In December of 2013 physicists discovered a way to approximate the amplitude of scattering sub-atomic particles in a way that is much, much simpler than the old method. The idea is that given a set of parameters and whatnot, a geometric object, which is being called an amplituhedron, can be constructed such that it's volume equals the amplitude of a scattered particle from a quantum interaction. The old method involved using hundreds to millions of Feynman diagrams, which show possible ways the particle could scatter, and summing the probability of each situation occurring. Even a simple interaction had to be modeled by a formula several billion terms long but the amplituhedron process reduces that to just a few pages of work. For example, the diagram to the left represents an 8 gluon particle interaction. If the same calculation were to be done with the Feynman method it would involve around 500 pages of calculations. The implications of this are enormous, and this may be a big step in the direction of a functional unified field theory.
I would like to take a step back from physics to propose another law on the effects of procrastination on the APlusPhysics blogs. I have already explored the relationships between amount of procrastination and both quality of blog posts and hours slept the night they are due. Every time I refresh the "dashboard" page five new posts pop up, and I have noticed that the same posts don't stay on the front page for very long. It would seem that we are all hurting ourselves in terms of views by all waiting until the last possible second to do these because in the time that it takes to write the next post, your last post has already disappeared, never to be seen again by anybody. On the other hand increased site traffic might expose your blog to more potential readers. All of this of course really only matters if you care about how many people read your posts (I do, just because I take the time to write them). I could also be mistaken about how the dashboard works....
I just found a video of a man playing a Tesla coil as a musical instrument. With a guitar. Basically, the guitar still works the same way but rather than sending its MIDI signals (notes and such) to an amp, it is being sent to a Tesla coil. Tesla coils work by sending alternating current through a wires coiled into a torus (donut shape). The changing current charges a larger torus trough electromagnetic induction. The voltage induced in the second coil is much greater than the first which allows a capacitor to be charged to the extreme where it trows visible electricity to the nearest conductor. When the coil is turned on it makes a noise, so the trick to making music with a Tesla coil is to alternate current at a frequency at which our brain can interpret music (it turns out to me about 440 hertz). Notes can be created by modulating the amplitude of the current. In the case of the guitar, the players input on the strings is used to modulate the amplitude. Here's the video i was talking about:
And then I found this and my mind was blown...
Kickstarter is full of cool stuff but a project called Altergaze really caught my eye. What it is is a 3D printed platform with a set of up to 3 lenses inside and a holder for your smartphone. The lenses magnify the screen so that it takes up your entire field of view, allowing you to watch video and whatnot in giant, beautiful panoramic views. And the beauty of it is that since it it 3D printed, the firm starting it is making the templates open source and offering partnerships to just about anyone with a 3D printer. They supply the lenses but you get to choose colors and can modify the phone holder to accommodate any kind of phone you want. You can check out their kickstarter page here: https://www.kickstarter.com/projects/278203173/altergaze-mobile-virtual-reality-for-your-smartpho?ref=category
The physics comes in with the lenses. The lenses magnify and bend your field of view by refracting light in such a way that makes your phone's screen everything you see.
The second major type of telescope is the reflecting telescope. The reflecting telescope was invented by Newton and considered an improvement on Galileo's design. Most reflecting scopes still use Newton's design. Reflecting scopes use a wide concave mirror at the back of the tube to bring light to a focal point in front of the mirror which is then usually reflected sideways toward the eyepiece by a flat, angled mirror. There are also compound scopes that work like reflecting scopes but there is a hole in the center of the concave mirror and the mirror at the foal point reflects light back through the hole where it is magnified by an eyepiece at the end of the tube. Below are diagrams of both reflecting and compound telescopes.
Now for some pros and cons. Refractor tubes are usually longer and skinnier, thus have smaller apertures (and cost more per unit of aperture length); while reflectors are wider and shorter with larger apertures (and less cost per unit of aperture length). Because of this, refractors are usually more expensive and better for observing close planets while reflectors are better for observing deep sky objects like galaxies and nebulae.
Last night I happened to look up as I was walking inside at around 10 and noticed that I could see a lot of stars. Like a lot. I am quite a fan of stargazing but despite owning a telescope I have always done it with my naked eyes. But I was in the mood to see some planets in detail so I lugged down the old telescope from the attic and dusted her off only to make a distressing discovery- all the eyepieces were missing (you need those if you want to see anything). My dad and I scoured the dust and cobweb infested boxes in our attic for half an hour but came up empty handed, and I had to resign to reading a book. Now that you have gotten through my exceptionally boring story, I would like to tell you how telescopes work.
The basic function of a telescope is to collect, focus and magnify the light emitted from celestial bodies (stars, planets, nebulae, galaxies, ect...). In many cases, it is actually more important to collect and filter light than it is to magnify it. The ability of a telescope to collect light is related to it's aperture- which is it's lens or mirror diameter- and it's ability to magnify depends on magnification. Aperture is usually harder to expand as it depends on the diameter of the telescope tube but magnification can be changed as easily as screwing in a new eyepiece. The first telescope created by Galileo was a refracting telescope. Contrary to popular belief, Galileo did not invent this technology but he was the first to apply it to the art of stargazing. Refracting scopes use a large objective lens at the front of the tube to collect and bring light into a focal point in the middle of the tube. From there it can be focused and magnified by the eyepiece. Below is a diagram of how light travels through refracting lenses. Check out my next post for reflecting telescopes and closing thoughts.
In December of 2013 the European Space Agency launched Gaia, the most accurate telescope to ever be put into space. Its 1 gigapixel camera (that's 1 billion pixels or 1000 megapixels) is said to be able to measure a human thumbnail from the moon or detect the width a human hair from a distance of 1000 Km, which is some pretty incredible imaging science right there. Whats more, telescopes work better where its dark, so the ESA is putting it in orbit around the sun, around the L2 lagrange point which is out past the moon- which sounds funky but let me explain. L2 is 1500000 Km from the Earth in the direction away from the sun, and from there Gaia will orbit the sun with the same period as the Earth, but free of much of the Earth's light and gravity. Rather than staying still at the L2 point however, ESA is using advanced flight dynamics to put Gaia into a 3 dimensional pendulum-like orbit about L2. [below are visuals of the L2 lagrange point and Gaia's motion around it] The period of Gaia's motion around L2 is going to be about a year an a half. From its orbit around L2, Gaia will operate for at least 5 years creating a very accurate map of over a billion stars, a million quasars and search for exoplanets. The images produced by NASA's hubble telescope are stunning, but with much superior imaging technology and being a million kilometers farther from earth than the Hubble, I can't wait to see what Gaia sends back.
I have been somewhat obsessed with space lately. I also recently learned that there are spacecraft outside of our solar system, which for some reason just seems really cool to me. In September of 2013 Voyager 1 officially left the heliosphere, which is the area in space dominated by solar winds and charged particles from the sun and extends about twice the distance from Pluto as Pluto is from the sun. The deep space probe Voyager 2 was launched on August 20th, 1977 and Voyager 1 was launched two weeks later on September 5th. Voyager 2 has yet to breach into interstellar space. Despite the fact that it was launched earlier, because it is traveling slower than Voyager 1 at some 15 Km/s relative to the sun compared to 1's 17 Km/s. The original purpose of the Voyager mission was to explore the outer planets of the solar system. After providing great data on Saturn, Neptune and Pluto in the 80's the mission was extended to gather data on interstellar space, space dominated by radiation from stars other than our sun. Both probes are still gathering and sending data back to the earth, which takes about 17 hours to travel from the probe's transmitter to NASA's Deep Space Network, a global array of giant radio communication dishes. The probes will be able to record and transmit data until 2025 when their nuclear batteries are expected to die and then they will sail though the cosmos for the rest of eternity, lonely travelers among unknown worlds.
A few days ago scientists confirmed that there is liquid water on Enceladus one of Saturn's 53 or so moons. The surface of Enceladus is covered in a thick sheet of ice but NASA's Cassini spacecraft which has been orbiting Saturn since 2004 has sent back images of geysers of ice, water vapor and organic compounds shooting out from cracks in the ice at the south pole of Enceladus. This was the first sign that there may be liquid water below the ice. Also, NASA noticed slight changes in Cassini's trajectory and the wavelength of it's radio signals which suggested that Enceladus has a greater mass at the south pole. In addition, it has long been known that Enceladus is flatter at the south pole than anywhere else. The best explanation for both phenomena is that there exists a large body of liquid water, which is both denser and has less volume than ice, underneath the south pole. This subterranean ocean is estimated to be about the size of lake superior and is particularly exciting because it is thought to sit above a layer of rock that could provide chemical reactions which when coupled with the organic molecules in the geysers could possibly produce simple organisms. Unfortunately Cassini doesn't have the instruments needed to properly test the makeup of the molecules in the geysers and the ice above the lake on Enceladus is somewhere around 20 miles thick so a much more sophisticated robot would need to be sent in order to search for life.
Below are a Cassini picture of the ice plumes at the south pole and a rendering of Enceladus's cross section.
First of all I have to say that I'm surprised that nobody here has blogged about this yet. But in case you haven't heard yet, March 17th was a big day for science, and physics in particular. Researchers from Harvard University and the Smithsonian released evidence of distortion in the cosmic background radiation (shown to the right) caused by gravitational waves from when the universe went through inflation after the big bang. The idea is that in the 1x10-35th of a second after the big bang the universe expanded very rapidly at a speed much larger than the speed of light (and yes, that is possible since its the universe itself was moving). So what exactly does this mean? First of all, it is direct evidence that the big bang happened. There still may be a little uncertainty but the team that found this distortion has been looking at it for three years ruling out every other possibility so chances are it's exactly what they say it is. It also may have profound effects on our understanding of physics. Gravity waves were the last untested part of Einstein's theory of general relativity and with this evidence its now a complete theory. There is also a chance that it may lead to a unified theory of modern physics. As of now general relativity (the physics of very large things) and quantum mechanics (physics of very small things) don't work together but this discovery could help bridge the gap between the two. Also, most of the current theories of inflation include the existence of multiple universes and this evidence narrows down the theories a lot to the ones that include a multi-verse. The possibilities with this are endless because there is a chance that other universes will have laws of physics different than our own, which would be crazy but awesome to study. Scientific breakthroughs of this magnitude don't happen often but when they do they usually lead to a vastly improved understanding of the mechanisms of the universe.
In the last few minutes I have noticed a lot of activity on the Aplusphysics blog, which is strange because it's almost midnight. Oh wait, blogs are due tomorrow? That explains something. Right now is the time when everyone cranks out those last couple posts that should have been done weeks ago, and I'm just as guilty as the rest of you. I want to be asleep right now more than anythi- hold it right there, if I'm writing this blog post I must want a good physics grade more than sleep. I also just discovered an interesting connection here. Amount of procrastination has an inverse relationship with hours of sleep the night before midterms start. I would also like to argue that the line illustrating this trend has a vertical asymptote at the y-axis because in theory if all of my work was done right now I could sleep for an infinite number of hours nevermind that was dumb- I won't live forever. I have created several graphs illustrating my point. I don't like them.
So the other day I was skiing along on one of those straight, flat trails so I was naturally a little bit bored. So I decided to see how high I could jump. I pushed off the ground pretty hard and... got like 2 inches of air. I was pretty disappointed in myself so I tried again. This time a squatted down and pushed off the ground with as much force as my skinny legs could muster and... 2.5 inches. Whats wrong with me? So I stopped and tried to jump vertically while not moving and I got much higher (although it was still pretty embargoing). I stood there for a minute and tried to figure out what was going on. Why can I jump higher while standing still than while moving? Eventually I hypothesized that while standing still the vector of the downward force created to make the jump is directed normal to the ground, maximizing the reaction from the ground; however if you try to jump while sliding across the snow on your skis some of the force is applied parallel to the ground due to your forward motion, in effect creating the same magnitude of the resultant force vector but at an angle which trades some vertical height for horizontal distance. Or maybe I'm just really bad at jumping...
Today was one of those days when all the roads were covered in snow, which is bad for driving and even worse for running. A few steps in that salty slush and you'll be slipping all over the place. What I've found is that snow sticks to the bottom of my shoes and stays there, so rather than my rubber soles trying to get traction with snow, there is just more snow trying to get traction with the snow. This drastically reduces the coefficient of static friction between my shoes and the road, causing my feet to slip every step which gets really annoying after about 20 feet. Also less frictional force means less effect from newton's third law and more energy wasted every step making running a tedious task at best.
This is a continuation of my last post: Another reason humans are so good at running is we have big butts. I'm not joking. Humans have larger gluteus maximus muscles than any other other species on earth and the gluteus maximus is the most powerful muscle in the human body. Daniel Lieberman, chair of the Department of Human Evolutionary Biology at Harvard University, conducted a study of gluteus maximus function and found that the glutes are much more active while running than while walking, indicating that they evolved for the purpose of running. So what does your butt do for you when you run? Primarily it provides the power needed to run, so much power in fact that double amputees without hamstrings or quadriceps like Rudy Garcia-Tolson are able to run with nothing but their glutes. The glutes also serve a secondary purpose of pushing the hips under the abdomen, eliminating lardosis (backwards bending) in the spine which reduces impact on the back and allows for more use of deep abdominal muscles such as the psoas (pronounces so-az). Another reason humans are so good at running for long distances is that unlike pretty much every other animal on earth that can run, our respiration isn't tied to our stride. In in which I described why cheetahs are so fast I explained how the breathing of some quadrupeds (animals that walk on 4 legs) is regulated by organ movemenet amplifying changes in chest cavity pressure which makes quadrupeds necessarily inhale and exhale once every stride cycle. Since humans are completely bipedal our respiratory system is entirely independent of whether we're running or not, allowing for varied breathing patterns. 1-1 and 2-2 patterns (ex. inhaling for 2 steps then exhaling for 2 steps) are great while running fast because they allow for more oxygen intake but it is hard to run far while hyperventilating. In contrast 4-4 (or 3-4/ 4-3) is a better pattern for running far but makes running fast more challenging (most runners usually wont go any slower than 4-4 because anything sustaining anything slower requires running pretty slow but I have been able to sustain an 11-11 pattern for a few minutes of slow jogging- it's not very practical but its cool to be able to do). The fact that humans can control their breathing independent of their speed allows us to maintain an ideal oxygen level for running very long distances.
In my last post I highlighted some of the incredible things that distance runners are able to do, including very long runs at altitude (lower oxygen) and in extreme conditions. But what allows these people to do these kinds of things? The short answer is training. With enough training almost anyone (for the most part excluding the very elderly) could finish an ultra marathon. But why is this? The answer lies in the fact that humans are better adapted to run for long distances than any other animal on the planet. First of all, humans are bipedal meaning that we move around on two feet, and while other primates are able to walk with two limbs humans are the only primates who walk exclusively with only two legs. Bipedalism in itself isn't incredibly unique as other mammals such as macropods (kangaroos, wallabies...) and large birds like ostriches and emus rely on bipedal movement as well, however humans have other adaptations to make bipedalism more efficient. You may not realize it but the human foot is a very intricate mechanical structure containing 26 bones, 33 joints and over 100 muscles and tendons. While running the foot, specifically the arch, acts as a spring which absorbs and returns force to the ground which is done as follows: the foot lands on the outside of the forefoot and pronates inward, stretching muscles which absorb and store force. The foot rocks forward while it pronates so that by the time the front pad of the foot is flat on the ground the toes are pushing off the ground with the energy stored in the foot's muscles. In addition to the feet the rest of the muscles act as springs which store energy from the foot strike to be used as propulsion for that step. As a result, running is basically a process of converting kinetic energy (foot strike) into potential energy (stretched muscles) and back into kinetic energy (push off). Of course as in any system, energy is lost as heat thus cells must break down glucose during anaerobic and aerobic respiration to create ATP for your muscles to use to create additional energy to put into the ground.
First things first: I would like to complain about the fact that people are not at all creative while heckling runners. You may think that shouting "Run Forrest, run!" out of your car window is funny and original, but its not. I've heard that at least 20 times in the last few years. In case you have never seen the movie Forrest Gump (shame on you if you haven't, you don't deserve to be a person) this is a reference to the scene when protagonist Forrest is being chased by bullies and his friend Jenny yells "Run Forrest, run!" so he does causing the braces to break off his legs and allowing him to take off full sprint through a field, escaping the bullies and discovering his running ability (I shouldn't have even had to explain that...) Later in the movie Forrest runs across the US several times which is quite the display of distance running ability. But this is far from fiction- since 1909 there have been 283 recorded crossing of the continental US on foot by 252 individuals. Other extreme running feats include the Ultramarathon which is a race longer than a marathon, which is 26.2 miles (42.2 km). Some extreme examples include the Leadville 100 and Western States Endurance Run, which are both 100 mile races run on mountain trails at elevations of over 10000 feet and contain 15000 to 18000 feet of climbing and descending, and the Badwater Ultramarathon which is run 135 miles through death valley (average air temperature of 120 degrees F) and finishes by climbing 13000 feet up Mount Whitney. In the during this race the road surface gets so hot that runners must run on the white lines on the side of the road to keep the soles of their shoes from melting though participants usually go through several pairs throughout the race anyway
According to Einstein, nothing can move faster than the speed of light (which is exactly 299,792,458 m/s in a vacuum). However this hasn't stopped people from trying to think of clever ways to move something faster than this cosmic speed limit. It has been claimed that by shining a laser on the surface of the moon from earth and moving the laser quickly, the beam moves across the surface at faster than the speed of light, which is partially true. What is actually happening is that photons traveling at the speed of light are hitting the moon's surface in quick succession to form an imaginary spot that moves at faster than the speed of light, so nothing actually moves faster than light. A similar idea involves applying torque to a very long (in the magnitude of 500,000 km) rigid pole that pivots around one end, the idea being that the other end of the pole will move at faster than the speed of light. Unfortunately this is impossible since forces cannot move through materials at faster than the speed of sound and at that distance it is more than likely that all of the energy applied in the form of torque would be lost as heat in the process of the atoms in the material hitting each other in order to move your force through the object. (A related idea involves pushing one end of a light-year long pole in hopes that the other end would react instantaneously but this faces the same problems as the previous theory.) Finally, an idea similar to applying torque to a long pole is creating a spacecraft that spins with high rpm and torque and extends very long arms of something like carbon nano tubes to a very long length so that eventually the ends of the arms move the speed of light. The problem with this is that even with something as strong as carbon nano tubes, the required thickness of the arms would be literally impossible to make; and even with an impossibly strong material the electromagnetic force that hold the material together relies on the transmission of photons which only move at the speed of light.
*I did not come up with this on my own, I am just paraphrasing a Veritasium video which can be seen below.
The other night I watched the movie Black Hawk Down, which is based on the book of the same name (written by Mark Bowden) which was based on the actual events of the Battle of Mogadishu. The short story is that the US sent Army Rangers, Delta Force operators and pilots from the 160th Special Operations Aviation Regiment to remove Somalian dictator Mohamed Farrah Aidid from power and in October of 1993 they conducted a raid with the intent of capturing two of Aidid's highest advisers. The operation was supposed to take no longer than an hour and incurr no casualties but after a series of complications it became a full battle lasting through the night and into the next morning. The main problem that occurred was that one of the 8 Black Hawk helicopters crashed after losing its tail rotor, which is where physics comes in. Most helicopters have a single horizontal main rotor and a vertical tail rotor. A two rotor system is necessary because the main rotor produces torque in on direction which would cause the helicopter to spin out of control (a notable exception is the NOTAR system which involves a single main rotor and a ducted fan in the tail takes the place of a second rotor). The tail rotor provides a counter torque force (static equilibrium in one axis to move in a straight line) and rotational turning in the x-z plane (other configurations include NOTAR and double main rotor configurations such as 2 coaxial rotors, angled meshed rotors, and front and back or side to side flat rotors). Anyway, in the movie (and real life) the Black Hawks tail rotor is blown off by an RPG causing the pilot to lose control as the craft began to spiral uncontrollably due to unopposed torque and crash. The operation was then updated to include the rescue the crew of the downed helicopter (who all unfortunately died). In the process many Americans were wounded or killed and a second Black Hawk was shot down the same way as the first causing even more problems. Having read the book In the Company of Heros, also by Mark Bowden, which is the true story Michael Durant (the pilot and only survivor of the second crashed helicopter who was taken prisoner and held for 11 days with a broken back and leg) I found the movie to be very close to the actual events and included the shootout in which two delta force snipers sacrificed their lives to protect Durant and a conversation that Durant actually had with one of Aidid's advisers. By the time the battle was over 18 Americans lost their lives with another 80 wounded. A dark day for the American military but a true display of courage on the part of all the soldiers involved.
Warning: not only is this a lame story, its also slightly graphic
Whoever said that running isn't a contact sport was dead wrong, and my right arm can prove it. But more on that later. In the last few years I have seen more kids than I count fall during races, often getting trampled by other runners who are wearing shoes with metal spikes, up to half an inch long, protruding from the bottom. These poor souls always pick themselves up, battered and bloody (literally) and finish the race. I had never personally fallen during a race until last weekend when I tripped while running the 600 meter dash. The 600 is literally the worst race to fall in because it is the shortest track race not run in lanes so it is therefore the fastest you can be running in a pack of other runners. I was in the front of the pack when I fell, thankfully I wasn't stepped on. Unfortunately for me, track surfaces are designed with a high coefficient of friction so that people don't slip on the turns or lose their footing while sprinting; which is great while you're running upright, not so good when you're sliding on the front side of your body... So after hitting the ground and sliding with enough force to skin a cat, the track fought back (Newton's 3rd law) and ripped some skin off my hand while literally burning my left shoulder, ribs and hip. It didn't actually hurt that much but I have some advice: exposing healing skin to hot running water will cause extreme pain, as I found out when I took a shower that night...
So here's something neat that I just stumbled across on YouTube. It also connects to our current unit of rotational dynamics perfectly. Its called "Cubli" which a compound of the English word 'cube' and the German word 'li' meaning something small in size. Cubli is basically a 15x15cm cube that can move and balance with the help of angular momentum. It contains three flywheels are able to achieve high angular velocity (ω) and acceleration and react quickly to external forces with the help of sensors that detect changes in inertia and then change the angular velocity of the wheels. The system is accurate enough to balance cubli on its edges and corners, and remain balanced even after being pushed. Whats more, by spinning the flywheels very fast to create angular momentum and then stopping suddenly cubli can create enough force pop itself up from laying flat to balancing on a corner. This is because of the impulse-momentum theorem which states that impulse=momentum so angular momentum=L=Iω=imulse=FΔt, so Iω=FΔt, and solving for force F=Iω/Δt. Since I (moment of inertia) is a constant, cubli is able to spin its flywheels fast enough and stop them is such little time that it is able to create enough force throw its mass onto an edge and then corner, and then react fast enough to balance. Here's a video of the cubli in action.
Here's something I just stumbled upon a few minutes ago. Its Olympus Mons, Mars' largest mountain. Olympus Mons is also the largest volcano in the solar system and the 2nd tallest mountain in the solar system (behind the Rheasilvia peak on the asteroid 4 Vesta). Olympus Mons is a shield volcano and was formed the same way that the Hawaiian islands were, by lava flows hardening and building up over hundreds of millions of years. The difference is that while the Hawaiian chain was formed by Earths crust moving over a hot spot in the mantle, Mars does not have mobile tectonic plates so the hotspot that releases lava is always in the center of the mountain. Olympus Mons is located near the martian equator and is 370 miles wide and 13 miles tall, with cliffs up to 5 miles tall. The base covers an area roughly the size of the state of Arizona and is 2.5 times taller than mount Everest. The atmospheric pressure at the highest point is estimated to be 0.03kPa, which is 12% of the average martian atmospheric pressure of .6kPa. What's interesting about this is that the air pressure at the summit of Olympus Mons is a much higher percentage of the surface pressure than it would be on Earth. The atmospheric pressure on Earth at an altitude of 13 miles is approximately 4.5kPa, just 4.43% of the average sea level pressure of 101.33kPa. This happens because the acceleration due to gravity on mars in 3.7m/s2, less than half of that on Earth, which increases the scale height of Mars' atmosphere, so there is relatively higher atmospheric pressure at higher altitudes.
It's amazing to think that there are mountains out there on other planets that dwarf anything we have on Earth. I've always been interested in space but my interest just peaked (pun intended) as I look out at the night sky and wonder what else is out there.
This is the followup to my last post about climbing Giant Mountain. You may have notice that I only talked about the energy I expended climbing the mountain. If you're thinking "Couldn't he have just doubled the energy going up to get total energy", you're wrong and need to: 1) read this 2) stop acting like you know me. The main problem was that, as I mentioned in the last post, the trail became increasingly snowy and icy as we neared the summit. Actually it was like starting in New York in October, climbing through NY in December and then ending up in Alaska at the summit. That wasn't so bad on the way up but the way down it turned into a deathtrap. Every bare rock surface was covered in black ice and everything else was blanketed in slush. The key to surviving the descent (not an exaggeration) was to first of all lower your center of gravity. By crouching down or even sitting and sliding there is a much lesser chance of falling because having more mass closer to the ground means better traction and control in the event of a fall. We got down most of the top half of the mountain by sliding on our butts, so the key to that was to align yourself with where you wanted to go. In a low friction environment its difficult to change the direction of ones momentum because the low coefficient of friction means that inertia altering forces are hard to apply since hands and feet just slip. So If one starts an intentional slide in the direction of a cliff and there's nothing to grab onto, guess where that someone is going to end up? The rick (to not dying) is to slide towards trees or roots or large rocks and not get going to fast so you have time to stop yourself. In the end we all made it down relativity injury free (although I did take a few hard falls), but I just wish someone had given me the forecast of "snow, ice, wind and high chance of death."
Yesterday I climbed Giant Mountain, one of the 46 Adirondack High Peaks. With a summit elevation of 4,627 feet (1,410 m) Giant is the 12th tallest of the high peaks and with an elevation change of 3000 ft in 3 miles it's also on of the steepest. The journey began at the car near the trail head where I was deciding on footwear. The 2 options were hiking boots (0.92 kg a pair) of Nike frees (.42 kg a pair). The boots would be heavier and require more work to ascend the mountain, but would provide better traction and keep my feet dry. The frees would require less energy but likely slip on everything, provide less support and get my feet drenched within minutes. I chose the boots, so how much more work did I do climbing the mountain? The ideal approach to figuring this out would be to multiply the number of steps that I took while ascending and descending the mountain by the average distance that I lifted my feet with each step; and then multiply that by the force I exerted against the weight of my boots/shoes (work=force*displacement). However I didn't count my steps because counting for 5 hours would have driven me insane and the vertical distance that I lifted my feet varried widely on the diffenrt sorts of terain I encountered. So I'll just use the vertical displacement up the mountain as my displacement. The difference im energy expendature can be found by multiplying the difference in weight of the shoes by the displacement up the mountain.
Difference in weight=(.92kg-.42kg)(9.8m/s2)=4.9N
Difference in work=(4.9N)(914m)=4497.6J
So by choosing the boots I expended about an extra 4500 Joules (about 1070 calories) of energy (but I estimate that in reality It was probably closer to double that). However as we climbed further the trail became covered in snow and ice, making it incredibly wet and slippery, so without the boots I likely would have fallen off the the mountain and gotten frostbite on my feet. In the end think 4500J is a fair tradeoff for not dying.
So in my last post I promised to follow up by talking about why humans can run so far, but I'm putting that off for a little bit.
So I was just sitting here, daydreaming about everything I've done this XC season, and I suddenly realized how long it's been since the last time I went out and did my first true love: longboarding. I got into longboarding in 5th or 6th grade, I can't really remember, and its not an understatement to say that it has been a focal point of my life; but I haven't touched a board since August in fear of hurting myself and not being able to run (which I now realize was dumb).
So as I think about tearing down Thomas Ave. at 30+ mph, the physics applications of longboarding seem limitless. But for now I'll talk about sliding and freeride. Sliding on a longboard is actually just what it sounds like: making the board slide downhill (or on flat ground with enough speed) rather than roll. The concept is simple enough: shift weight on the board to apply enough force to get the wheels to break static friction with the road, but in practice this requires much skill, balance, and knowledge of the slide characteristics of your board setup (which is found "experimentally"). Most of the time longboard wheels rely on static friction to allow the wheels to stick to the road while turning, but with sliding its all about the slip. And not just any slip will suffice; while the goal is to get wheels to have less friction with the road, too little friction can be a bad thing. Too little friction will create fast, loud, uncontrollable slides, and wheels that create these kind of slides are known as being "icy", while wheels with pleasant, quiet, controllable slides are referred to as "buttery" or even "sugary". One of the downsides of sliding polyurethane wheels across the road is that they wear down over time as the urethane wears down. Since more pressure is put on the outer edge of the wheel the outer edge wears more and wheels usually become conical over time. With some wheels you can even see what wore off on the road, and these marks are known as thane lines. There are many forms of sliding and those who master the slide master friction itself.
Sergio Yuppie demonstrating technical downhill sliding (with some freeride, skip to 1:00 for the skating)
Some sweet freeride
World record longest standup slide on dry pavement (skip to 2:25 for the actual slide)
Cheetahs are basically the supercars of the animal kingdom. They have a top speed of 75 miles per hour and a 0 to 60 time of 3 seconds, faster than a vast majority of production sports cars. A light and aerodynamic bone structure reduces drag forces to the absolute minimum, a long tail provides balance while sprinting and counter-forces while turning which allows for extreme agility, and flat paws provide better traction than most cats. A light weight of 125 pounds on average allow the cheetahs powerful muscles do the minimum amount of work (since work=displacement*force) and thus energy is conserved to allow for more running. While cheetahs can only sustain top speed for about 550 meters, they are able to travel faster than most anything they're hunting due to some interesting bio-mechanics.
For starters, cheetahs have an incredibly long stride length of 25 feet, a little over 4 times longer than the average stride of an elite miler and just over 3 times longer than the enormous 8 foot stride of 100m world record holder Usain Bolt. Just as Bolt dominates international competition by traveling farther on each stride than the competition, cheetahs can easily reach 70 mph by taking giant bounding strides. The cardiovascular system of the worlds fastest cat is a marvel in itself, with a much larger than average heart pumping more blood per beat than many other animals can manage. However to supply oxygen to this heart is a unique respiratory reflex. Like most four legged animals, cheetahs are forced to breath one breath for every full stride which while makes for large air intake, severely restricts endurance. What makes cheetahs unique is the fact that their abdominal cavities are tied to their diaphragms. When they push off with their hind legs the body tips up away from the ground a little and the organs slide back in the abdominal cavity, drawing the diaphragm back and forcing inhalation. When the front paws hit ground the body tips forward and the organs slide forward, expelling air from the lungs. The motion of the internal organs along with expansion and contraction of the abdominal cavity allow for cheetahs to take in the enormous amount of oxygen they need to sustain speeds of 70 to 75 mph. For a nice video of this check out:
stay posted for the reasoning why cheetahs can't run far and humans can't run fast.
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