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Cartoon Laws of Physics
Cartoon Law I
Any body suspended in space will remain in space until made aware of its situation.
Daffy Duck steps off a cliff, expecting further pastureland. He loiters in midair, soliloquizing flippantly, until he chances to look down. At this point, the familiar principle of 32 feet per second per second takes over.
Cartoon Law II
Any body in motion will tend to remain in motion until solid matter intervenes suddenly.
Whether shot from a cannon or in hot pursuit on foot, cartoon characters are so absolute in their momentum that only a telephone pole or an outsize boulder retards their forward motion absolutely. Sir Isaac Newton called this sudden termination of motion the stooge’s surcease.
Cartoon Law III
Any body passing through solid matter will leave a perforation conforming to its perimeter.
Also called the silhouette of passage, this phenomenon is the speciality of victims of directed-pressure explosions and of reckless cowards who are so eager to escape that they exit directly through the wall of a house, leaving a cookie-cutout-perfect hole. The threat of skunks or matrimony often catalyzes this reaction.
Cartoon Law IV
The time required for an object to fall twenty stories is greater than or equal to the time it takes for whoever knocked it off the ledge to spiral down twenty flights to attempt to capture it unbroken.
Such an object is inevitably priceless, the attempt to capture it inevitably unsuccessful.
Cartoon Law V
All principles of gravity are negated by fear.
Psychic forces are sufficient in most bodies for a shock to propel them directly away from the earth’s surface. A spooky noise or an adversary’s signature sound will induce motion upward, usually to the cradle of a chandelier, a treetop, or the crest of a flagpole. The feet of a character who is running or the wheels of a speeding auto need never touch the ground, especially when in flight.
Cartoon Law VI
As speed increases, objects can be in several places at once.
This is particularly true of tooth-and-claw fights, in which a character’s head may be glimpsed emerging from the cloud of altercation at several places simultaneously. This effect is common as well among bodies that are spinning or being throttled. A ‘wacky’ character has the option of self- replication only at manic high speeds and may ricochet off walls to achieve the velocity required.
Cartoon Law VII
Certain bodies can pass through solid walls painted to resemble tunnel entrances; others cannot.
This trompe l’oeil inconsistency has baffled generations, but at least it is known that whoever paints an entrance on a wall’s surface to trick an opponent will be unable to pursue him into this theoretical space. The painter is flattened against the wall when he attempts to follow into the painting. This is ultimately a problem of art, not of science.
Cartoon Law VIII
Any violent rearrangement of feline matter is impermanent.
Cartoon cats possess even more deaths than the traditional nine lives might comfortably afford. They can be decimated, spliced, splayed, accordion-pleated, spindled, or disassembled, but they cannot be destroyed. After a few moments of blinking self pity, they reinflate, elongate, snap back, or solidify.
Corollary: A cat will assume the shape of its container.
Cartoon Law IX
Everything falls faster than an anvil.
Cartoon Law X
For every vengea nce there is an equal and opposite revengeance.
This is the one law of animated cartoon motion that also applies to the physical world at large. For that reason, we need the relief of watching it happen to a duck instead.
Cartoon Law Amendment A
A sharp object will always propel a character upward.
When poked (usually in the buttocks) with a sharp object (usually a pin), a character will defy gravity by shooting straight up, with great velocity.
Cartoon Law Amendment B
The laws of object permanence are nullified for “cool” characters.
Characters who are intended to be “cool” can make previously nonexistent objects appear from behind their backs at will. For instance, the Road Runner can materialize signs to express himself without speaking.
Cartoon Law Amendment C
Explosive weapons cannot cause fatal injuries.
They merely turn characters temporarily black and smoky.
Cartoon Law Amendment D
Gravity is transmitted by slow-moving waves of large wavelengths.
Their operation can be wittnessed by observing the behavior of a canine suspended over a large vertical drop. Its feet will begin to fall first, causing its legs to stretch. As the wave reaches its torso, that part will begin to fall, causing the neck to stretch. As the head begins to fall, tension is released and the canine will resume its regular proportions until such time as it strikes the ground.
Cartoon Law Amendment E
Dynamite is spontaneously generated in “C-spaces” (spaces in which cartoon laws hold).
The process is analogous to steady-state theories of the universe which postulated that the tensions involved in maintaining a space would cause the creation of hydrogen from nothing. Dynamite quanta are quite large (stick sized) and unstable (lit). Such quanta are attracted to psychic forces generated by feelings of distress in “cool” characters (see Amendment B, which may be a special case of this law), who are able to use said quanta to their advantage. One may imagine C-spaces where all matter and energy result from primal masses of dynamite exploding. A big bang indeed.
© 1997 William Geoffrey Shotts. Last update: Thursday, December 4, 1997
Mousetrap racer build project
Your task is to build a mousetrap powered car!
It can be built from wood, paper, plastic, metal, erector sets, pens, rulers, old toys, Legos, and other materials.
We need a fair comparison between race cars. Therefore it must be powered by only 1 mousetrap.
You may not modify the mousetrap, such as by over-winding the metal coil, because that would unfairly increase its potential energy storage.
A rat trap, or trap for any other animal, is not safe or acceptable.
2 people may collaborate to make 1 car.
If you do not have your car on the day that it is due, you lose 5 points per day.
I suggest working in groups, making your own local mousetrap racer “factory”. This approach is easier and more fun.
Clearly print your names somewhere on the car!
Giving time to do this
Day 1 – We introduce the project, discuss the physics and engineering principles, show some videos and photos.
Day 2 – (Which could be any day that fits our class schedule) – Have students bring in the building materials they have procured so far. Also, as a teacher I will help make materials available in class. Both teacher and some volunteer students will show in class how to assemble a mousetrap racer. The way that it is shown in class is not the only way to do it.
Day 3 – Classroom build. Students individually or in pairs work on the mousetrap racer. First start off with a brief review of physics principles – storing energy as PE, simple machines, how mechanical devices can transform PE into kinetic energy, etc.
Day 4 – Run the mousetrap racers! Find a long hallway with a smooth floor. We will have competitions:
(A) Fastest: Which car goes to the finish line in the shortest amount of time?
(B) Furthest distance: Which car goes the furthest?
Much information on mouse trap racers is available online. However, you may not use a kit to build your racer.
Instructables (several ideas here)
Mousetrap cars and kits from Doc Fizzix. Great for ideas
Gallery of great mousetrap racers. from UCI Summer Science Institute
What is a mousetrap powered car? How does it work?
It is a vehicle powered by a mousetrap spring. We tie one end of a string to the tip of a mousetrap’s snapper arm, and the other end of the string has a loop that is designed to “catch” a hook that is glued to a drive axle.
Once the loop is placed over the axle hook, the string is wound around the drive axle by turning the wheels in the opposite direction to the vehicle intended motion.
As the string is wound around the axle, the lever arm is pulled closer to the drive axle causing the mousetrap’s spring to “wind-up” and store energy.
When the drive wheels are released, the string is pulled off the drive axle by the mousetrap, causing the wheels to rotate.
How do you build a mouse trap powered racer?
There is no one “right way” to build a mousetrap powered vehicle. The first step to making a good mouse trap powered car is simple: put something together and find out how it works.
Once you have something working you can begin to isolate the variables that are affecting the performance and learn to adjust to improve your results.
Build, test, have fun spectacular failures, and improve, just like SpaceX rockets.
What’s the difference between a FAST Racer and a LONG distance traveler?
When you build a mouse-trap car for distance, you want a small energy consumption per second or a small power usage. Smaller power outputs will produce less wasted energy and have greater efficiency.
When you build a vehicle for speed, you want to use your energy quickly or at a high power output.
We change the power ratio of a vehicle by changing one or all of the following:
* where the string attaches to the mouse-trap’s lever arm
* the drive wheel diameter
* the drive axle diameter.
The amount of energy released by using a short lever arm or a long lever arm is the same, but the length of the lever arm will determine the rate at which the energy is released and this is called the power output.
Long lever arms decrease the pulling force and power output but increase the pulling distance.
Short lever arms increase the pulling force and the power output by decrease the pulling distance but increasing the speed.
Building for speed
If you are building a mouse-trap car for speed, you will want to maximize the power output to a point just before the wheels begin to spin-out on the floor. Maximum power output means more energy is being transferred into energy of motion in a shorter amount of time. Greater acceleration can be achieved by having a short length lever arm and/or by having a small axle to wheel ratio.
Building for distance
Minimize the power output or transfer stored energy into energy of motion at a slow rate. This usually means having a long lever arm and a large axle-to-wheel ratio.
If you make the lever arm too long, you may not have enough torque through the entire pulling distance to keep the vehicle moving, in which case you will have to attach the string to a lower point or change the axle-to wheel ratio.
Supplies
Most parts can be scavenged from toys, or recycled materials. You may also consider stores such as Michael’s Art Supply, Home Depot, or A. C. Moore. Mousetraps are available in 2 packs, for less than $2, from supermarkets.
Learning Standards
Next Generation Science Standards
DCI – Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as, within the system, energy is continually transferred from one object to another and between its various possible forms.
Conservation of energy means that the total change of energy in any system is always equal to the total energy transferred into or out of the system.
Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems.
Mathematical expressions, which quantify how the stored energy in a system depends on its configuration (e.g., relative positions of charged particles, compression of a spring) and how kinetic energy depends on mass and speed, allow the concept of conservation of energy to be used to predict and describe system behavior.
The availability of energy limits what can occur in any system.
Next Generation Science Standards: Science – Engineering Design (6-8)
• Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem.
Massachusetts Science and Technology/Engineering Curriculum Framework
HS-ETS4-5(MA). Explain how a machine converts energy, through mechanical means, to do work. Collect and analyze data to determine the efficiency of simple and complex machines.
HS-PS3-3. Design and evaluate a device that works within given constraints to convert one form of energy into another form of energy.
• Emphasis is on both qualitative and quantitative evaluations of devices.
• Examples of devices could include Rube Goldberg devices, wind turbines, solar cells, solar ovens, and generators.
Appendix VIII Value of Crosscutting Concepts and Nature of Science in Curricula
Cause and Effect: Mechanism and Explanation. Events have causes, sometimes simple, sometimes multifaceted. A major activity of science and engineering is investigating and explaining causal relationships and the mechanisms by which they are mediated. Such mechanisms can then be tested across given contexts and used to predict and explain events in new contexts or design solutions.
Anomalous sounds
Here’s an actual news story: “Loud booms heard across Southern New Hampshire: Source of the noise still unclear.”
Nashua police say they don’t know what caused several loud “booms” Saturday afternoon that were heard across Southern New Hampshire. Many reports came from Nashua and surrounding towns, but the sounds were reported as far north as Manchester and as far south as Westford, Massachusetts. Some who heard it in Nashua said they felt their houses shake. Police and fire departments said they have not been alerted to any incidents related to the noise in the area. The cause is still unclear.
– WMUR 9 News. (An ABC affiliated TV station) 2/10/18
How is it possible that such loud, possibly building shaking sounds could be heard in some parts of this town – yet in other parts of the city other residents reported no sound? Also, in a town next door no reports have yet surfaced of anyone hearing them – yet in a town after that, some residents also reported these booming sound.
The answer? It’s complicated, but basically:
(a) there are a wide variety of ways that sounds are produced – including some bizarre ways that most people have never heard of
(b) Sound waves don’t always move in a straight path like many people imagine; changing temperature/density of the air can cause sound waves to bend and diffract, so:
(b1) sound can sometimes travel much further distances than one would expect
(b2) sound can come from a location very different from what “seems obvious” just by listening
(b3) local wind can mask sound, so the same loud sound might be heard in one neighborhood, yet be undetectable by people just a mile away.
Basic physics idea:
Right off the bat, let’s realize that sound doesn’t move in a straight line: It spreads out radially from it’s source, and then – because of a phenomenon known as diffraction – it can even bend around obstacles.
Source: Hyperphysics, Diffraction of sound, http://hyperphysics.phy-astr.gsu.edu/
“If the air above the earth is warmer than that at the surface, sound will be bent back downward toward the surface by refraction.” – Hyperphysics
Normally, only sound initially directed toward the listener can be heard, but refraction can bend sound downward – effectively amplifying the sound. This can occur over cool lakes.
Sounds also can bounce off of objects, and come to our ears from a direction totally different than the original source.
ABD Engineering writes:
…wind alters sound propagation by the mechanism of refraction; that is, wind bends sound waves. Wind nearer to the ground moves more slowly than wind at higher altitudes, due to surface characteristics such as hills, trees, and man-made structures that interfere with the wind.
This wind gradient, with faster wind at higher elevation and slower wind at lower elevation causes sound waves to bend downward when they are traveling to a location downwind of the source and to bend upward when traveling toward a location upwind of the source.
Waves bending downward means that a listener standing downwind of the source will hear louder noise levels than the listener standing upwind of the source.
Temperature gradients in the atmosphere. On a typical sunny afternoon, air is warmest near the ground and temperature decreases at higher altitudes. This temperature gradient causes sound waves to refract upward, away from the ground and results in lower noise levels being heard at the listener’s position.
In the evening, this temperature gradient will reverse, resulting in cooler temperatures near the ground. This condition, often referred to is a temperature inversion will cause sound to bend downward toward the ground and results in louder noise levels at the listener position.
How Weather Affects an Outdoor Noise Study by ABD Engineering and Design
Cheung Kai-chung, from Physics World (Hong Kong), (Translation by Janny Leung) offers this explanation
Sound wave will be refracted to the ground when traveling with the wind.
Sound wave will be refracted upwards when traveling against the wind.
Can wind mask even loud sounds?
A discussion to consider, from Physics forums, includes this phenomenon: “Yes. I have a freeway about 10 blocks South of my house. I can hear the traffic very clearly with no wind, or a South wind. If there is even a slight North wind, the traffic noise becomes almost inaudible. If there is a brisk North wind (over 15 MPH), the sound is completely gone.”
https://www.physicsforums.com/threads/does-wind-affect-how-far-sound-can-travel.149392/
Sound refraction due to cold air:
Also this “…if the air close to the ground is colder than the air above it then sound waves traveling upwards will be bent downwards. This is called Refraction. These refracted sound waves can act to amplify the sound to someone standing far away.”
http://sciencewows.ie/blog/does-sound-travel-faster-in-warm-or-cold-air/
Sound seems amplified when traveling over water.
In School-for-Champions we read
“If you are sitting in a boat, a sound coming from the shore will seem louder than the same sound heard by a person on land. Sound seems to be amplified when it travels over water. The reason is that the water cools the air above its surface, which then slows down the sound waves near the surface. This causes refraction or bending of the sound wave, such that more sound reaches the boat passenger. Sound waves skimming the surface of the water can add to the amplification effect, if the water is calm.”
See their full lesson here School-for-champions.com: Sound_amplified_over_water
Can snow on the ground affect sound?
“When the ground has a thick layer of fresh, fluffy snow, sound waves are readily absorbed at the surface of the snow. However, the snow surface can become smooth and hard as it ages or if there have been strong winds. Then the snow surface will actually help reflect sound waves. Sounds seem clearer and travel farther under these circumstances.” – Colorado State Climatologist Nolan Doesken
Related topic: The Hum is a phenomenon, or collection of phenomena, involving widespread reports of a persistent and invasive low-frequency humming,rumbling, or droning noise not audible to all people. Hums have been widely reported by national media in the UK and the United States. The Hum is sometimes prefixed with the name of a locality where the problem has been particularly publicized: e.g., the “Bristol Hum” or the “Taos Hum”. It is unclear whether it is a single phenomenon; different causes have been attributed. ”
Human reactions to infrasound – https://en.wikipedia.org/wiki/Infrasound#Human_reactions
Skyquakes or mystery booms are unexplained reports of a phenomenon that sounds like a cannon or a sonic boom coming from the sky. They have been heard in several locations around the world. – https://en.wikipedia.org/wiki/Skyquake
And: The microwave auditory effect, also known as the microwave hearing effect or the Frey effect, consists of audible clicks (or, with speech modulation, spoken words[citation needed]) induced by pulsed/modulated microwave frequencies. The clicks are generated directly inside the human head without the need of any receiving electronic device. The effect was first reported by persons working in the vicinity of radar transponders during World War II. (Wikipedia)
Find The Guns of Barisal and Anomalous Sound Propagation
https://www.du.edu/~jcalvert/waves/barisal.htm
References
Our first article.
How Weather Affects an Outdoor Noise Study by ABD Engineering and Design
This following discussion has helpful images.
A discussion to consider, from Physics forums, includes this phenomenon:
“Yes. I have a freeway about 10 blocks South of my house. I can hear the traffic very clearly with no wind, or a South wind. If there is even a slight North wind, the traffic noise becomes almost inaudible. If there is a brisk North wind (over 15 MPH), the sound is completely gone.”
https://www.physicsforums.com/threads/does-wind-affect-how-far-sound-can-travel.149392/
Also this “…if the air close to the ground is colder than the air above it then sound waves traveling upwards will be bent downwards. This is called Refraction. These refracted sound waves can act to amplify the sound to someone standing far away.”
http://sciencewows.ie/blog/does-sound-travel-faster-in-warm-or-cold-air/
Sound seems amplified when traveling over water
https://www.school-for-champions.com/science/sound_amplified_over_water.htm#.WoBbQ5M-fVo
Diffraction of sound waves
https://katrinasiron21.wordpress.com/properties-of-sound-waves/diffraction-of-sound-waves/
Temperature inversion and sound waves
http://kxan.com/blog/2015/02/13/why-does-sound-carry-farther-on-cold-calm-mornings/
Also look into: Humans hearing infra sound waves
“Colorado State Climatologist Nolan Doesken says: “When the ground has a thick layer of fresh, fluffy snow, sound waves are readily absorbed at the surface of the snow. However, the snow surface can become smooth and hard as it ages or if there have been strong winds. Then the snow surface will actually help reflect sound waves. Sounds seem clearer and travel farther under these circumstances.””
Related topic: The Hum is a phenomenon, or collection of phenomena, involving widespread reports of a persistent and invasive low-frequency humming,rumbling, or droning noise not audible to all people. Hums have been widely reported by national media in the UK and the United States. The Hum is sometimes prefixed with the name of a locality where the problem has been particularly publicized: e.g., the “Bristol Hum” or the “Taos Hum”. It is unclear whether it is a single phenomenon; different causes have been attributed. ”
Human reactions to infrasound – https://en.wikipedia.org/wiki/Infrasound#Human_reactions
Skyquakes or mystery booms are unexplained reports of a phenomenon that sounds like a cannon or a sonic boom coming from the sky. They have been heard in several locations around the world. – https://en.wikipedia.org/wiki/Skyquake
Learning Standards
Skeptical analysis of unexplained phenomenon.
The Massachusetts STEM Curriculum Framework addresses “Understandings about the Nature of Science”
Scientific inquiry is characterized by a common set of values that include: logical thinking, precision, open-mindedness, objectivity, skepticism, replicability of results, and honest and ethical reporting of findings.
Science disciplines share common rules of evidence used to evaluate explanations about natural systems. Science includes the process of coordinating patterns of evidence with current theory.
Most scientific knowledge is quite durable but is, in principle, subject to change based on new evidence and/or reinterpretation of existing evidence.
The “College Board Standards for College Success: Science” addresses these same skeptical inquiry methods in Standard SP.1: Scientific Questions and Predictions. Asking scientific questions that can be tested empirically and structuring these questions in the form of testable predictions.
Students recognize, formulate, justify and revise scientific questions that can be addressed by science in order to construct explanations.
Students make and justify predictions concerning natural phenomena. Predictions and justifications are based on observations of the world, on knowledge of the discipline and on empirical evidence.
Students determine which data from a specific investigation can be used as evidence to address a scientific question or to support a prediction or an explanation, and distinguish credible data from noncredible data in terms of quality.
Students construct explanations that are based on observations and measurements of the world, on empirical evidence and on reasoning grounded in the theories, principles and concepts of the discipline.
The “Benchmarks for Science Literacy” (AAAS) addresses these same skeptical inquiry methods:
In science, a new theory rarely gains widespread acceptance until its advocates can show that it is borne out by the evidence, is logically consistent with other principles that are not in question, explains more than its rival theories, and has the potential to lead to new knowledge. 12A/H3** (SFAA)
Scientists value evidence that can be verified, hypotheses that can be tested, and theories that can be used to make predictions. 12A/H4** (SFAA)
Curiosity motivates scientists to ask questions about the world around them and seek answers to those questions. Being open to new ideas motivates scientists to consider ideas that they had not previously considered. Skepticism motivates scientists to question and test their own ideas and those that others propose. 12A/H5*
SAT subject test in Physics: Waves and optics
• General wave properties, such as wave speed, frequency, wavelength, superposition, standing wave diffraction, and Doppler effect
China’s Floating City Mirage
China’s Floating City – Was this a real mirage, a misinterpretation of a reflection, or a hoax?
from “Floating Cities are Generally not Fata Morgana Mirage.” Discussion by Mick West, Oct 20, 2015, on Metabunk.org.
A video is being widely shared on social media (and the “weird news” sections of more traditional media) claiming to show the image of an impossibly large city rising above the fog in the city of Foshan (佛山), Guangdong province, China. Here is a composite image from the video.
Some have said this is an example of a fata morgana, a type of mirage where light is bent though the atmosphere in such a way to create the illusion of buildings on the horizon.
This is utterly impossible in this case, as fata morgana only creates a very thin strip of such an illusion very close to the horizon, and appears small and far away. It does not create images high in the sky.
Besides, a fata morgana might create the illusion of buildings by stretching landscape features, or it might distort existing buildings. But what it cannot do it create a perfect image of existing nearby buildings, complete with windows.
It is important to note that no expert has actually looked at this video and said it was a fata morgana.
The second and more common type of “floating city” illusions is with buildings that are simply rising up out of clouds or low fog, and hence appear to be floating above them. This has led to “floating city” stories in the past, with this recent example, also from China.
This is simply a photo of building across the river, but when cropped it appears like they are floating, which led to all kinds of wild stories of “ghost cities”.
This actually came from mistranslations of the original news reports, where local people (who knew exactly what they were looking at) were simply marveling at how pretty the scene looked, with the buildings appearing to float above clouds.
Could the Foshan video be of real buildings obscured by clouds? It does not appear so. Look at some real buildings in Foshan (and keep in mind it’s not entirely clear if Foshan is the actual setting of either the top or the bottom of the video.
Consider what it would take for these buildings to appear like they do in the video, with the road beneath them. The scale is simply impossible. The image has to be composited somehow, and the possibilities are:
-
Computer generated buildings spliced into the video of the road.
-
Two different videos spliced together
-
The video is shot though glass, and the buildings are behind the camera, or to the side (with the glass at around 45°, like a half open window/door)
It’s unfortunate that many people leap for the “fata morgana” or other mirage explanation when it’s quite clear that this is far too high in the sky to be anything like that.
Resources
https://www.metabunk.org/floating-cities-are-generally-not-fata-morgana-mirages.t6922/
http://www.cnn.com/2015/10/20/world/china-floating-city-video-feat/index.html
https://www.snopes.com/floating-city-china/
An Introduction to Mirages, Andrew T. Young
Fata Morgana between the Continental Divide and the Missouri River
Learning Standards
2016 Massachusetts Science and Technology/Engineering Curriculum Framework
HS-PS4-3. Evaluate the claims, evidence, and reasoning behind the idea that electromagnetic radiation can be described by either a wave model or a particle model, and that for some situations involving resonance, interference, diffraction, refraction, or the photoelectric effect, one model is more useful than the other.
A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)
Core Idea PS4: Waves and Their Applications in Technologies for Information Transfer
When a wave passes an object that is small compared with its wavelength, the wave is not much affected; for this reason, some things are too small to see with visible light, which is a wave phenomenon with a limited range of wavelengths corresponding to each color. When a wave meets the surface between two different materials or conditions (e.g., air to water), part of the wave is reflected at that surface and another part continues on, but at a different speed. The change of speed of the wave when passing from one medium to another can cause the wave to change direction or refract. These wave properties are used in many applications (e.g., lenses, seismic probing of Earth).
The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing. The reflection, refraction, and transmission of waves at an interface between two media can be modeled on the basis of these properties.
All electromagnetic radiation travels through a vacuum at the same speed, called the speed of light. Its speed in any given medium depends on its wavelength and the properties of that medium. At the surface between two media, like any wave, light can be reflected, refracted (its path bent), or absorbed. What occurs depends on properties of the surface and the wavelength of the light.
SAT Subject Area Test in Physics
Waves and optics:
- Reflection and refraction, such as Snell’s law and changes in wavelength and speed
- Ray optics, such as image formation using pinholes, mirrors, and lenses
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the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;
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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)
How do point particles create atoms with size?
This article is archived for use with my students from Ask Ethan: If Matter Is Made Of Point Particles, Why Does Everything Have A Size?
Forbes, Stars With a Bang, by Ethan Siegel 9/16/17
Proton Structure Brookhaven National Laboratory
The big idea of atomic theory is that, at some smallest, fundamental level, the matter that makes up everything can be divided no further. Those ultimate building blocks would be literally ἄ-τομος, or un-cuttable.
As we’ve gone down to progressively smaller scales, we’ve found that molecules are made of atoms, which are made of protons, neutrons, and electrons, and that protons and neutrons can be further split into quark and gluons. Yet even though quarks, gluons, electrons, and more appear to be truly point-like, all the matter made out of them has a real, finite size. Why is that? That’s what Brian Cobb wants to know:
Many sources state that quarks are point particles… so one would think that objects composed of them — in this instance, neutrons — would also be points. Is my logic flawed? Or would they be bound to each other in such a way that they would cause the resulting neutron to have angular size?
Let’s take a journey down to the smallest scales, and find out what’s truly going on.
Magdalena Kowalska / CERN / ISOLDE team
If we take a look at matter, things behave similar to how we expect they should, in the macroscopic world, down to about the size of molecules: nanometer (10-9meter) scales. On smaller scales than that, the quantum rules that govern individual particles start to become important.
Single atoms, with electrons orbiting a nucleus, come in at about the size of an Angstrom: 10-10 meters. The atomic nucleus itself, made up of protons and neutrons, is 100,000 times smaller than the atoms in which they are found: a scale of 10-15 meters. Within each individual proton or neutron, quarks and gluons reside.
While molecules, atoms, and nuclei all have sizes associated with them, the fundamental particles they’re made out of — quarks, gluons, and electrons — are truly point-like.
E. Siegel / Beyond The Galaxy
The way we determine whether something is point-like or not is simply to collide whatever we can with it at the highest possible energies, and to look for evidence that there’s a composite structure inside.
In the quantum world, particles don’t just have a physical size, they also have a wavelength associated with them, determined by their energy. Higher energy means smaller wavelength, which means we can probe smaller and more intricate structures. X-rays are high-enough in energy to probe the structure of atoms, with images from X-ray diffraction and crystallography shedding light on what molecules look like and how individual bonds look.
Imperial College London
At even higher energies, we can get even better resolution. Particle accelerators could not only blast atomic nuclei apart, but deep inelastic scattering revealed the internal structure of the proton and neutron: the quarks and gluons lying within.
It’s possible that, at some point down the road, we’ll find that some of the particles we presently think are fundamental are actually made of smaller entities themselves. At the present point, however, thanks to the energies reached by the LHC, we know that if quarks, gluons, or electrons aren’t fundamental, their structures must be smaller than 10-18 to 10-19 meters. To the best of our knowledge, they’re truly points.
Brookhaven National Laboratory
So how, then, are the things made out of them larger than points? It’s the interplay of (up to) three things: Forces, Particle properties, and Energy.
The quarks that we know don’t just have an electric charge, but also (like the gluons) have a color charge. While the electric charge can be positive or negative, and while like charges repel while opposites attract, the force arising from the color charges — the strong nuclear force — is always attractive. And it works, believe it or not, much like a spring does.
Warning: Analogy ahead!
Here we go:
How did the Proton Get Its Spin? Brookhaven National Laboratory
Above: The internal structure of a proton, with quarks, gluons, and quark spin shown. The nuclear force acts like a spring, with negligible force when unstretched but large, attractive forces when stretched to large distances
When two color-charged objects are close together, the force between them drops away to zero, like a coiled spring that isn’t stretched at all.
When quarks are close together, the electrical force takes over, which often leads to a mutual repulsion.
But when the color-charged objects are far apart, the strong force gets stronger. Like a stretched spring, it works to pull the quarks back together.
Based on the magnitude of the color charges and the strength of the strong force, along with the electric charges of each of the quarks, that’s how we arrive at the size of the proton and the neutron: where the strong and electromagnetic forces roughly balance.
APS/Alan Stonebraker
The three valence quarks of a proton contribute to its spin, but so do the gluons, sea quarks and antiquarks, and orbital angular momentum as well. The electrostatic repulsion and the attractive strong nuclear force, in tandem, are what give the proton its size.
On slightly larger scales, the strong force holds protons and neutrons together in an atomic nucleus, overcoming the electrostatic repulsion between the individual protons. This nuclear force is a residual effect of the strong nuclear force, which only works over very short distances.
Because individual protons and neutrons themselves are color-neutral, the exchange is mediated by virtual, unstable particles known as pions, which explains why nuclei beyond a certain size become unstable; it’s too difficult for pions to be exchanged across larger distances. Only in the case of neutron stars does the addition of gravitational binding energy suppress the nucleus’ tendency to rearrange itself into a more stable configuration.
Wikimedia Commons user Manishearth
And on the scale of the atom itself, the key is that the lowest-energy configuration of any electron bound to a nucleus isn’t a zero-energy state, but is actually a relatively high-energy one compared to the electron’s rest mass.
This quantum configuration means that the electron itself needs to zip around at very high speeds inside the atom; even though the nucleus and the electron are oppositely charged, the electron won’t simply hit the nucleus and remain at the center.
Instead, the electron exists in a cloud-like configuration, zipping and swirling around the nucleus (and passing through it) at a distance that’s almost a million times as great as the size of the nucleus itself.
The energy levels and electron wavefunctions that correspond to different states within a hydrogen atom, although the configurations are extremely similar for all atoms. The energy levels are quantized in multiples of Planck’s constant, but the sizes of the orbitals and atoms are determined by the ground-state energy and the electron’s mass.
There are some fun caveats that allow us to explore how these sizes change in extreme conditions. In extremely massive planets, the atoms themselves begin to get compressed due to large gravitational forces, meaning you can pack more of them into a small space.
Jupiter, for example, has three times the mass of Saturn, but is only about 20% larger in size. If you replace an electron in a hydrogen atom with a muon, an unstable electron-like particle that has the same charge but 206 times the mass, the muonic hydrogen atom will be only 1/206th the size of normal hydrogen.
And a Uranium atom is actually larger in size than the individual protons-and-neutrons would be if you packed them together, due to the long-range nature of the electrostatic repulsion of the protons, compared to the short-range nature of the strong force.
Image credit: Calvin Hamilton.
The planets of the Solar System, shown to the scale of their physical sizes, show a Saturn that’s almost as large as Jupiter. However, Jupiter is 3 times as massive, indicating that its atoms are substantially compressed due to gravitational pressure.
By having different forces at play of different strengths, you can build a proton, neutron, or other hadron of finite size out of point-like quarks. By combining protons and neutrons, you can build nuclei of larger sizes than their individual components, bound together, would give you. And by binding electrons to the nucleus, you can build a much larger structure, all owing to the fact that the zero-point energy of an electron bound to an atom is much greater than zero.
In order to get a Universe filled with structures that take up a finite amount of space and have a non-zero size, you don’t need anything more than zero-dimensional, point-like building blocks. Forces, energy, and the quantum properties inherent to particles themselves are more than enough to do the job.
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Ethan Siegel is the founder and primary writer of Starts With A Bang!
This website is educational. Materials within it are being used in accord with the Fair Use doctrine, as defined by United States law.
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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;
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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)
Radar
Radar was developed secretly for military use by several nations, before and during World War II.The term was coined in 1940 by the United States Navy as an acronym for RAdio Detection And Ranging. It entered English and other languages as a common noun, losing all capitalization.
Radar uses radio waves to determine the range, angle, or velocity of objects.
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EM waves can be of many different wavelengths.
Longer wavelengths we perceive as orange and red
Shorter wavelengths are towards the blue end of the spectrum
Fields are at right-angles to each other
They travel through vacuum (empty space) at the speed of light
c = speed of light
c = 3 x 108 m/s = 186,282 miles/second
So all parts of the EM spectrum – radio, light, Wi-Fi, X-rays,
are all made of exactly the same thing! The only thing different among them? wavelength and frequency!
Our eyes can only see a tiny amount of the EM spectrum.
There are longer and shorter waves as well.
Is used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain.
A radar system consists of:
transmitter producing electromagnetic radio waves
a receiving antenna (often the same antenna is used for transmitting and receiving)
a receiver and processor to determine properties of the object(s)
Radio waves from the transmitter reflect off the object and return to the receiver
This gives info about the object’s location and speed.
Uses
air and terrestrial traffic control
radar astronomy
air-defence systems / antimissile systems
tba
marine radars to locate landmarks and other ships
aircraft anticollision systems
outer space surveillance and rendezvous systems
meteorological (weather) precipitation monitoring
flight control systems
guided missile target locating systems
ground-penetrating radar for geological observation
Learning Standards
2016 Massachusetts Science and Technology/Engineering Curriculum Framework
6.MS-PS4-1. Use diagrams of a simple wave to explain that (a) a wave has a repeating pattern with a specific amplitude, frequency, and wavelength, and (b) the amplitude of a wave is related to the energy of the wave.
HS-PS4-1. Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling within various media. Recognize that electromagnetic waves can travel through empty space (without a medium) as compared to mechanical waves that require a medium.
HS-PS4-5. Communicate technical information about how some technological devices use the principles of wave behavior and wave interactions with matter to transmit and capture information and energy. Clarification Statements:
• Emphasis is on qualitative information and descriptions.
• Examples of technological devices could include solar cells capturing light and
converting it to electricity, medical imaging, and communications technology.
Massachusetts Science and Technology/Engineering Curriculum Framework (2006)
6. Electromagnetic Radiation Central Concept: Oscillating electric or magnetic fields can generate electromagnetic waves over a wide spectrum. 6.1 Recognize that electromagnetic waves are transverse waves and travel at the speed of light through a vacuum. 6.2 Describe the electromagnetic spectrum in terms of frequency and wavelength, and identify the locations of radio waves, microwaves, infrared radiation, visible light (red, orange, yellow, green, blue, indigo, and violet), ultraviolet rays, x-rays, and gamma rays on the spectrum.
Can we stop a hurricane
Can we stop a hurricane? Sounds like something out of science fiction, a proposal fitting of mad scientists, right?
Remember Hurricane Katrina? August 2005. It was a destructive Category 5 Atlantic hurricane that caused over 1,800 fatalities and $125 billion in damage. Damaged the are of and around the city of New Orleans. What if there had been a way to shift its course, or reduce its intensity?
In Hurricane Forcing: Can Tropical Cyclones Be Stopped? by Christopher Mims, Scientific American, October 23, 2009, we read
This past June, a plan to reduce the severity and frequency of hurricanes leaked to the public in the form of a patent application under Bill Gates’s name (along with many others), resuscitating speculation about a scheme that has been proposed off and on since the 1960s. The core of the idea remains the same: mixing the warm surface waters that fuel tropical cyclones with cooler waters below to drain storms of their energy. But now Stephen Salter an emeritus professor of engineering design at the University of Edinburgh proposes a new—and possibly more realistic—method of mixing.
Salter has outlined in an engineering paper the design for a floating structure 100 meters in diameter—basically a circular raft of lashed-together used tires (to reduce cost). It would support a thin plastic tube 100 meters in diameter and 200 meters in length.
When deployed in the open ocean, the tube would hang vertically, descending through the warm, well-mixed upper reaches of the ocean and terminating in a deeper part of the water column known as the thermocline, where water temperatures drop precipitously.
The point of this design is to transfer warm surface water into the deeper, cooler reaches of the ocean, mixing the two together and, hopefully, cooling the sea surface. Salter’s design is relatively simple, using a minimum of material in order to make the construction of each of his devices cheap (millions of used tires are thrown away each year, worldwide); his scheme would also require the deployment of hundreds of these devices.
Using horizontal wave action at the ocean surface, passive no-return valves would capture energy by closing after a wave has passed through them, allowing the circular interior of each device to raise the level of the seawater within the device by, on average, 20 centimeters. The weight of the gathered warm water would thereby create downward pressure, pushing it down the tube.
The idea is that hundreds of these floating wave-powered seawater pumps would be deployed year-round in areas, such as the eastern tropical Atlantic and the Gulf of Mexico, where hurricanes typically spawn or grow in intensity. (The devices would not, as widely speculated, be deployed only in the path of a hurricane that already formed.) …
In Can Science Halt Hurricanes? we read
Until recently, the U.S. Department of Homeland Security has been investigating whether seeding storm clouds with pollution-size aerosols (particles suspended in gas) might help slow tropical cyclones. Computer models suggest that deploying aerosols can have “an appreciable impact on tropical cyclone intensity,” writes William Cotton, an atmospheric scientist at Colorado State University. He and his colleagues recently reviewed such work in the Journal of Weather Modification. In fact, human pollution may already be weakening storms, including August’s Hurricane Irene. “[Computer] models all predicted that the intensity of Irene would be much greater than it was,” Cotton notes. “Was that because they did not include aerosol effects?”…
In The Insider, Kelley Dickerson writes
Engineers could stop hurricanes with the ‘sunglasses effect’ — but it’d require a huge sacrifice
According to new research published in the journal Proceedings of the National Academy of Sciences, if we pumped sulfate gases into our planet’s upper atmosphere, we could cool down our oceans enough to cut the number of Katrina-force hurricanes in half over the next 50 years. It’d require about 10 billion tons of sulfates to get the job done, which is tens or hundreds of times the sulfates a typical volcanic eruption can form.
From Stanford University we read
Computer simulations by Professor Mark Z. Jacobson have shown that offshore wind farms with thousands of wind turbines could have sapped the power of three real-life hurricanes, significantly decreasing their winds and accompanying storm surge, and possibly preventing billions of dollars in damages…. he found that the wind turbines could disrupt a hurricane enough to reduce peak wind speeds by up to 92 mph and decrease storm surge by up to 79 percent.
The study, conducted by Jacobson, and Cristina Archer and Willett Kempton of the University of Delaware, was published online in Nature Climate Change….
Taming Hurricanes With Arrays of Offshore Wind Turbines (Nature Climate Change, 2014)
In this intriguing discussion, science fiction writers look into the real physics of the question, What would be need to stop a hurricane? What would we need to stop a hurricane? Worldbuilding @ Stackexchange
Also see these great topics at Hurricane Research Division NOAA, National Oceanic and Atmospheric Administration
Tropical Cyclone Modification and Myths
The Science and History of the Sea
Session 1: TBA at the USS Constitution Museum. Museum staff led.
Introductory movie (10 minutes)
- Design your own frigate based on the templates of Constitution’s ship designer Joshua Humphreys: Students will produce drawings.
- Made in America – what materials were used to create the USS Constitution? Students will create a list of 5 materials from the New England region.
- Which of these woods is the hardest? Through dropping balls into difference woods, we can study the difference in how the ball bounces back. The kinetic energy of the rebounding ball is related to the amount of energy absorbed by the wood. See the difference between kinetic energy and potential energy.
- Test your ship against other frigates in this hands-on challenge. Choose between three different types of ships for the ultimate test of size, speed and power: An interactive computer simulation.
- What’s so great about copper? Learn about the metals used in construction
- Build a ship: Assemble 2D pieces into a 3D model – how quickly can they accurately complete the task?
- Construction and launch: View this video, and then explain how a ship is safely launched from a drydock into the ocean. Students will demonstrate that they understand the procedure by writing a step-by-step paragraph explaining the sequence.
- How can a ship sail against the wind? Through a hands on experiment, see how changing the angle of the sail affects the motion of the boat: Students should be able to explain in complete sentences how the same wind can make a ship move forwards or backwards.
- On the 2nd story of the museum, operate a working block-and-tackle system. This uses a classic simple machine. It is a system of two or more pulleys with a rope or cable threaded between them, usually used to lift or pull heavy loads. Back in the school building, we’ll review each of the classic simple machines.
On the 2nd story of the museum, operate a working block-and-tackle system. This uses a classic simple machine: pulleys with a rope or cable threaded between them, to lift or pull heavy loads.
Session 2: USS Constitution Visitor Center, Building 5
10 minute orientation video
Can you locate where our school is on the 3D Boston Naval Shipyard model?
As students tour the visitor center, they practice ELA reading and writing skills (listed below) by briefly summarizing something they learn from each of these sections: They are encouraged to create drawings/tracings as they see fit to help illustrate their text.
- Describe how ropes are made from string in the ropewalk
- From wood & sail to steel & steam
- Preparing for new technology
- The shipyard in the Civil War
- Ships and shipbuilding
- The Navy Yard 1890-1974
- Chain Forge and Foundary
- The Navy Yard during World Wars I and II
- Shipyard workers 1890 to 1974
- The shipyard during the Cold War era 1945-1974
Session 4: Teaching math using the USS Constitition
Teaching math: Lessons from the USS Constitution
This teaching supplement contains math lessons organized in grade-level order. However, because many of the math skills used in these lessons are taught in multiple grades, both grade-level and lesson content are listed below.
Pre K–K
Estimating Numbers of ObjectsGrade 1
Estimating and Comparing Numbers of ObjectsGrade 2
Estimating and Comparing Length, Width and PerimeterGrade 3
Computing Time and Creating a ScheduleGrade 4
Drawing Conclusions from Data SetsGrade 5
Creating and Interpreting Graphs from TablesGrade 6
Range, Mean, Median and Mode and Stem-and-Leaf PlotsGrade 7
Converting Between Systems of MeasurementGrade 8
Calculating VolumeAlgebra I (Grade 9–10)
Describing Distance and Velocity GraphsAlgebra I (Grade 9–10)
Writing Linear EquationsAlgebra II (Grade 9–12)
Using Projectile Motion to Explore Maximums and ZerosPrecalculus & Advanced Math (Grade 10–12)
Using Parabolic Equations & Vectors to Describe the Path of Projectile Motion
Learning Standards
MA 2006 Science Curriculum Framework
2. Engineering Design. Central Concept: Engineering design requires creative thinking and consideration of a variety of ideas to solve practical problems. Identify tools and simple machines used for a specific purpose, e.g., ramp, wheel, pulley, lever.
Massachusetts Science and Technology/Engineering Curriculum Framework
HS-ETS4-5(MA). Explain how a machine converts energy, through mechanical means, to do work. Collect and analyze data to determine the efficiency of simple and complex machines.
Benchmarks, American Association for the Advancement of Science
In the 1700s, most manufacturing was still done in homes or small shops, using small, handmade machines that were powered by muscle, wind, or moving water. 10J/E1** (BSL)
In the 1800s, new machinery and steam engines to drive them made it possible to manufacture goods in factories, using fuels as a source of energy. In the factory system, workers, materials, and energy could be brought together efficiently. 10J/M1*
The invention of the steam engine was at the center of the Industrial Revolution. It converted the chemical energy stored in wood and coal into motion energy. The steam engine was widely used to solve the urgent problem of pumping water out of coal mines. As improved by James Watt, Scottish inventor and mechanical engineer, it was soon used to move coal; drive manufacturing machinery; and power locomotives, ships, and even the first automobiles. 10J/M2*
The Industrial Revolution developed in Great Britain because that country made practical use of science, had access by sea to world resources and markets, and had people who were willing to work in factories. 10J/H1*
The Industrial Revolution increased the productivity of each worker, but it also increased child labor and unhealthy working conditions, and it gradually destroyed the craft tradition. The economic imbalances of the Industrial Revolution led to a growing conflict between factory owners and workers and contributed to the main political ideologies of the 20th century. 10J/H2
Today, changes in technology continue to affect patterns of work and bring with them economic and social consequences. 10J/H3*
Massachusetts History and Social Science Curriculum Frameworks
5.11 Explain the importance of maritime commerce in the development of the economy of colonial Massachusetts, using historical societies and museums as needed. (H, E)
5.32 Describe the causes of the war of 1812 and how events during the war contributed to a sense of American nationalism. A. British restrictions on trade and impressment. B. Major battles and events of the war, including the role of the USS Constitution, the burning of the Capitol and the White House, and the Battle of New Orleans.
National Council for the Social Studies: National Curriculum Standards for Social Studies
Time, Continuity and Change: Through the study of the past and its legacy, learners examine the institutions, values, and beliefs of people in the past, acquire skills in historical inquiry and interpretation, and gain an understanding of how important historical events and developments have shaped the modern world. This theme appears in courses in history, as well as in other social studies courses for which knowledge of the past is important.
A study of the War of 1812 enables students to understand the roots of our modern nation. It was this time period and struggle that propelled us from a struggling young collection of states to a unified player on the world stage. Out of the conflict the nation gained a number of symbols including USS Constitution. The victories she brought home lifted the morale of the entire nation and endure in our nation’s memory today. – USS Constitution Museum, National Education Standards
Common Core ELA: Reading Instructional Texts
CCSS.ELA-LITERACY.RI.9-10.1
Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.
CCSS.ELA-LITERACY.RI.9-10.4
Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings
CCSS.ELA-LITERACY.W.9-10.1.C
Use words, phrases, and clauses to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims.
CCSS.ELA-LITERACY.W.9-10.1.D
Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.
CCSS.ELA-LITERACY.W.9-10.4
Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.
External links
What kinds of radiation cause cancer
For most people the biggest cancer risk from radiation hovers in the sky above us giving us all warmth and light. There is no cancer risk from Wi-Fi or microwaves.
Wear sunscreen, but use WiFi without fear. (Image: Spazturtle/SMS (CC))
What is radiation, and where does it come from? nuclear chemistry
What is cancer? How is caused? Cancer
Microwaves, Radio Waves, and Other Types of Radiofrequency Radiation: American Cancer Society
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Soundly Proving the Curvature of the Earth at Lake Pontchartrain
Excerpted from an article by Mick West
A classic experiment to demonstrate the curvature of a body of water is to place markers (like flags) a fixed distance above the water in a straight line, and then view them along that line in a telescope. If the water surface is flat then the markers will appear also in a straight line. If the surface of the water is curved (as it is here on Earth) then the markers in the middle will appear higher than the markers at the ends.
Here’s a highly exaggerated diagram of the effect by Alfred Russel Wallace in 1870, superimposed over an actual photograph.
This is a difficult experiment to do as you need a few miles for the curvature to be apparent. You also need the markers to be quite high above the surface of the water, as temperature differences between the water and the air tend to create significant refraction effects close to the water.
However Youtuber Soundly has found a spot where there’s a very long line of markers permanently fixed at constant heights above the water line, clearly demonstrating the curve. It’s a line of power transmission towers at Lake Pontchartrain, near New Orleans, Louisiana.
The line of power lines is straight, and they are all the same size, and the same height above the water. They are also very tall, and form a straight line nearly 16 miles long. Far better than any experiment one could set up on a canal or a lake. You just need to get into a position where you can see along the line of towers, and then use a powerful zoom lense to look along the line to make any curve apparent
One can see quite clearly in the video and photos that there’s a curve. Soundly has gone to great lengths to provide multiple videos and photos of the curve from multiple perspectives. They all show the same thing: a curve.
One objection you might make is that the towers could be curving to the right. However the same curve is apparent from both sides, so it can only be curving over the horizon.
c
People have asked why the curve is so apparent in one direction, but not in the other. The answer is compressed perspective. Here’s a physical example:
c
That’s my car, the roof of which is slightly curved both front to back and left to right. I’ve put some equal sized chess pawns on it in two straight lines. If we step back a bit and zoom in we get:
Notice a very distinct curve from the white pieces, but the “horizon” seems to barely curve at all.
Similarly in the front-back direction, where there’s an even greater curve:
There’s a lot more discussion with photos here Soundly Proving the Curvature of the Earth at Lake Pontchartrain
KaiserScience 