geodesy:

Geodesists basically assign addresses to points all over the Earth. By looking at the height, angles, and distances between these locations, geodesists create a spatial reference system that everyone can use.

Building roads and bridges, conducting land surveys, and making maps are some of the important activities that depend on a spatial reference system.

For example, if you build a bridge, you need to know where to start on both sides of the river. If you don’t, your bridge may not meet in the middle.

As positioning and navigation have become fundamental to the functions of society, geodesy has become increasingly important.

More info

https://www.ngs.noaa.gov/INFO/WhatWeDo.shtml

https://oceanservice.noaa.gov/facts/geodesy.html

Precise Geodetic Infrastructure: National Requirements for a Shared Resource (2010) – Geodesy for the Benefit of Society

Seismic waves

Seismic waves are waves of energy that travel through the Earth’s layers.

They are a result of earthquakes, volcanic eruptions, magma movement, large landslides and large man-made explosions.

They are studied by geophysicists called seismologists.

They are recorded by a seismometer/ seismograph, a hydrophone (when in water), or by an accelerometer.

P waves

Earth Science, Tarbuck & Lutgens, Chapter 8

Earth Science, Tarbuck & Lutgens, Chapter 8

Animation

S waves

Earth Science, Tarbuck & Lutgens, Chapter 8

Earth Science, Tarbuck & Lutgens, Chapter 8

Animation

Surface waves

Tarbuck & Lutgens

Tarbuck & Lutgens

Water waves are an example

Rayleigh surface waves

“The Rayleigh surface waves are the waves that cause the most damage during an earthquake. They travel with velocities slower than S waves, and arrive later, but with much greater amplitudes. These are also the waves that are most easily felt during an earthquake and involve both up-down and side-to-side motion.”

How do we measure motions of the Earth?

What is a seismograph?

Intro to be written

Earth Science, Tarbuck & Lutgens, Chapter 8

Earth Science, Tarbuck & Lutgens, Chapter 8

This is a seismograph record.

Earth Science, Tarbuck & Lutgens, Chapter 8

Earth Science, Tarbuck & Lutgens, Chapter 8

 

Mineral Identification

Mineral Identification Kit Properties

How do we distinguish one mineral from another? By any or all these properties:

 

Cleavage and fracture

Hit a rock with a hammer. What happens? The resulting cleavage or fracture can tell us a lot.

cleavage rocks

Crystal habit

The tendency for a mineral to grow into a special shape. This shape depends on the crystal’s structure (see next section), and also on the environment in which that mineral sample developed. (Where was it underground, how much heat, time, pressure?0

Crystal habits shapes

Crystal structure

All crystals are atoms in a three dimensional pattern. Here some examples.

Crystal structure Cubic Hexagonal

Image from Molecular and Solid State Physics, http://lampx.tugraz.at

 

Diaphaneity/transparency

The way that light passes through and reflects from a surface.

Diaphaneity Minerals Light

From left to right – Calcite is transparent, muscovite is translucent, and cinnabar is opaque.

Lustre

The appearance of a freshly cut mineral surface in light.

Mineral Luster Light

Magnetism

Some minerals are naturally magnetic.  These are some of the more common minerals that demonstrate magnetic properties

Hardness

The Mohs scale characterizes minerals by the ability of harder material to scratch softer material.

Mohs hardness scale minerals 2

Odor – So accustomed are we to associate odors with flowers or food that we scarcely appreciate the fact that certain minerals have a characteristic odor.

Selenium – horse-radish.

Arsenic – garlic.

Sulfides (such as pyrite) – rotten egg.

Antozonite (type of fluorite) – acid, reeking pungent smell.

Anthraconite – tar smell.

 

Specific gravity

How dense something is, compared to the density of water. This has to do with with how many atoms are in a unit volume (and also, with the density of those atoms themselves.)

density 3d

Streak

The streak of a mineral is the color of the powder produced when it is dragged across a flat surface.

cinnabar pyrite streak

 

Tenacity

Tenacity is how a rock sample responds to stress.  Put some force on it, try to crush, bend, break, or tear it. What happens to the sample? Whatever happens as a result is a way of distinguishing one sample from another.

Brittleness

If a mineral is hammered and the result is a powder or small crumbs, it is considered brittle. Brittle minerals leave a fine powder if scratched, which is the way to test a mineral to see if it is brittle.”

Broken Brittle Rock

Malleability

If a mineral can be flattened by pounding with a hammer, it is malleable. All true metals are malleable.”

Malleability malleable

Ductility

“A mineral that can be stretched into a wire is ductile. All true metals are ductile.”

Here, reddish copper is inside a steel cup, with a small hole. Pressure is applied to the copper – and a small amount is pushed out through the hole. A tool grabs this exposed copper, and slowly pulls. As it pulls, more and more copper is drawn out in a tube.

ductile draw into wire

Sectility

“Sectile minerals can be separated with a knife, much like wax but usually not as soft. An example is Gypsum.”

Many metals and some minerals can be cut with knife such as aluminum, gypsum, lead, lithium, and magnesium.

Cutting metal Lithium Knife

.

 

Cleavage and fracture

Many forces can act on tectonic plates, on mountains, even on individual rocks. Those rocks usually stay together as one piece, because the atoms and molecules are holding each other with strong bonds.

If a force becomes stronger than the bonds holding the rock together then the rock breaks apart. It will cleave or fracture.

 

Cleavage

Cleavage planes form along the weakest area of mineral’s structure.

These breaks create flat, planar surfaces.

These surfaces are determined by the structure of its crystal lattice.

These cleavage planes are smooth and are usually reflective.

Note – If a mineral’s structure is equally strong in all directions then it will not have cleavage planes – then it will show fracture (see next section.)

cleavage rocks

Example

Mica has 1d cleavage

Mica has cleavage mineral

Lumen Geology, Identify and classify common rock forming minerals.

Fluorite octahedral cleavage

Calcite has rhombohedral cleavage.

 

Fracture

If a mineral’s structure is equally strong in all directions then it will not have cleavage planes. Then it will just break unevenly.

Fractures have no definite shape.

fracture crystal

Chrysotile has splintery fracture.

Chrysotile has splintery fracture

Quartz has conchodial fracture

Quartz conchodial fracture

Obsidian conchoidal fracture

Obsidian Conchoidal fracture

Limonite, bog iron ore, earthy fracture

Limonite bog iron ore Earthy fracture

Crystals of native copper Hackly fracture (jagged fracture)

Crystals of native copper Hackly fracture (jagged fracture)

Magnetite uneven fracture

Magnetite uneven fracture

 

Samples with both cleavage and fracture

Cleavage and fracture in potassium feldspar

Cleavage and fracture in potassium feldspar

Further examples

GG101 Lab Minerals

 

Terminology

Cleavage terms (only use if cleavage planes can be recognized):

Perfect – Produces smooth surfaces (often seen as parallel sets of straight lines), e.g. mica;

Imperfect – Produces planes that are not smooth, e.g. pyroxene;

Poor – Less regular.

Non-existent.

 

Fracture terms (use in all other cases):

Conchoidal – Fracture surface is a smooth curve, bowl-shaped (common in glass);

Hackly – Fracture surface has sharp, jagged edges;

Uneven – Fracture surface is rough and irregular;

Fibrous – Fracture surface shows fibres or splinters.

This section from

Geololgy, Rocks and Minerals, Univ. of Auckland

What are laws of nature?

You’ve heard of “laws of nature.” What are they?

A Serious Man Colorful Physics Chalkboard

Well, let’s start with the word “law: – what does it mean? Don’t shoot the messenger, but the same word sometimes means very different things. And this matters in science, especially when it comes to the “laws of nature.”

In ELA class you’ve hopefully learned about homographs – words spelled the same but have different meanings. For instance, what is a “bow?”

Homograph

bow – noun, the front of a boat

bow – verb, to bend at the waist.

bow – noun, a type of ribbon we used to decorate a present.

bow – noun, sporting equipment used to shoot arrows.

Wow, so all of these look and sound the same, yet they are entirely different words! Well, the same is true for the word “law.” It can refer to three different things:

* law, as in laws are made up by people, laws passed by governments

* law, as in natural law

* law, as in a law of nature

And all three of these things have nothing to do with each other! Let’s look at all three of these carefully:

———————————-

* “Law,” as in laws are made up by people, and passed by governments, aren’t actually “real” in any scientific sense. They aren’t part of the universe. They aren’t universally agreed on. And they don’t stay the same. They change all the time.

How old does one have to be in order to vote? How fast can you drive a car on the road? How much property tax does a homeowner have to pay on a house? None of those rules are part of the universe. These “laws”are just things that people agree on. Nothing more. People get together in communities or groups, they create clubs, or governments, and they make up rules so that (hopefully) society runs safely and smoothly. So in this sense, “law” means “a rule that, for now, our community has decided to follow.”

Writing Laws Legal Books

———————————-

* “Law,” as in natural law, is a belief that many people hold: there are universal moral laws in nature that mankind is capable of learning, and obligated to follow.

This idea is held by some religious groups and some schools of philosophy. It isn’t necessarily related to religion; there are many non-religious people who believe in the necessary existence of natural law.

ethics-morality

image from commons.wikimedia.org

———————————-

* “Law,” as in a law of nature, again is totally different from the other terms. Laws of nature are what we learn about in physics! In science, a “law” of nature is a rule for how things in the physical world work. Humans don’t decide what these laws are. Rather, we investigate the universe and discover what they are.

-> Laws of nature are factual truths, not logical. For instance, electrical charge is conserved – the total electric charge in an isolated system never changes. We can’t pass a law that says “positive charges can now be created.” Won’t work. Nothing humans say will change the way that the universe works,

Conservation of charge

-> Laws of nature are true for every time and every place. They are just as true on the moon, Mars as on Earth. They are just as true in Boston, Tokyo, or Kiev. And just as true 10,000 years ago as today, and as next year.

Rotating space stations in fact and science fiction

This resource is aligned with Artificial gravity in a space station. Some classes may prefer to start right here, learning about space stations in science fiction. This may inspire many students to be interested in science fiction as storytelling and literature. From there many students want to learn about how all this works. Other classes may prefer to start with the physics first, and then come back here for examples.

NASA 1950s concept

From Dan Beaumont Space Museum

In a 1952 series of articles written in Collier’s, Dr. Wernher von Braun, then Technical Director of the Army Ordnance Guided Missiles Development Group at Redstone Arsenal, wrote of a large wheel-like space station in a 1,075-mile orbit.

This station, made of flexible nylon, would be carried into space by a fully reusable three-stage launch vehicle. Once in space, the station’s collapsible nylon body would be inflated much like an automobile tire.

The 250-foot-wide wheel would rotate to provide artificial gravity, an important consideration at the time because little was known about the effects of prolonged zero-gravity on humans.

Von Braun’s wheel was slated for a number of important missions: a way station for space exploration, a meteorological observatory and a navigation aid. This concept was illustrated by artist Chesley Bonestell.

NASA/MSFC Negative Number: 9132079. Reference Number MSFC-75-SA-4105-2C

Wernher von Braun' Space Station Chesley Bonestell

2001 A Space Odyssey 

Perhaps the most scientifically accurate design of a rotating space ship comes from 2001: A Space Odyssey. This was a 1968 epic science fiction film by Stanley Kubrick, and the concurrently written novel by Arthur C. Clarke. The story was inspired by Clarke’s 1951 short story “The Sentinel.”

The film is noted for its scientifically accurate depiction of space flight. The space station was based on a 1950s conceptual design by NASA scientist Wernher Von Braun.

Space Station 2001 A Space Odyssey

Classic rotating spacestation designs

The High Frontier: Human Colonies in Space is a 1976 book by Gerard K. O’Neill, a road map for what the United States might do in outer space after the Apollo program, the drive to place a man on the Moon and beyond.

It envisions large manned habitats in the Earth-Moon system, especially near stable Lagrangian points. Three designs are proposed:

Island one (a modified Bernal sphere)

Island two (a Stanford torus)

Island 3, two O’Neill cylinders. See below.

These would be constructed using raw materials from the lunar surface launched into space using a mass driver and from near-Earth asteroids. The habitats spin for simulated gravity. They would be illuminated and powered by the Sun.

 O’Neill cylinder

Consists of two counter-rotating cylinders. The cylinders would rotate in opposite directions in order to cancel out any gyroscopic effects that would otherwise make it difficult to keep them aimed toward the Sun.

Each could be 5 miles (8.0 km) in diameter and 20 miles (32 km) long, connected at each end by a rod via a bearing system. They would rotate so as to provide artificial gravity via centrifugal force on their inner surfaces.

(This section adapted from Wikipedia.)

A pair of O'Neill cylinders. NASA ID number AC75-1085

A pair of O’Neill cylinders. NASA ID number AC75-1085

Rick Guidice, NASA Ames Research Center; color-corrector unknown

Rick Guidice, NASA Ames Research Center; color-corrector unknown

Inhabitants on the inside of the outer edge experience 1 g. When at halfway between the axis and the outer edge they would experience only 0.5 g. At the axis itself they would experience 0 g.

https://www.youtube.com/watch?v=qD3GMwg4qZo

Visions Of The High Frontier Space Colonies of 1970

Rama

In his 1973 science fiction novel Rendezvous with Rama, Arthur C. Clarke provides a vivid description of a rotating cylindrical spaceship, built by unknown minds for an unknown purpose.

http://www.nss.org/settlement/space/rama.htm

Rama video YouTube

Rama video – artist’s homepage and resources

RENDEZVOUS WITH RAMA (1)

Babylon 5

Babylon 5 was an American hard sci-fi, space-opera, TV series created by J. Michael Straczynski, that aired in the 1990’s. It was conceived of as a novel for television, each episode would be a single chapter. A coherent story unfolds over five 22-episode seasons. The station is modeled after the O’Neil design (above.)

It is an O’Neill cylinder 5 miles (8.0 km) long and 0.5–1.0 mile (0.80–1.61 km) in diameter.

Babylon 5 space station

Ringworld

Ringworld is a 1970 science fiction novel by Larry Niven, a classic of science fiction literature. It tells the story of Louis Wu and his companions on a mission to the Ringworld, a rotating wheel space station, an alien construct in space 186 million miles in diameter –  approximately the diameter of Earth’s orbit. It encircles a sunlike star.

It rotates to provide artificial gravity and has a habitable, flat inner surface – equivalent in area to approximately three million Earths. It has a breathable atmosphere and a temperature optimal for humans. Night is provided by an inner ring of shadow squares which are connected to each other by thin, ultra-strong wire.

Ringworld video

Ringworld Niven

Halo

Halo is a science fiction media franchise centered on a series of video games. The focus of the franchise builds off the experiences of Master Chief. The term “Halo” refers to the Halo Array: a group of immense, habitable, ring-shaped superweapons. They are similar to the Orbitals in Iain M. Banks’ Culture novels, and to a lesser degree to author Larry Niven’s Ringworld concept.

HALO

 

ELA/Literary connections

Short Story – “Spirals” by Larry Niven and Jerry Pournelle. First appeared in Jim Baen’s Destinies, April-June 1979. Story summary – Cornelius Riggs, Metallurgist, answers an ad claiming “high pay, long hours, high risk. Guaranteed wealthy in ten years if you live through it.”

The position turns out to be an engineering post aboard humanity’s orbiting habitat. The founders of “the Shack” dream of a livable biosphere beyond Earth’s gravity, a permanent settlement in space. However, Earth’s the economic conditions are getting worse, and the supply ships become more and more infrequent.

See the short story Spirals by Larry Niven and Jerry Pournelle.

Computer & math connections

The O’Neill Cylinder Simulator, by David Kann, Australia.

“In our discussion we came across the thought of what it might look like to throw a ball in the air in a zero-gravity rotating space station. I was stumped so I brought the question to my colleagues. They were stumped. Eventually I was able to make a pair of parametric equations for position in time to model the motion of the ball but it didn’t tell me much unless I could visualize the graph of the equations. The next logical step was to simulate the equations in software. Enter the O’Neill Cylinder Simulator:”

“When I saw the parametric equation animated (like above) it blew my mind a little. Here we see someone throwing a ball up and to the left, it circles above their head, and returns to them from the right. Throwing a ball in an O’Neill Cylinder apparently is nothing like on Earth. You can do some really sweet patterns:”

Spiral space station 1

Learning Standards

SAT Subject Test in Physics
Circular motion, such as uniform circular motion and centripetal force

2016 Massachusetts Science and Technology/Engineering Curriculum Framework
HS-PS2-1. Analyze data to support the claim that Newton’s second law of motion is a
mathematical model describing change in motion (the acceleration) of objects when
acted on by a net force.

HS-PS2-10(MA). Use free-body force diagrams, algebraic expressions, and Newton’s laws of motion to predict changes to velocity and acceleration for an object moving in one dimension in various situations

Massachusetts Science and Technology/Engineering Curriculum Framework (2006)
1. Motion and Forces. Central Concept: Newton’s laws of motion and gravitation describe and predict the motion of most objects.
1.8 Describe conceptually the forces involved in circular motion.

Great physics discussion questions!

Great physics discussion questions! These were written by Physicist Dr. Matt Caplan, who used to run the QuarksAndCoffee blog. That blog no longer exists, links to archived copies exist.

If everyone was Kung fu fighting, and their kicks really were fast as lightning, what would happen?

How many calories do superheroes burn using their powers?

What would happen if a 10 meter plasma sphere was transported from the Sun to Earth?

Dyson Sphere: Is there enough material in the solar system to build a shell to enclose the sun?

If it was cold enough for the atmosphere to condense, how deep would the ‘liquid air’ be?

Does my phone weigh more when the battery is charged?

How loud would a literal ‘shot heard round the world’ be?

Why are there seven colors in the rainbow?

Math

What are the odds of solving a Rubik’s cube by making random moves?

Why are some moons spherical while others are shaped like potatoes?

Why are some moons spherical while others are shaped like potatoes?

This blog post was written by Physicist Dr. Matt Caplan, who used to run the QuarksAndCoffee blog. That blog no longer exists, but I’m showing this archived copy of one of his posts for my students.

Short answer: Gravity likes to pull things together, which makes spheres. If the body is small enough gravity isn’t strong enough to deform it, which makes potatoes.

Long answer: Put a ball on top of a hill. What happens? It rolls down to the bottom. Why? Because gravity said so. This isn’t just how it works on the earth, but everywhere in the universe. Clearly, gravity is trying to make spheres. If you tried to dig a super deep hole stuff would fall in from the edges to fill it up. And what happen if we start to pile up rocks? Eventually, the pile of rocks reaches the point where it will all crumble down under its own weight. A sphere is the only shape that has no holes to fill or hills to crush. This is why every planet and star in the universe is round.

Of course, the earth and moon and planets aren’t perfect spheres. They’re lumpy. They’ve got hills and valleys and although none of them are that big compared to the planet, they’re still there. This is because gravity is strong enough to destroy (or prevent the formation) of a really big mountain, but not a small mountain. A small mountain’s own rigidness is enough to support its weight against gravity [1].

Mountain failure How High

This image shows two failure modes for mountains. The mountain on the left experiences shear failure, with the stress from the weight above the diagonal line exceeding the breaking point of the material. The mountain on the right fails due to compression of the base material.

Because materials have some intrinsic rigidity there must be bodies whose gravity isn’t strong enough to pull them into a sphere. Rather, the material is stiff enough to keep an oblong shape. After all, satellites and astronauts and cows don’t collapse into spheres in space.

The limit where gravity is strong enough to overcome the material properties of a body and pull it into a sphere is called the Potato Radius, and it effectively marks the transition from asteroid to dwarf planet [2]. It’s about 200-300 km, with rocky bodies having a slightly larger Potato Radius than icy bodies.

You can use some complicated math with material elasticity, density, and gravity to calculate the Potato Radius from scratch, or you could just look at Mt Everest. It turns out that the same physics determining the maximum height of mountains can be used to determine the Potato Radius – after all, they’re both just the behavior of rocks under gravity.

Check this out. The heights of the tallest mountains on Earth and Mars obey an interesting relation:

height gravity mountains equation

If you know the height of Everest and that Mars surface gravity is 2/5ths of Earth, then you know that Olympus Mons (tallest mountain on Mars) is about 5/2× taller than Everest! This relation also works with Maxwell Montes, the tallest mountain on Venus, but not for Mercury. Planetary science is a lot like medicine in this sense- there are always exceptions because everything is completely dependent on the body you’re looking at.

This is more than a curiosity. It tells us something important. The height of the tallest mountain a planet can support, multiplied by that planet’s surface gravity, is a constant.

For this sake of this piece I’ll call it the Rock Constant because that sounds cool. So why am I spending so long on a tangent about mountains in a piece about potato moons? It’s because the Potato Radius and Rock Constant are determined by the same things – gravity and the elasticity of rock! We can use the Rock Constant to estimate the Potato Radius!

Consider an oblong asteroid. Let’s pretend this asteroid is actually a sphere with a large mountain whose height is equal to the radius of that sphere.

potato shaped asteroid or moon

As the radius of a body increases the maximum height of a mountain decreases. If the radius was any bigger the mountain would have to be shorter and our asteroid would be entering ‘sphere’ territory.

Let’s check if the radius of this imaginary asteroid is close to the Potato Radius using our relation for the Rock Constant:

height asteroid gravity equation

Height asteroid 3

And now we have everything we need:

 

height asteroid 4

This works out to about 240 km [1], right in the middle of the 200-300 km range of the more rigorous calculation!

(1) How High Can A Mountain Be? P. A. G. Scheuer, Journal of Astrophysics and Astronomy, vol. 2, June 1981, p. 165-169.

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How high can a mountain grow?

There is some kind of process that builds mountains, but there also must be something limiting that process. After all, we don’t see mountains 20 or 30 miles tall, right? So we must ask, how high can a mountain grow?

We start by asking, what are the highest mountains on Earth?

Which then brings up the next question, what do we mean by “highest”? The answer isn’t obvious because there are three different ways to think about “highest” – see this diagram.

Highest Mountain on the Earth

Given this, we next notice that most mountains on Earth are nowhere near this height. For instance, the highest mountain in New England is Mount Washington New Hampshire 1,900 m (6,300 ft.). The highest mountain in the Rocky Mountains in Mount Elbert in Colorado 4400 m (14,000 ft.)

In general, almost everywhere on our planet, the highest that a mountain can be is about half the height of Everest.  This is as tall as a mountain can grow on a lithospheric tectonic plate.

So our next question is, “why is there one set of rules for the highest that a mountain can be almost everywhere on Earth, and why do some locations have exceptions?”

What factors control the height of a mountain?

There is a balance of the forces:

Tectonic plate forces pushes the Earth’s crust upward.

Gravity pulls the mountain downward.

And, when the mountain is high & big enough, the weight of the mountain can crack and shatter the rock inside of it. This causes the mountain to crumble, and settle down to a lower height.

Don’t believe me? Even rock has a maximum amount of strength. Here is a GIF of what happens to solid rock when you put enough pressure on it! 🙂

Source: Unconfined compressive strength test of rock

Thus, if the weight of mountain > yield strength of the base rock then the mountain’s base will crumble.

Then he mountain will compress down to the maximum allowable height.

Of course, when this happens depends on what the mountain is made of. SiO2 is the most common molecule. But there are many minerals that are lighter, or stronger, or both, that can also be found in a mountain.

By the way, this gives us a neat relation – the surface gravity X maximum height of a mountain should be a constant.

Formula lets us relate height of Mt Everest on earth and Olympus Mons on Mars. Or find max deformation of asteroid before gravity pulls it into a sphere.

All the other downward forces on a mountain

Erosion wears the mountain down

How well does the mountain resist weathering/erosion? This depends on what kind of chemicals it is made out of.

Does being in the ocean affect how high a mountain can be?

Consider Mauna Kea, in Hawaii.

Much of Mauna Kea is underwater. It’s base can support more pressure since it’s underwater. Underwater, there is a buoyant force on the object that counteracts the force of gravity. Since nothing counteracts the gravity on Mount Everest, the mountain’s base can only support so much pressure.

Roy Blitz

What else makes mountains rise or grow?

Even while a mountain is eroding, the underlying plate activity may be forcing the mountain to grow higher.

A tectonic plate pushing more directly against another plate will create higher mountains than a plate moving less directly (say, at an angle) against another plate.

How strong are the crustal roots of the mountain?

As a mountain range grows in height, this root grows in depth, and thus the pressure and temperature experienced by the bottom of this root increases.

At a certain point, rocks in the base of this crustal root metamorphose into a rock called eclogite. At that point this rock will be denser than the material supporting the crustal root.

This causes delamination to occur. Depending on the amount of material removed, the rate of new material added, and erosion, scenarios with net increases or decreases in elevation are possible after a delamination event. This sets another limit on how thick a crustal root can get (and thus how high a mountain range grow on the long term).

Source, Reddit comment

Why are there some special spots on Earth where mountains can grow twice as high?

George W Hatcher writes

Mauna Kea rests on oceanic crust, which is denser than continental crust and able to support more weight without displacement. Being mostly inundated with seawater precludes some of the erosional processes to which mountains exposed to the upper atmosphere are subjected.

In addition, the very material of which Mauna Kea is composed (basaltic igneous rocks) is stronger than the variety of rocks that make up the continental crust and uplifted limestone seafloor that can be found atop Everest.

The actual lithospheric limit to mountain height averages about half the height of Everest, which is why Fourteeners are so famous in Colorado. Mountains that exceed this limit have local geologic circumstances that make their height possible, e.g. stronger or denser rocks.

In the case of Everest and the Himalayas, you have a geologic situation that is very rare in Earth history. The Indian plate is ramming into the Eurasian plate with such force that instead of just wrinkling the crust on either side into mountain ranges it has actually succeeded in lifting the Eurasian plate up on top.

So the Himalayas have double the thickness of the average continental plate, thus double the mountain height that would be considered “normal”.

George W Hatcher, Planetary Scientist, Aerospace Engineer

References

How high can a mountain possibly get? Earth Science StackExchange

How High can a mountain get? 2 Earth Science Stack Exchange

How tall can a mountain become on Earth? Quora

What is the theoretical limit to how tall mountains can get on Earth? Reddit

Glacial Buzz Saw Hypothesis: New Scientist article

Examples with math details

Why are some moons spherical while others are shaped like potatoes? Quarks & Coffee

How High Can Mountains Be? Talking Physics

How High Could A Mountain Be? Physics World hk-phy.org

How tall can I make a column of stone? Rhett Allain, Wired magazine columnist

Related lab ideas

Play Doh Modeling Folds: Block Diagrams and Structure Contours

Play-Doh Modeling Folds: Block Diagrams and Structure Contours

Play Doh Introduction to Igneous Intrusions

Play Doh Unconformities

Unmasking mask myths

We are living in an era of a viral pandemic, COVID-19, in which viral particles are spread through the air from one person to another. Numerous scientific studies show that if most people even simple cloth face masks while near each other, this dramatically reduced the viral particles in the air, and increases safety. The effect of wearing masks is so effective that in areas where people follow social distancing & mask rules, the incidence of COVID is shrinking.

However, there has been a growing resistance to wearing a mask, fueled by conspiracy theories, pseudoscience, and Russian social media troll farms deliberately spreading misinformation. It now appears that millions of Americans believe that wearing a face mask is unhealthy.

Many of us have met individuals who claimed that face masks either “block oxygen from getting in” or “make us breathe carbon monoxide.”  Both claims are literally impossible, yet widely believed. So if we have a student make such a claim then how can we turn this into a teachable moment?

Face masks

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Addressing the carbon monoxide claim

Revisit the equation for cellular respiration. This process is how all cells in our body work – and this process doesn’t produce carbon monoxide!

So if someone makes this claim then ask them “Where, specifically, is this carbon monoxide coming from?”

If they give a vague response ask them to clarify and back up their answer with a source.  If they look into it for even a minute they will quickly see that their claim is impossible.

Addressing the “air can’t get through the mask” claim

Conspiracy theorists try to have it both ways: They claim that the virus particles are so small that they can get through the mask (and supposedly, therefore would make us sick) yet also claim that the oxygen molecules are too large to pass through the mask, so we (supposedly) get low oxygen and brain damage.

The obvious problem is that the virus particle is over 250 times larger than an oxygen molecule!  The covid molecule is 0.125 microns while an O2 molecule is only 0.0005 microns.

Also, to be clear, single viral particles don’t make people sick. The disease is only spread if people inhale multiple exhalation water-virus droplets, each drop let being thousands of times larger than a viral particle, and each drop containing at least many hundreds of viral particles each. And these drops are what the masks are pretty good at filtering.

CoVid-19 coronavirus particle

Image created by Fusion Animation.

Addressing the low amount of oxygen claim

First off, even without a virus, your body automatically adapts to lower levels of oxygen in the air. If that weren’t the case then anyone who visited a high altitude city like Denver, Colorado, would have died!  As we all know, up in Denver the air is thinner, so there are a lot less O2 molecules around. But we adjust, and as long as we don’t play NFL caliber football for an hour, we’re just fine.

The other claim is that these face masks “trap our breath” preventing us from getting oxygen, so that our O2 blood levels fall.  But see for yourself – they don’t do that!

covid Mask blood oxygen level

Photo credit. Dr. Megan Hall

Dr. Megan Hall writes:

Below is me in 4 scenarios. I wore each mask for 5 minutes and checked my oxygen saturation (shown as the percentage below) along with my heart rate (HR, in beats per minute) using noninvasive pulse oximetry. Keep in mind, immediately prior to this, I had been wearing the surgical mask for 5 hours.

Results:
No mask: 98%, HR 64
Surgical mask: 98%, HR 68
N95 mask: 99%, HR 69
N95 plus surgical mask (which is how most healthcare providers are wearing masks): 99%, HR 69.

Finally, if “breathing in your own breath is dangerous” then how come it was perfectly safe – and sometimes necessary! – to perform CPR with mouth to mouth resuscitation?

The air that a person exhales has more than enough O2 to keep someone else alive, and there never was any concern about CO (carbon monoxide) or CO2 from our exhalation harming someone else.

How well do masks work?

They don’t need to stop all droplets. COVID is dangerous not because some particles are airborne (thats true for tons of viruses) but because (a) it transmits more easily, and (b) causes more damage.  When we reduce the number of droplets released, then the spread of covid significantly decreases.

Here is a video from Dr. Joe Hanson, from “It’s ok to be smart.” It is an awesome, slow-motion schlieren imaging experiment that demonstrates why masks work.

How Well Do Masks Work? (Schlieren Imaging In Slow Motion!)

References for “How Well Do Masks Work?”

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