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What does “law” mean in “laws of nature?” ELA and Science
What does the word “law” mean in the phrase “laws of nature?” We won’t be able to understand the science until we understand the English.
In our English language arts classes we have learned about homographs – words spelled the same but have different meanings.
For instance, what is a “bow?” With the same spelling it used for 4 entirely different words.
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.
The same is true for the word “law.” It can refer to three different things:
Laws made up by people
City, state, or national “laws” aren’t real in any scientific sense. They aren’t part of the universe. They don’t even 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, clubs, or governments, and decide upon rules so that (hopefully) their society runs safely and smoothly.
Natural law
The idea of natural law is a somewhat controversial idea in philosophy, ethics, and religion. The idea is that 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.
image from commons.wikimedia.org
Laws of nature
In physics, a law of nature is something scientists have learned about how things in our physical world actually work.
A law of nature is a precise relationship between physical quantities, and is expressed as an equation.
Laws of nature are relationships universally agreed upon – but not agree upon because we want this relationship to exist. Rather, the law is only accepted because repeated experiments show us that this relationship exists.
People don’t decide what nature’s laws are. People can only investigate and discover what they are.
Here’s an example: Electrical charge is conserved. The total electric charge in an isolated system never changes. People can’t pass a law that says “positive charges can now be created.” That won’t work. Nothing humans say changes the way that the universe works,
Laws of nature are true for every time and every place. They are just as true in Michigan, Moscow, or Miami, just as true on the Moon or on Mars. They are just as true 10,000 years ago as today, and as next year.
We explore the concept of laws of nature in more detail here – What are laws of nature? What are theories?
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Thanks for reading. While you’re here see our other articles on astronomy, biology, chemistry, Earth science, mathematics, physics, the scientific method, and making science connections through books, TV and movies.
Rotating space stations in fact and science fiction
This resource – rotating space stations in fact and science fiction – may be used with our resource on Artificial gravity in a space station.
Some people prefer to start here, learning the ideas and designs first, and then look at the physics in more detail. Others prefer the reverse order. Both ways are fine.
Big idea: Building a rotating space station with artificial gravity isn’t a far-out sci-fi idea. The idea has its roots in firm, realistic engineering & science. Most of the designs based on this idea are quite realistic (at least until we get to the world-sized megastructures at the end of this unit.)
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.
Graphic – NASA/MSFC Negative Number: 9132079. Reference Number MSFC-75-SA-4105-2C
2001 A Space Odyssey
Perhaps the most classic 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.
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.
The space station in the TV series Babylon 5 is modeled after this kind of design.
(This section adapted from Wikipedia.)
A pair of O’Neill cylinders. NASA ID number AC75-1085
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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 – artist’s homepage and resources
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.
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 sun-like 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. These are far from the surface of the ringworld, orbiting closer to the star. These squares are connected to each other by thin, ultra-strong wire.
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.
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:”
Also see Rotating space stations with counter rotating segments
Thanks for reading. While you’re here see our other articles on astronomy, biology, chemistry, Earth science, mathematics, physics, the scientific method, and making science connections through books, TV and movies.
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.
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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].
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:
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.
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:
And now we have everything we need:
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.
Web.archive.org copy
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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.
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.
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).
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
How Do Airplanes Fly?
How do airplanes fly? And for that matter, how do sharks swim through water? Both are massive objects with interesting shapes moving through a fluid (both air and water are fluids.)
After all this time you’d think that we know all the details of how an airplane flies. There must be some specific and agreed-upon explanation. Air hits a plane, air and plane then follow laws of physics, and voilà, the plane flies, right?
Although flight indeed is in accord with the laws of physics, the specific ideas about how this happens are incomplete and controversial.
What’s the controversy about? What new ideas are being proposed?
Bernoulli theorem idea
(Here the class will look into the general idea.)
image from http://www.thaitechnics.com
This explanation is from the Scientific American article.
Newton’s laws of motion
(Here the class will look into the general idea.)
This explanation is from the Scientific American article.
New Theories of lift
These ideas are also from the Scientific American article.
How do fish fly through water?
Just as aerodynamics explains how airplanes generate lift and fly through the air. hydrodynamics explains how fish generate lift and fly through water.
And yes, fish do fly through water. If they stop moving, then they literally fall down to the bottom of the ocean.
We all know how interesting hammerhead sharks are. Why do their heads have this peculiar shape?
Part of it has to do with the fact that their head is a giant electromagnetic sensor; it can detect the EM fields of nearby prey. But evolution optimizes body design in more than one way. Sharks need to do more than sense prey, they need to move efficiently.
This recent paper, A hydrodynamics assessment of the hammerhead shark cephalofoil, shows that the shape of their head may increase maneuverability as well as produce dynamic lift similar to a cambered airplane wing.
See Gaylord, M.K., Blades, E.L. & Parsons, G.R. A hydrodynamics assessment of the hammerhead shark cephalofoil. Scientific Reports 10, 14495 (2020). https://doi.org/10.1038/s41598-020-71472-2
Also see : Pioneers of flight, How do airplanes fly?, the graveyard spiral, and breaking the sound barrier – Flight
References
No One Can Explain Why Planes Stay in the Air: Do recent explanations solve the mysteries of aerodynamic lift? By Ed Regis
Scientific American, February 2020, Volume 322, Issue 2
Aerodynamic Lift, Part 1: The Science, Doug McLean, The Physics Teacher Vol. 56, issue 8, 516 (2018)
https://doi.org/10.1119/1.5064558
Aerodynamic Lift, Part 2: A Comprehensive Physical Explanation, Doug McLean, The Physics Teacher Vol. 56, 521 (2018)
https://doi.org/10.1119/1.5064559
Understanding Aerodynamics: Arguing from the Real Physics, Doug McLean. Wiley, 2012
You Will Never Understand Lift. Peter Garrison, Flying; June 4, 2012.
Flight Vehicle Aerodynamics. Mark Drela, MIT Press, 2014.
#Flight #aerodynamics #Bernoulli #Lift
Learning Standards
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.
A FRAMEWORK FOR K-12 SCIENCE EDUCATION: Practices, Crosscutting Concepts, and Core Ideas
PS2.A: FORCES AND MOTION
How can one predict an object’s continued motion, changes in motion, or stability?
Interactions of an object with another object can be explained and predicted using the concept of forces, which can cause a change in motion of one or both of the interacting objects… At the macroscale, the motion of an object subject to forces is governed by Newton’s second law of motion… An understanding of the forces between objects is important for describing how their motions change, as well as for predicting stability or instability in systems at any scale.
NGSS
2016 High School Technology/Engineering
HS-ETS1-2. Break a complex real-world problem into smaller, more manageable problems that each can be solved using scientific and engineering principles.
HS-ETS1-4. Use a computer simulation to model the impact of a proposed solution to a complex real-world problem that has numerous criteria and constraints on the interactions within and between systems relevant to the problem.
College Board Standards for College Success: Science
PS-PE.1.2.2 Analyze force diagrams to determine if they accurately represent different real-world situations.
PS-PE.1.2.4 Given real-world situations involving contact, gravitational, magnetic or electric charge forces and an identified object of interest:
PS-PE.1.2.4a Identify the objects involved in the interaction, and identify the pattern of motion (no motion, moving with a constant speed, speeding up, slowing down or changing [reversing] direction of motion) for each object.
PS-PE.1.2.4b Make a claim about the types of interactions involved in the various situations. Justification is based on the defining characteristics of each type of interaction.PS-PE.1.2.4c Represent the forces acting on the object of interest by drawing a force diagram.
PS-PE.1.2.4d Explain the observed motion of the object. Justification is based on the forces acting on the object.
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Iridescence and thin film interference
Iridescence is a spectacular optical trick – it is the creation of color without pigment!
Consider surfaces that gradually change color as the angle changes. Soap bubbles, feathers, butterfly wings, some seashells, and certain minerals. Let’s dig in to what causes this phenomenon.
The word iridescence comes from Iris (Ἶρις) the Greek goddess of the rainbow.
There are three ways to get color
Additive color – mixing together light of two or more different colors. Red, green, and blue are the additive primary colors normally used in additive color systems such as smartphones, TVs, projectors and computer displays.
Subtractive color – uses dyes, inks, or pigments to absorb some wavelengths of light and not others. The color that we see comes from the wavelengths of light that are not absorbed by these chemicals.
But iridescence is nature’s special, third way of producing color. In this method, color is created by wave interference with tiny physical structures on the scale of the color’s wavelength.
Iridescence in animals
Iridescence: a functional perspective
Iridescence in minerals
Bismuth is a great example of thin-film interference.
The colors come from a thin film of bismuth(III) oxide that forms on the surface if the crystals are formed in air.
Chemistry.stackexchange What causes the iridescent colour in bismuth?
The physics of thin film interference
Thin-film interference is a natural phenomenon.
In it, light waves reflected by the upper and lower boundaries of a thin film interfere with one another. The result either enhances or reduces the reflected light.
When the thickness of the film is an odd multiple of one quarter-wavelength of the light on it, the reflected waves from both surfaces interfere to cancel each other.
Since the wave cannot be reflected, it is completely transmitted instead.
When the thickness is a multiple of a half-wavelength of the light, the two reflected waves reinforce each other, thus increasing the reflection and reducing the transmission.
Thus when white light, which consists of a range of wavelengths, is incident on the film, certain wavelengths (colors) are intensified while others are attenuated.
Thin-film interference explains the multiple colors seen in light reflected from soap bubbles and oil films on water.
It is also the mechanism behind the action of antireflection coatings used on glasses and camera lenses.
https://en.wikipedia.org/wiki/Thin-film_interference
http://physics.highpoint.edu/~jregester/potl/Waves/InterferenceColors/interfcolors.html
Videos for thin film interference
Apps
Molecular Expressions Interference Phenomena in Soap Bubbles
https://micro.magnet.fsu.edu/primer/java/interference/soapbubbles/
Optical Interference – Java Tutorial
https://www.olympus-lifescience.com/en/microscope-resource/primer/java/interference/
Molecular Expressions – Interference Between Parallel Light Waves
https://micro.magnet.fsu.edu/primer/java/interference/waveinteractions2/index.html
Physics Hanukkah Fun
A goal of Social Studies is to expose students to the diversity of ethnic, religious, and cultural observances in our world. The College, Career, and Civic Life (C3) Framework for Social Studies State Standards notes that students should be able to describe how religions are embedded in culture and cannot only be isolated to the “private” sphere, and identify which religious communities are represented or obscured in public discourse.
A goal of science education is to see how basic laws of nature allow us to understand all phenomenon in our physical universe, from the simplest (fire and candles) to the most complex (how stars work.)
During the holiday season many science teachers do something fun on the physics of Christmas (Google that; thousands of results.) Yet there are more religions than Christianity and more phenomenon related to holidays. In the spirit of science and multiculturalism here we can look at the physics and chemistry of Hanukkah.
What is Hanukkah about?
Hanukkah is a minor Jewish holiday. It doesn’t come from the Hebrew Bible but instead from the book of Maccabees, part of the Jewish apocrypha. It is also known as Hag ha’urim, the Festival of Lights.
Hanukkah is a Hebrew word meaning “dedication.” It refers to the eight-day celebration during which Jews commemorate the victory of the Maccabees over the Hellenistic Syrians in 165 B.C.E. and the subsequent rededication of the Temple in Jerusalem. Hanukkah is specifically about countering antisemitism and was the first successful war for religious freedom.
Celebrations center around the lighting of the hanukkiyah (menorah,) foods prepared in oil, including latkes (potato pancakes) and sufganiyot (jelly doughnuts), songs and games. – Intro to Hanukkah
The Hebrew name Maccabee means “hammer”, and referred first to a leader of the revolt, Judas, the third son of Mattathias.
Capillary action
During the holiday Jewish people light a Chanukah menorah מנורת חנוכה, also called a Ḥanukiyah חַנֻכִּיָּה.
The wick is above the oil, drawing fluid up the wick through capillary action. What exactly is capillary action?
Capillary action & molecule forces
Oil is drawn up through capillary action, also called wicking.
This is a tale of two competing forces:
There is an adhesive force between the oil molecules and the cotton molecules.
And there is an intermolecular/cohesive force between the oil molecules.
Cohesion = ability of like molecules to stick together
Adhesion = ability of dissimilar molecules to stick together
from Bioninja
When the adhesion force > cohesion force then the oil molecules are slowly pulled into the wick.
From Hyperphysics, Surface tension
The following explanation is adapted from the discussion by Sean Snider, on Quora.
A fluid such as heating oil will tend to flow upwards against gravity due to capillary motion.
The individual atoms in the oil will interact with the fiber atoms to cause adhesion.
The oil atoms will bump into the fiber atoms – and move upwards due to intermolecular forces.
The difference in charge between the two types of atoms causes them to repel in all directions, including up.
The oil atoms will keep moving up – unless the forces between them cause them to clump together so that intermolecular forces weaken.
In that case their collective mass is too much to repel the force of gravity.
Typically the density of the fiber itself prevents the oil particles from clumping enough to reach this threshold. Thus they continue to move upward.
This allows the oil to reach the top of the wick and burn.
Instead of the fiber burning quickly, the oil burns.
(Some of the fiber also burns, but much less quickly.)
Capillary action student activities
Wick lab/game! sciensation.org
Capillary action and diffusion lab
Lights, Camera, (Capillary) Action! Scientific American
Convection & temperature differentials
The heat from the flame warms up the small olive oil vessels, below.
Those vessels are often transparent.
That heat causes a temperature differential: warmer oil at the top and cooler oil at the bottom.
This would cause convection and/or turbulence in the fluid.
This should be visible if we record it with a high speed, high-resolution smartphone camera.
Convection, turbulence, and related topics are usually left out of high school physics curriculum, so this might be a fun way to introduce it.
Experiment: Add a drop of coloring into oil. Light the wick.
Then we can visually observe the convection currents.
Dreidel physics
A dreidel (Yiddish: דרײדל) or sevivon (Hebrew: סביבון) is a four-sided spinning top, played by children during the Jewish holiday of Hanukkah. Contrary to popular belief, this toy is not part of the Hanukkah story. It is a Jewish variant on the teetotum, a gaming toy found in many European cultures.
Through use and observation of a dreidel students may be inspired to understand how it works, which requires knowledge of angular momentum, rotational motion, gyroscopes, and precession.
One idea for class use is to record the motion with a high speed camera, and then play the footage back in slow motion, to reveal details of motion that would not be clearly visible to the naked eye.
Let’s take a look at Extreme High-Speed Dreidel Physics by Alexander R. Klotz:
… a dreidel is an example of a spinning top, a source of extremely difficult homework problems in undergraduate classical mechanics related to torque and angular momentum and rigid body motion and whatnot. I was chatting with a theorist I know who mentioned that it would be fun to calculate some of these spinning-top phenomena for the dreidel’s specific geometry (essentially a square prism with a hyperboloid or paraboloid base), and I suggested trying to compare it to high-speed footage [1000 frames per second] ….
Check out the article and videos here.
Related dreidel topics to investigate
What keeps spinning tops upright? Ask a Mathematician/Physicist
What is precession? It is a change in the orientation of the rotational axis of a rotating body. In geometry we would say that if the axis of rotation of a body is itself rotating about a second axis, that body is said to be precessing about the second axis.
Precession (Wikipedia)
Dreidels also follow the law of conservation of angular momentum. We learn more about that in Angular momentum
And a dreidel itself is similar to a gyroscope.
The statistics of dreidel motion
Are dreidels fair? In other words, does the average dreidel have an equal chance of turning up any one of its four sides? Dreidel Fairness Study
Ultra High Speed Physics.
You’re not a mad scientist unless you ask questions like “Imagine a game of dreidel with a 60-billion-RPM top….” Focus: The Fastest Spinners. APS Physics
How is the holiday spelled? ELA connections
Why write “Hanukkah” instead of “Chanukah” – surely one spelling is right and the other is wrong? The reason for the spelling confusion is the limitations of the English alphabet. Hanukkah is a Hebrew word (חנוכה)
That first Hebrew letter of this word, ח , has a guttural sound. This sound used to exist in ancient English but doesn’t exist in modern English. The modern pronunciation of this letter is a voiceless uvular fricative (/χ/)
As such there is no one correct-and-only way to transliterate this letter. Over the past 2 centuries four ways have developed:
KH – Khanukah (used in old fashioned translations of Yiddish)
CH – Chanukah
H – Hanukkah (the extra ‘k’ is added just to make it 8 letters long.)
H – Ḥanukah (notice the H with a dot under it.)
Each of these is equally valid.
History, art, and social justice connections
Hanukkah and the Maccabees have been a common theme in classical Christian art, sculpture, and music. The story of the Maccabees is a part of Western Civilization through both Jewish and Christian culture. In this article one can see the art, music, and sculpture of Hanukkah.
On a related social justice note, a big part of being anti-racist is listening to voices. Make space to learn from the lived experiences of our students, their families, and their communities. As such I would like to share this:
Hanukkah is about countering antisemitism: Be aware of Hanukkah Erasure.
Learning Standards
College Board Standards for College Success in Science
ESM-PE.1.2.1 Describe and contrast the processes of convection, conduction and radiation, and give examples of natural phenomena that demonstrate these processes.
ESM-PE.1.2.1c Use representations and models (e.g., a burning candle or a pot of boiling water) to demonstrate how convection currents drive the motion of fluids. Identify areas of uneven heating, relative temperature and density of fluids, and direction of fluid movement.
Next Generation Science Standards
MS-PS1-4. Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed.
Massachusetts Science and Technology/Engineering Curriculum Framework
7.MS-PS3-6 (MA). Use a model to explain how thermal energy is transferred out of hotter regions or objects and into colder ones by convection, conduction, and radiation.
College, Career, and Civic Life (C3) Framework for Social Studies State Standards
College, Career, and Civic ready students:
D2.Rel.4.9-12: Describe and analyze examples of how religions are embedded in all aspects of culture and cannot only be isolated to the “private” sphere.
D2.Rel.12.9-12: Identify which religious individuals, communities, and institutions are represented in public discourse, and explain how some are obscured.
Transliteration of Hebrew letters
Library of Congress (USA) ALA-LC Romanization Tables
The nature of time
What is time?
What is time? Where does time come from?
In what way is time really something objective? (something actually out there?)
In what ways is time not objective? (so it would be just a way that humans use to describe our perception of the universe)
What is time?
Why does time never go backward?
The answer apparently lies not in the laws of nature, which hardly distinguish between past and future, but in the conditions prevailing in the early universe.
The Arrow of Time, Scientific American article. David Layzer
Is there a relationship between time and the second law of thermodynamics?
Before reading further, understand that these topics require at least some familiarity with the laws of Thermodynamics
“According to many, there might be a link between what we perceive as the arrow of time and a quantity called entropy…. [but] as far as we can tell, the second law of thermodynamics is true: entropy never decreases for any closed system in the Universe, including for the entirety of the observable Universe itself. It’s also true that time always runs in one direction only, forward, for all observers. What many don’t appreciate is that these two types of arrows — the thermodynamic arrow of entropy and the perceptive arrow of time — are not interchangeable.”
No, Thermodynamics Does Not Explain Our Perceived Arrow Of Time, Starts With A Bang, Ethan Siegel, Forbes
No, Thermodynamics Does Not Explain Our Perceived Arrow Of Time
Is time (and perhaps space,) quantized?
Ethan Siegel leads us in a fascination discussion:
The idea that space (or space and time, since they’re inextricably linked by Einstein’s theories of relativity) could be quantized goes way back to Heisenberg himself.
Famous for the Uncertainty Principle, which fundamentally limits how precisely we can measure certain pairs of quantities (like position and momentum), Heisenberg realized that certain quantities diverged, or went to infinity, when you tried to calculate them in quantum field theory….
It’s possible that the problems that we perceive now, on the other hand, aren’t insurmountable problems, but are rather artifacts of having an incomplete theory of the quantum Universe.
It’s possible that space and time are really continuous backgrounds, and even though they’re quantum in nature, they cannot be broken up into fundamental units. It might be a foamy kind of spacetime, with large energy fluctuations on tiny scales, but there might not be a smallest scale. When we do successfully find a quantum theory of gravity, it may have a continuous-but-quantum fabric, after all.
Are Space And Time Quantized? Maybe Not, Says Science
Even In A Quantum Universe, Space And Time Might Be Continuous, Not Discrete
Theoretical physics: The origins of space and time
Avogadro’s law
Previously in Chemistry one has learned about Avogadro’s hypothesis:
Equal volumes of any gas, at the same temperature and pressure, contain the same number of molecules.
Reasoning
(from Modern Chemistry, Davis, HRW)
In 1811, Avogadro found a way to explain Gay-Lussac’s simple ratios of combining volumes without violating Dalton’s idea of indivisible atoms. He did this by rejecting Dalton’s idea that reactant elements are always in monatomic form when they combine to form products. He reasoned that these molecules could contain more than one atom.
Avogadro also put forth an idea known today as Avogadro’s law: equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.
It follows that at the same temperature and pressure, the volume of any given gas varies directly with the number of molecules.
Avogadro’s law also indicates that gas volume is directly proportional to the amount of gas, at a given temperature and pressure.
Note the equation for this relationship.
V = kn
Here, n is the amount of gas, in moles, and k is a constant.
Avogadro’s reasoning applies to the combining volumes for the reaction of hydrogen and oxygen to form water vapor.
Dalton had guessed that the formula of water was HO, because this formula seemed to be the most likely formula for such a common compound.
But Avogadro’s reasoning established that water must contain twice as many H atoms as O atoms, consistent with the formula H2O.
As shown below, the coefficients in a chemical reaction involving gases indicate the relative numbers of molecules, the relative numbers of moles, and the relative volumes.
The simplest hypothetical formula for oxygen indicated 2 oxygen atoms, which turns out to be correct. The simplest possible molecule of water indicated 2 hydrogen atoms and 1 oxygen atom per molecule, which is also correct.
Experiments eventually showed that all elements that are gases near room temperature, except the noble gases, normally exist as diatomic molecules.
As an equation
Avogadro’s Law – also known as Avogadro–Ampère law
when temperature and pressure are held constant:
volume of a gas is directly proportional to the # moles (or # particles) of gas
n1 / V1 = n2 / V2
or
What does this imply?
As # of moles of gas increases, the volume of the gas also increases.
As # of moles of gas is decreased, the volume also decreases.
Thus, # of molecules (or atoms) in a specific volume of ideal gas is independent of their size (or molar mass) of the gas.
Important! This is not a law of physics!
Rather, this is a generally useful rule, which is only valid when gas temperature and pressure is low enough for the atoms to usually be far apart from each other. As we begin to deal with more extreme cases, this rule doesn’t hold up.
At what point does Avogadro’s law not apply?
Example problems
These problems are from The Chem Team, Kinetic Molecular Theory and Gas Laws
Example #1: 5.00 L of a gas is known to contain 0.965 mol. If the amount of gas is increased to 1.80 mol, what new volume will result (at an unchanged temperature and pressure)?
Solution:
I’ll use V1n2 = V2n1
(5.00 L) (1.80 mol) = (x) (0.965 mol)
x = 9.33 L (to three sig figs)
Example #2: A cylinder with a movable piston contains 2.00 g of helium, He, at room temperature. More helium was added to the cylinder and the volume was adjusted so that the gas pressure remained the same. How many grams of helium were added to the cylinder if the volume was changed from 2.00 L to 2.70 L? (The temperature was held constant.)
Solution:
1) Convert grams of He to moles:
2.00 g / 4.00 g/mol = 0.500 mol
2) Use Avogadro’s Law:
V1 / n1 = V2 / n2
2.00 L / 0.500 mol = 2.70 L / x
x = 0.675 mol
3) Compute grams of He added:
0.675 mol – 0.500 mol = 0.175 mol
0.175 mol x 4.00 g/mol = 0.7 grams of He added
Example #3: A balloon contains a certain mass of neon gas. The temperature is kept constant, and the same mass of argon gas is added to the balloon. What happens?
(a) The balloon doubles in volume.
(b) The volume of the balloon expands by more than two times.
(c) The volume of the balloon expands by less than two times.
(d) The balloon stays the same size but the pressure increases.
(e) None of the above.
Solution:
We can perform a calculation using Avogadro’s Law:
V1 / n1 = V2 / n2
Let’s assign V1 to be 1 L and V2 will be our unknown.
Let us assign 1 mole for the amount of neon gas and assign it to be n1.
The mass of argon now added is exactly equal to the neon, but argon has a higher gram-atomic weight (molar mass) than neon. Therefore less than 1 mole of Ar will be added. Let us use 1.5 mol for the total moles in the balloon (which will be n2) after the Ar is added. (I picked 1.5 because neon weighs about 20 g/mol and argon weighs about 40 g/mol.)
1 / 1 = x / 1.5
x = 1.5
answer choice (c).
Example #4: A flexible container at an initial volume of 5.120 L contains 8.500 mol of gas. More gas is then added to the container until it reaches a final volume of 18.10 L. Assuming the pressure and temperature of the gas remain constant, calculate the number of moles of gas added to the container.
Solution:
V1 / n1 = V2 / n2
| 5.120 L | 18.10 L | |
| –––––––– | = | –––––– |
| 8.500 mol | x |
x = 30.05 mol <— total moles, not the moles added
30.05 – 8.500 = 21.55 mol (to four sig figs)
KaiserScience 
