Buoyancy of balloons in Up
Up is a 2009 American computer-animated comedy-drama film produced by Pixar Animation Studios and released by Walt Disney Pictures.
In this movie, the hero releases many, many helium filled balloons out of the house. Could that actually be enough to make a house float?
In Physics and the movie UP – floating a house, 6/3/2009, Wired Magazine, Rhett Allain writes:
…The first time I saw this trailer I thought the balloons were stored in his house. After re-watching in slow motion, it seems the balloons were maybe in the back yard held down by some large tarps. … [but] what if he had the balloons in his house and then released them? Would that make the house float more? Here is a diagram:
There is a buoyancy force when objects displace air or a fluid. This buoyancy force can be calculated with Archimedes’ principle which states: The buoyancy force is equal to the weight of the fluid displaced.
The easiest way to make sense of this is to think of some water floating in water. Of course water floats in water. For floating water, it’s weight has to be equal to it’s buoyant force. Now replace the floating water with a brick or something. The water outside the brick will have the exact same interactions that they did with the floating water. So the brick will have a buoyancy force equal to the weight of the water displaced. For a normal brick, this will not be enough to make it float, but there will still be a buoyant force on it.
What is being displaced? What is the mass of the object. It really is not as clear in this case. What is clear is the thing that is providing the buoyancy is the air. So, the buoyancy force is equal to the weight of the air displaced.
What is displacing air? In this case, it is mostly the house, all the stuff in the house, the balloons and the helium in the balloons.
In the two cases above, the volume of the air displaced does not change. This is because the balloons are in the air in the house. (Remember, I already said that I see that this NOT how it was shown in the movie).
So, if you (somehow) had enough balloons to make your house fly and you put them IN your house, your house would float before you let them outside.
Why doesn’t the balloon house keep rising? The reason the balloon reaches a certain height is that the buoyant force is not constant with altitude.
As the balloon rises, the density of the air decreases. This has the effect of a lower buoyant force.
At some point, the buoyant force and the weight are equal and the balloon no longer changes in altitude.
http://scienceblogs.com/dotphysics/2009/06/03/physics-and-the-movie-up-floating-a-house/
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https://en.wikipedia.org/wiki/Larry_Walters
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Mythbusters : Lets talk buoyancy – Pirates of the Carribean
Adam and Jamie explore the possibility of raising a ship with ping-pong balls, originally conceived in the 1949 Donald Duck story The Sunken Yacht by Carl Barks.
MythBusters S02E13 Pingpong Rescue, 2004
Doing the math of MythBusters – Warning: Science content
More on the movie Up! (or Upper)
Rhett Allain on June 9, 2009
If the house were lifted by standard party balloons, what would it look like? The thing with party balloons is that they are not packed tightly, there is space between them. This makes it look like it takes up much more space. Let me just use Slate’s calculation of 9.4 million party balloons….
Pixar said they used 20,600 balloons in the lift off sequence. From that and the picture I used above and the same pixel size trick, the volume of balloons is about the same as a sphere of radius 14 meters. This would make a volume of 12,000 m3…
And then this would lead to an apparent volume of the giant cluster of 9.4 million balloons:
If this were a spherical cluster, the radius would be 110 meters. Here is what that would look like:
How long would it take this guy to blow up this many balloons? You can see that there is no point stopping now. I have gone this far, why would I stop? That would be silly.
The first thing to answer this question is, how long does it take to fill one balloon. I am no expert, I will estimate low. 10 seconds seems to be WAY too quick.
But look, the guy is filling 9.4 million balloons, you might learn a few tricks to speed up the process. If that were the case, it would take 94 million seconds or 3 years….
What if it was just 20,600 balloons like Pixar used in the animation? At 10 seconds a balloon, that would be 2.3 days (and I think that is a pretty fast time for a balloon fill). Remember that MythBusters episode where they filled balloons to lift a small boy? Took a while, didn’t it?
How many tanks of helium would he need? According this site, a large helium cylinder can fill 520 of the 11″ party balloons and costs about $190. If he had to fill 9.4 million balloons, this would take (9.4 million balloons)(1 tank)/(520 balloons)= 18,000 tanks at a cost of 3.4 million dollars.
http://scienceblogs.com/dotphysics/2009/06/09/more-on-the-movie-up-or-upper/
Backup The Particle Physics of You
This is a class backup of the article, The particle physics of you, 11/03/15 By Ali Sundermier. Symmetry Magazine.
Not only are we made of fundamental particles, we also produce them and are constantly bombarded by them throughout the day.
https://www.symmetrymagazine.org/article/the-particle-physics-of-you
Fourteen billion years ago, when the hot, dense speck that was our universe quickly expanded, all of the matter and antimatter that existed should have annihilated and left us nothing but energy. And yet, a small amount of matter survived.
We ended up with a world filled with particles. And not just any particles—particles whose masses and charges were just precise enough to allow human life. Here are a few facts about the particle physics of you that will get your electrons jumping.
The particles we’re made of
About 99 percent of your body is made up of atoms of hydrogen, carbon, nitrogen and oxygen. You also contain much smaller amounts of the other elements that are essential for life.
While most of the cells in your body regenerate every seven to 15 years, many of the particles that make up those cells have actually existed for millions of millennia. The hydrogen atoms in you were produced in the big bang, and the carbon, nitrogen and oxygen atoms were made in burning stars. The very heavy elements in you were made in exploding stars.
The size of an atom is governed by the average location of its electrons. Nuclei are around 100,000 times smaller than the atoms they’re housed in. If the nucleus were the size of a peanut, the atom would be about the size of a baseball stadium. If we lost all the dead space inside our atoms, we would each be able to fit into a particle of lead dust, and the entire human race would fit into the volume of a sugar cube.
As you might guess, these spaced-out particles make up only a tiny portion of your mass. The protons and neutrons inside of an atom’s nucleus are each made up of three quarks. The mass of the quarks, which comes from their interaction with the Higgs field, accounts for just a few percent of the mass of a proton or neutron. Gluons, carriers of the strong nuclear force that holds these quarks together, are completely massless.
If your mass doesn’t come from the masses of these particles, where does it come from? Energy. Scientists believe that almost all of your body’s mass comes from the kinetic energy of the quarks and the binding energy of the gluons.
The particles we make
Your body is a small-scale mine of radioactive particles. You receive an annual 40-millirem dose from the natural radioactivity originating inside of you. That’s the same amount of radiation you’d be exposed to from having four chest X-rays.
Your radiation dose level can go up by one or two millirem for every eight hours you spend sleeping next to your similarly radioactive loved one.
You emit radiation because many of the foods you eat, the beverages you drink and even the air you breathe contain radionuclides such as Potassium-40 and Carbon-14. They are incorporated into your molecules and eventually decay and produce radiation in your body.
When Potassium-40 decays, it releases a positron, the electron’s antimatter twin, so you also contain a small amount of antimatter.
The average human produces more than 4000 positrons per day, about 180 per hour. But it’s not long before these positrons bump into your electrons and annihilate into radiation in the form of gamma rays.
The particles we meet
The radioactivity born inside your body is only a fraction of the radiation you naturally (and harmlessly) come in contact with on an everyday basis. The average American receives a radiation dose of about 620 millirem every year. The food you eat, the house you live in and the rocks and soil you walk on all expose you to low levels of radioactivity. Just eating a Brazil nut or going to the dentist can up your radiation dose level by a few millirem. Smoking cigarettes can increase it up to 16,000 millirem.
Cosmic rays, high-energy radiation from outer space, constantly smack into our atmosphere. There, they collide with other nuclei and produce mesons, many of which decay into particles such as muons and neutrinos. All of these shower down on the surface of the Earth and pass through you at a rate of about 10 per second. They add about 27 millirem to your yearly dose of radiation. These cosmic particles can sometimes disrupt our genetics, causing subtle mutations, and may be a contributing factor in evolution.
In addition to bombarding us with photons that dictate the way we see the world around us, our sun also releases an onslaught of particles called neutrinos. Neutrinos are constant visitors in your body, zipping through at a rate of nearly 100 trillion every second. Aside from the sun, neutrinos stream out from other sources, including nuclear reactions in other stars and on our own planet.
Many neutrinos have been around since the first few seconds of the early universe, outdating even your own atoms. But these particles are so weakly interacting that they pass right through you, leaving no sign of their visit.
You are also likely facing a constant shower of particles of dark matter. Dark matter doesn’t emit, reflect or absorb light, making it quite hard to detect, yet scientists think it makes up about 80 percent of the matter in the universe.
Looking at the density of dark matter throughout the universe, scientists calculate that hundreds of thousands of these particles might be passing through you every second, colliding with your atoms about once a minute. But dark matter doesn’t interact very strongly with the matter you’re made of, so they are unlikely to have any noticeable effects on your body.
The next time you’re wondering how particle physics applies to your life, just take a look inside yourself.
Artwork by Sandbox Studio, Chicago with Ana Kova.
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This website is educational. Materials within it are being used in accord with the Fair Use doctrine, as defined by United States law.
§107. Limitations on Exclusive Rights: Fair Use. Notwithstanding the provisions of section 106, the fair use of a copyrighted work, including such use by reproduction in copies or phone records or by any other means specified by that section, for purposes such as criticism, comment, news reporting, teaching (including multiple copies for classroom use), scholarship, or research, is not an infringement of copyright. In determining whether the use made of a work in any particular case is a fair use, the factors to be considered shall include: the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes; the nature of the copyrighted work; the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and the effect of the use upon the potential market for or value of the copyrighted work. (added pub. l 94-553, Title I, 101, Oct 19, 1976, 90 Stat 2546)
Saturn
Saturn is a gas giant planet, the sixth planet from the Sun, and the second largest planet in our solar system.
A gas giant is a giant planet composed mainly of hydrogen and helium.
Jupiter and Saturn are the Solar System’s gas giants.
Gas giants consist mostly of hydrogen and helium. Heavier elements make up between 3 and 13 percent of the mass.
They have an outer layer of hydrogen gas, surrounding a layer of liquid metallic hydrogen. They likely have a molten, rocky core.
The outermost portion of the atmosphere has many layers of visible clouds, composed of water and ammonia.
The layer of metallic hydrogen makes up the bulk of each planet. This is referred to as “metallic” because the very high pressure turns hydrogen into an electrical conductor.
In Roman mythology, Saturn is the god of agriculture and wealth.
Its radius is about nine times that of Earth. It’s volume is about 95 times larger than Earth.
It has one-eighth the average density of Earth.
Its astronomical symbol (♄) represents Saturn’s sickle.
Saturn’s rings
What are they made of?
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How were they formed?
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What does it look like as we travel trough them?
Go to this NASA press release for an amazing short movie.
Cassini’s ‘Inside-Out’ Rings Movie: NASA JPL
This movie sequence of images from NASA’s Cassini spacecraft offers a unique perspective on Saturn’s ring system. Cassini captured the images from within the gap between the planet and its rings, looking outward as the spacecraft made one of its final dives through the gap as part of the mission’s Grand Finale.
Using its wide-angle camera, Cassini took the 21 images in the sequence over a span of about four minutes during its dive through the gap on Aug. 20, 2017. The images have an original size of 512 x 512 pixels; the smaller image size allowed for more images to be taken over the short span of time.
The entirety of the main rings can be seen here, but due to the low viewing angle, the rings appear extremely foreshortened. The perspective shifts from the sunlit side of the rings to the unlit side, where sunlight filters through.
On the sunlit side, the grayish C ring looks larger in the foreground because it is closer; beyond it is the bright B ring and slightly less-bright A ring, with the Cassini Division between them. The F ring is also fairly easy to make out.
More resources
Planets: Gas giants and Ice giants
A 3d model of Saturn and It’s Major Moons, from 3dwarehouse
Possible habitat for life on Enceladus, a moon of Saturn
How Saturn and the other planets got their names
Backup: Get to know Maxwell’s Equations
This is a backup of an article on Wired,’Get to know Maxwell’s Equations – You’re Using Them Right Now,” by Rhett Allain , 8/6/19
Maxwell’s equations are sort of a big deal in physics. They’re how we can model an electromagnetic wave—also known as light. Oh, it’s also how most electric generators work and even electric motors. Essentially, you are using Maxwell’s equations right now, even if you don’t know it. Why are they called “Maxwell’s equations”? That’s after James Clark Maxwell. He was the 19th-century scientist who sort of put them together, even though many others contributed.
There are four of these equations, and I’ll go over each one and give a conceptual explanation. Don’t worry, you won’t need to refresh your calculus skills. If you do want to follow the math, let me point out that there are two different ways to write these equations, either as integrals or as spatial derivatives. I’ll give both versions—but again, if the math looks uninviting, just ignore it.
The short version is that Gauss’ law describes the electric field pattern due to electric charges. What is a field? I like this description – “It’s an energy field created by all living things. It surrounds us, penetrates us, and binds the galaxy together.”
Oh wait. That was Obi Wan’s description of the Force in Star Wars Episode IV. But it’s not a terrible description of an electric field. Here is another definition (by me):
If you take two electric charges, there is an interaction force between them. The electric field is the force per unit charge on one of those charges. So, it’s sort of like a region that describes how an electric charge would feel a force. But is it even real? Well, a field can have both energy and momentum—so it’s at least as real as those things.
Don’t worry about the actual equation. It’s sort of complicated, and I just want to get to the idea behind it. (If you have seen this physics equation before, you might think I am going to go into electric flux, but let’s see if I can do this with “no flux given.”) So let’s just say that Gauss’ law says that electric fields point away from positive charges and towards negative charges. We can call this a Coulomb field (named after Charles-Augustin de Coulomb).
Everyone knows that positive charges are red and negative charges are blue. Actually, I don’t know why I always make the positive red—you can’t see them anyway.
Also, you might notice that the electric field due to the negative charges looks shorter. That’s because those arrows start farther away from the charge. One of the key ideas of a Coulomb field is that the strength of the field decreases with distance from a single point charge.
But wait! Not all electric fields look like this. The electric field also follows the superposition principle. This means that the total electric field at any location is the vector sum of the electric field due to whatever point charges are nearby. This means you can make cool fields like the one below, which are the result of two equal and opposite charges (called a dipole).
And here’s the Python code I used to create it. https://trinket.io/glowscript/18196b0cf1
This dipole field is going to be important for the next equation.
Yes, this looks very similar to the other Gauss’ law. But why isn’t the previous equation called “Gauss’ law for electricism”? First, that’s because “electricism” isn’t a real word (yet). Second, the other Gauss’ law came first, so it gets the simple name. It’s like that time in third grade when a class had a student named John. Then another John joined the class and everyone called him John 2. It’s not fair—but that’s just how things go sometimes.
OK, the first thing about this equation is the B. We use this to represent the magnetic field. But you will notice that the other side of the equation is zero. The reason for this is the lack of magnetic monopoles. Take a look at this picture of iron filings around a bar magnet (surely you have seen something like this before).
This looks very similar to the electric field due to a dipole (except for the clumps of filings because I can’t spread them out). It looks similar because it is mathematically the same. The magnetic field due to a bar magnet looks like the electric field due to a dipole. But can I get a single magnetic “charge” by itself and get something that looks like the electric field due to a point charge? Nope.
Here’s what happens when you break a magnet in half. Yes, I cheated. The picture above shows two bar magnets. But trust me—if you break a magnet into two pieces, it will look like this.
It’s still a dipole. You can’t get a magnetic field to look like the electric field due to a point charge because there are no individual magnetic charges (called a magnetic monopole). That’s basically what Gauss’ law for magnetism says—that there’s no such thing as a magnetic monopole. OK, I should be clear here. We have never seen a magnetic monopole. They might exist.
Faraday’s law
The super-short version of this equation is that there is another way to make an electric field. It’s not just electric charges that make electric fields. In fact, you can also make an electric field with a changing magnetic field. This is a HUGE idea as it makes a connection between electric and magnetic fields.
Let me start with a classic demonstration. Here is a magnet, a coil of wire, and a galvanometer (it basically measures tiny electric currents). When I move the magnet in or out of the coil, I get a current.
If you just hold the magnet in the coil, there is no current. It has to be a changing magnetic field. Oh, but where is the electric field? Well, the way to make an electric current is to have an electric field in the direction of the wire. This electric field inside the wire pushes electric charges to create the current.
But there is something different about this electric field. Instead of pointing away from positive charges and pointing towards negative charges, the field pattern just makes circles. I will use the name “curly electric field” for a case like this (I adopted the term from my favorite physics textbook authors). With that, we can call the electric field made from charges a “Coulomb field” (because of Coulomb’s law).
Here is a rough diagram showing the relationship between the changing magnetic field and an induced curly electric field.
Note that I am showing the direction of the magnetic field inside of that circle, but it’s really the direction of the change in magnetic field that matters.
AMPERE-MAXWELL LAW
Do you see the similarity? This equation sort of looks like Faraday’s law, right? Well, it replaces E with B and it adds in an extra term. The basic idea here is that this equation tells us the two ways to make a magnetic field. The first way is with an electric current.
Here is a super-quick demo. I have a magnetic compass with a wire over it. When an electric current flows, it creates a magnetic field that moves the compass needle.
It’s difficult to see from this demo, but the shape of this magnetic field is a curly field. You can sort of see this if I put some iron filings on paper with an electric current running through it.
Maybe you can see the shape of this field a little better with this output from a numerical calculation. This shows a small part of a wire with electric current and the resulting magnetic field.
Actually, that image might seem complicated to create but it’s really not too terribly difficult. Here is a tutorial on using Python to calculate the magnetic field. There is another way to create a curly magnetic field—with a changing electric field. Yes, it’s the same way a changing magnetic field creates a curly electric field. Here’s what it would look like.
Notice that I even changed the vector colors to match the previous curly field picture—that’s because I care about the details. But let me just summarize the coolest part. Changing electric fields make curly magnetic fields. Changing magnetic fields make curly electric fields. AWESOME.
What About Light?
The most common topic linked to Maxwell’s Equations is that of an electromagnetic wave. How does that work? Suppose you have a region of space with nothing but an electric field and magnetic field. There are no electric charges and there isn’t an electric current. Let’s say it looks like this.
Let me explain what’s going on here. There is an electric field pointing INTO your computer screen (yes, it’s tough dealing with three dimensions with a 2D screen) and a magnetic field pointing down. This region with a field is moving to the right with some velocity v.
What about that box? That’s just an outline of some region. But here’s the deal. As the electric field moves into that box, there is a changing field that can make a magnetic field. If you draw another box perpendicular to that, you can see that there will be a changing magnetic field that can make a magnetic field. In fact, if this region of space moves at the speed of light (3 x 108 m/s), then the changing magnetic field can make a changing electric field. These fields can support each other without any charges or currents. This is an electromagnetic pulse.
An electromagnetic wave is an oscillating electric field that creates an oscillating magnetic field that creates an oscillating electric field. Most waves need some type of medium to move through. A sound wave needs air (or some other material), a wave in the ocean needs water. An EM wave does not need this. It is its own medium. It can travel through empty space—which is nice, so that we can get light from the sun here on Earth.
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This website is educational. Materials within it are being used in accord with the Fair Use doctrine, as defined by United States law.
§107. Limitations on Exclusive Rights: Fair Use. Notwithstanding the provisions of section 106, the fair use of a copyrighted work, including such use by reproduction in copies or phone records or by any other means specified by that section, for purposes such as criticism, comment, news reporting, teaching (including multiple copies for classroom use), scholarship, or research, is not an infringement of copyright. In determining whether the use made of a work in any particular case is a fair use, the factors to be considered shall include: the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes; the nature of the copyrighted work; the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and the effect of the use upon the potential market for or value of the copyrighted work. (added pub. l 94-553, Title I, 101, Oct 19, 1976, 90 Stat 2546)
Origin of the oceans
The origin of water on Earth is studied by scientists in planetary science, astronomy, and astrobiology.
Earth is unique among the rocky planets in the Solar System in that it is the only planet known to have oceans of liquid water on its surface.
Liquid water, necessary for life as we know it, exists on the surface of Earth because we are far enough from the Sun to avoid a runaway greenhouse effect, but not so far that low temperatures cause all water on the planet to freeze.
Where did our water oceans come from? Many people hypothesized that water and other volatiles must have been delivered to Earth from the outer Solar System later in its history. Recent research, however, indicates that hydrogen inside the Earth played a role in the formation of the ocean.
The two ideas are not mutually exclusive, as there is also evidence water was delivered to Earth by impacts from icy planetesimals similar in composition to asteroids in the outer edges of the asteroid belt.
This introduction excerpted and adapted from Origin of water on Earth, Wikipedia.
What the surface of Earth likely looked like when it was around one billion years old. It is presently 4.5 billions years old.
There is at least an ocean’s worth of water molecules trapped underground, deep within the earth’s crust.
Much water may have been brought to earth by comets and water-rich asteroids.
Large amounts of water are bound up with other minerals, under the surface of the Earth.
More TBA
Packet
Packet (Word document) How the ocean came to be
Astrooceanography
The study of oceans outside planet Earth. Unlike other planetary sciences like astrobiology, astrochemistry and planetary geology, it only began after the discovery of underground oceans in Saturn’s Titan and Jupiter’s Ganymede.
This field remains speculative until further missions reach the oceans beneath the rock or ice layer of the moons.
There are many theories about oceans or even ocean worlds of celestial bodies in the Solar System, from oceans made of diamond in Neptune to a gigantic ocean of liquid hydrogen that may exist underneath Jupiter’s surface.
Early in their geologic histories, Mars and Venus are theorized to have had large water oceans. The Mars ocean hypothesis suggests that nearly a third of the surface of Mars was once covered by water, and a runaway greenhouse effect may have boiled away the global ocean of Venus.
Unconfirmed oceans are speculated beneath the surface of many dwarf planets and natural satellites; notably, the ocean of the moon Europa is estimated to have over twice the water volume of Earth.
Also see Extraterrestrial liquid water
This section excerpted from Astrooceanography, Wikipedia
Research
Ancient Earth was a water world, Paul Voosen, Science (magazine) 3/9/2021
External articles
The Guardian, Earth-may-have-underground-ocean-three-times-that-on-surface
Extremetech.com, An ocean-400-miles-beneath-our-feet-that-could-fill-our-oceans-three-times-over
Water-rich gem points to vast ‘oceans’ beneath Earth’s surface, study suggests
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RNA World
Background vocabulary: monomer and polymer
Life today
Living things have genetic information stored in a polymer of DNA.
That info gets copied into polymers of RNA.
That is translated, with the help of mRNA, into polymers of proteins.
And each of these steps needs special enzymes.
Interesting thought
Life in today’s cells, and even viruses, is wicked complicated.
Hard to imagine all it all evolved, all at once. But who says it had to do it all at once?
Maybe one simple kind of reaction developed, then later, other kinds of reactions, and then over a loooong period of time, even other types.
Life in the very beginning
Perhaps once upon a time, RNA was all that life had.
Pieces of RNA were both the genes and the catalyst.
e.g. RNA could do base pairing with itself, bend, and graph other molecules.
RNA sequences could be copied by other RNAs.
Only later did DNA and proteins evolve.
This is the idea of the RNA world
A hypothetical stage in the history of life on Earth
Idea – RNA developed before DNA and proteins developed.
Alexander Rich first proposed the concept in 1962
Growing amounts of evidence for this is strong enough that the hypothesis has gained wide acceptance.
How is RNA like DNA?
Both can store and replicate genetic information;
How is RNA like an enzyme?
Both can catalyze (start) chemical reactions.
Are any enzymes today made of RNA?
the ribosome is composed primarily of RNA.
Ribosomes are part of many important enzymes, such as Acetyl-CoA, NADH, etc.
So why does life depend on DNA replication nowadays?
DNA is more stable than RNA
What does RNA, and DNA, look like?
How would RNA monomers assemble into polymers?
How could copies be made?
So let us look at the possible in steps, in order.
At the far left is long ago… then an RNA based world of life developed… and later a DNA and protein based world of life developed.
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Environmental Science Syllabus
Primary textbook: Environmental Science. by Michael R. Heithaus and Karen Arms. Originally published by Holt, Rinehart and Winston, now by Houghton Mifflin Harcourt.
Workbook “Environmental Science Active Reading Worksheets.”
Environmental science is an interdisciplinary field. It integrates physical, biological and information sciences. It covers the intersection of many fields: ecology, biology, physics, chemistry, plant science, zoology, mineralogy, oceanography, soil science, physical geography, and atmospheric science.
On a college level it incorporates social sciences for understanding human perceptions, which held design effective environmental policies.
Environmental scientists work on subjects like alternative energy systems, pollution control and mitigation, natural resource management, and the effects of global climate change.
Terminology: In common usage, “environmental science” and “ecology” are often used interchangeably. However, technically, ecology refers only to the study of organisms, and their interactions with each other and their environment. In this sense ecology is a subset of environmental science. (Ecology is also a subset of biology.)
Weekly guide to what we’re doing in class
PEMDAS The Math Equation That Tried to Stump the Internet
from The Math Equation That Tried to Stump the Internet
Excerpted from the NY Times article, The Math Equation That Tried to Stump the Internet, by Steven Strogatz, 8/2/2019
… The question above has a clear and definite answer, provided we all agree to play by the same rules governing “the order of operations.” When, as in this case, we are faced with several mathematical operations to perform — to evaluate expressions in parentheses, carry out multiplications or divisions, or do additions or subtractions — the order in which we do them can make a huge difference.
When confronted with 8 ÷ 2(2+2), everyone on Twitter agreed that the 2+2 in parentheses should be evaluated first. That’s what our teachers told us: Deal with whatever is in parentheses first. Of course, 2+2 = 4. So the question boils down to 8÷2×4.
And there’s the rub. Now that we’re faced with a division and a multiplication, which one takes priority? If we carry out the division first, we get 4×4 = 16; if we carry out the multiplication first, we get 8÷8 = 1.
Which way is correct? The standard convention holds that multiplication and division have equal priority. To break the tie, we work from left to right. So the division goes first, followed by the multiplication. Thus, the right answer is 16.
More generally, the conventional order of operations is to evaluate expressions in parentheses first. Then you deal with any exponents. Next come multiplication and division, which, as I said, are considered to have equal priority, with ambiguities dispelled by working from left to right. Finally come addition and subtraction, which are also of equal priority, with ambiguities broken again by working from left to right.
Now realize… PEMDAS is arbitrary. Furthermore, in my experience as a mathematician, expressions like 8÷2×4 look absurdly contrived.
No professional mathematician would ever write something so obviously ambiguous. We would insert parentheses to indicate our meaning and to signal whether the division should be carried out first, or the multiplication.
The last time this came up on Twitter, I reacted with indignation: It seemed ridiculous that we spend so much time in our high-school curriculum on such sophistry. But now, having been enlightened by some of my computer-oriented friends on Twitter, I’ve come to appreciate that conventions are important, and lives can depend on them.
We know this whenever we take to the highway. If everyone else is driving on the right side of the road (as in the U.S.), you would be wise to follow suit. The same goes if everyone else is driving on the left, as in the United Kingdom. It doesn’t matter which convention is adopted, as long as everyone follows it.
Likewise, it’s essential that everyone writing software for computers, spreadsheets and calculators knows the rules for the order of operations and follows them. For the rest of us, the intricacies of PEMDAS are less important than the larger lesson that conventions have their place. They are the double-yellow line down the center of the road — an unending equals sign — and a joint agreement to understand one another, work together, and avoid colliding head-on.
Ultimately, 8 ÷ 2(2+2) is less a statement than a brickbat; it’s like writing the phrase “Eats shoots and leaves” and concluding that language is capricious. Well, yes, in the absence of punctuation, it is; that’s why we invented the stuff.
– Steven Strogatz is a professor of mathematics at Cornell and the author of “Infinite Powers: How Calculus Reveals the Secrets of the Universe.”_
Ambiguous PEMDAS
Professor Oliver Knill addresses the same phenomenon here:
Even in mathematics, ambiguities can be hard to spot. The phenomenon seen here in arithmetic goes beyond the usual PEMDAS rule and illustrates an ambiguity which can lead to heated arguments and discussions.
What is 2x/3y-1 if x=9 and y=2 ?
Did you get 11 or 2? If you got 11, then you are in the BEMDAS camp, if you got 2, you are in the BEDMAS camp. In either case you can relax because you have passed the test. If you got something different you are in trouble although! There are arguments for both sides. But first a story….[and there is a very cool story here, click the link below. But here is the important conclusion]
The PEMDAS problem is not a “problem to be solved”. It is a matter of fact that there are different interpretations and that a human for example reads x/yz with x=3,y=4 and z=5 as 3/20 while a machine (practically all programming languages) give a different result.
There are authorities which have assigned rules (most pupils are taught PEMDAS) which is one reason why many humans asked about 3/4*5 give 3/20 which most machines asked give 15/4:
I type this in Mathematica x=3; y=4; z=5; x/y z and get 15/4
It is a linguistic problem, not a mathematical problem. In case of a linguistic problem, one can not solve it by imposing a new rule. The only way to solve the problem is to avoid it. One can avoid it to put brackets.
Ambiguous PEMDAS, from Oliver Knill at Harvard University
That Vexing Math Equation? Here’s an Addition
Steven Strogatz, professor of Applied Mathematics, Cornell Univ, looks at a similar problem, and agrees that “questions” like these are deliberately badly written:
Recently I wrote about a math equation that had managed to stir up a debate online. The equation was this one: 8 ÷ 2(2+2) = ?
The issue was that it generated two different answers, 16 or 1, depending on the order in which the mathematical operations were carried out….
… The question was not meant to ask anything clearly. Quite the contrary, its obscurity seems almost intentional. It is certainly artfully perverse, as if constructed to cause mischief.
The expression 8 ÷ 2(2+2) uses parentheses – typically a tool for reducing confusion – in a jujitsu manner to exacerbate the murkiness. It does this by juxtaposing the numeral 2 and the expression (2+2), signifying implicitly that they are meant to be multiplied, but without placing an explicit multiplication sign between them. The viewer is left wondering whether to use the sophisticated convention for implicit multiplication from algebra class or to fall back on the elementary PEMDAS convention from middle school.
Picks: “So the problem, as posed, mixes elementary school notation with high school notation in a way that doesn’t make sense. People who remember their elementary school math well say the answer is 16. People who remember their algebra are more likely to answer 1.”
Much as we might prefer a clear-cut answer to this question, there isn’t one. You say tomato, I say tomahto. Some spreadsheets and software systems flatly refuse to answer the question – they balk at its garbled structure. That’s my instinct, too, and that of most mathematicians I’ve spoken with. If you want a clearer answer, ask a clearer question.
That Vexing Math Equation? Here’s an Addition, The New York Times, Aug 5, 2019
Oils
“Oil” is a general name for any kind of molecule which is
nonpolar
that just means that its electrons are evenly distributed
PHET Polar molecules app
liquid at room temperature
of course, it could become solid if cooled, or evaporate if heated
Molecule has one end which is hydrophobic and another end which is lipophilic
The hydrophobic end likes to stick to water molecules. But hates sticking to oils.
The lipophilic end likes to stick to oil molecules, but hates sticking to water,
Made with many C and H atoms
Oils are usually flammable. Here we see oils in an orange skin interacting with a candle.
So Petroleum is?
Petroleum is a mix of naturally forming oils, which we drill from the Earth, and use in a variety of ways. See our article on petroleum and producing power.
Giant Dikes in northeast America
A dike (or dyke) is a sheet of rock that is formed in a fracture in a pre-existing rock body.
A ring dike is an intrusive igneous body. Their chemistry, petrology and field appearance precisely match those of dikes or sill, but their concentric or radial geometric distribution around a centre of volcanic activity indicates their subvolcanic origins. See here for more details: Ring dikes
Topic 2 – Giant Dikes: Patterns and Plate Tectonics
This is a photo of Shiprock (7178 ft) and southern dike, southwest of Shiprock, NM. View to the northwest. Note the several small satellite volcanic necks at the base of Shiprock.
Where is this? Shiprock is a monadnock rising nearly 1,583 feet above the high-desert plain of the Navajo Nation in San Juan County, New Mexico, United States.
Photo by Louis J. Maher, Jr., http://geoscience.wisc.edu/~maher/air/air00.htm
The following section has been excerpted from Giant Dikes: Patterns and Plate Tectonics, by J. Gregory McHone, Don L. Anderson & Yuri A. Fialko, published on Mantleplumes .org.
Giant Dikes: Patterns and Plate Tectonics
Giant dikes typically exceed 30 m in width and 100 km in length, with some examples over 100 m wide and 1,000 km long. Dikes are self-induced magma-filled fractures, and they are the dominant mechanism by which basaltic melts are transported through the lithosphere and the crust.
These spectacular intrusions are likely to have fed flood basalts in large igneous provinces (LIPs), including provinces where the surface basalts have been diminished or removed by erosion.
Although giant dikes can intermingle with denser swarms of smaller dikes of similar composition (and probably similar origin), others occur in sets of several to a few dozen extremely large quasi-linear or co-linear intrusions, which may gently bend and converge/diverge at low angles across many degrees of latitude.
Tectonic controls on the formation of giant dikes appear to be independent and different from structures related to smaller dike swarms. Theoretical modeling and field observations help us to understand the essential physics of magma migration from its source to its final destination in the upper lithosphere.
…in northeastern North America, huge but widespread dikes in Canada and New England diverge to the NE and ENE from a focus point east of New Jersey, but that is also not a plume center.
The dikes change their trends across the “New England Salient,” which is a bend in terrane suture zones and primary structures of this section of the Appalachian Orogen.
In addition, the giant dikes did not form together in a radial generation, but instead decrease systematically in age from the SE toward the NW.
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