running_dry

I can't wait for the whole thing

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 Vertical displacement=(3000ft)(1mi/5280ft)(1609m/mi)=914m work=force*displacement 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)

No, you watch too many movies

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.

it is on the equator!

There's one thing that has always bugged me about the sport of cross country: the proximity of the start line to the finish line. Nine times out of ten I would estimate that the positions at which I start and finish a 5000 meter race are within 400 meters of one another. Now obviosly i understand that its a 5k race, not a 400, but it makes me seem very slow. With my (rather quick) personal best time of 15 minutes, 21 seconds (921 seconds) my average velocity (speed=distance/time) over a 5km distance is a respectable 5.42 m/s. However my actual velocity (dispacement/time, estimated that the start is 400 meters from the finish) is an abysmal 0.43 m/s. Every course has "tangents"- lines that can be run on the course that can cut off like 50 meters from 5000 but unfortunately theres nothing legal that can be done to cut off 4600. On the plus side I can say that I won a race with a velocity of .96 mph.

So in case nobody noticed, a few days ago the temperature dropped from levels typical of mid-June to somewhere off the charts that I would estimate to be pretty darn close to absolute zero. Actually, the temperature is now just slightly below the average for the season, but why did it get really cold really fast? To start, I'm sure the jet stream had something to do with it, pushing cold arctic air into upstate NY, and pushing out the warmer tropical air we had been experiencing. But more importantly, its now late October and it gets cold around this time every year. But why is that? First of all, the earth rotates on a tilted axis; so in other words the axis on which the earth spins is not perpendicular to the plane on which path of earth's orbit around the sun lies. The ends of the axis of rotation are the geographical north and south poles, not to be confused with magnetic poles. As the earth travels in a slightly elliptical path around the sun, the geographical north pole always points in the same direction in space, so during the summer in the northern hemisphere the pole is pointing in the general direction of the sun while in the winter the pole is pointing away from the sun. As a result, the angle at which the sun's rays strike the earths surface is closer to 90 degrees and less light waves are reflected into space, causing more energy to strike the earth, causing the temperature to rise. The opposite happens in the winter, and this is the reason why it is summer in the northern hemisphere while it is winter in the southern hemisphere. Therefore, the reason why it got cold is because light isn't hitting the earth like it used to. For a visual representation of this, watch this video.

There is one thing that can strike fear into the heart of any cross country runner: hills. Hilly courses are often hated because going uphill is hard, however for a long time I have been telling myself that what goes up must come down, and running downhill is ridiculously easy. The best example of this that I can think of is the Bowdoin Park course in Poughkeepsie, NY. This is widely regarded as one of the hardest XC courses in the state. It's a 5 km course that winds its way up and then down a large hill. The very top of the hill is exactly the half way mark of the course so there's 2.5 km on the "uphill" section and 2.5 on the "downhill" section, and the start and finish line are at exactly the same elevation. According to google earth there is a 65 meter elevation change from the start/ finish to the 2.5 km mark (although that seems a little low to me). Most runners hate this course because of all the work they must do against gravity in the first half of the race, but they forget that in the second half gravity is doing work on them. For example, since work=force*displacement, a 70 kg runner must do 4550J of work against gravity going uphill, but gravity does 4550J of work on them going downhill so net work (as far as climbing hills goes) for the course is 0 joules. Now obviously not even close to all the energy used running is returned, and running downhill isn't free fall so energy must used by the runner on the way down. Yes, hills are challenging but but I think that people need to stop complaining and accept that during races gravity helps them almost as much as it hurts them.

As a competitive runner, there is nothing more annoying than being passed at the very end of a race, and nothing more satisfying than doing the passing. The final surge of speed before the finish line is commonly referred to as a "kick" and runners who can consistently run the last 100 to 200 meters of a race in a convincingly Usain Bolt-like fashion are known as having "a kick". Getting passed by someone while they are "kicking" faster than you is called being "outkicked" Unfortunately I'm not fast when it comes to raw speed and therefore don't have much of a kick. As a result, I have been outkicked on more times than I care to count, leading to much regret and humiliation. My latest encounter with this phenomenon occurred at the McQuaid Cross Country Invitational last weekend. For 2 3/4 miles I had been fighting myself and a pack of aggressive cross country runners (a bit of an oxymoron...) for second place, and I thought I had broken away. Then, coming down the last hill before the final straight away someone catches up and I hear his coach yell "rock that 52 speed!" I groan inside, now knowing that the guy can run 400 meters in 52 seconds which is very fast, much faster than me. And that's where physics comes in. The maximum speed at which a person can run is determined by newtons 3rd law, which states that for every force applied, there will be an equal and opposite reaction force. While running, the foot and leg muscles apply a force to the ground in the opposite direction of the intended direction of travel, and via newton's 3rd law the ground applies an equal and opposite force to the runner, propelling then forward. The reason that my competitor was faster than me was that he was able to apply more force to the ground and therefore receive a greater push forward from the ground. The reaction force received from the ground because of newton's 3rd law is translated to speed by newton's 2nd law which states that net force equals mass times acceleration, or acceleration equals net force divided by mass. Assuming that me and this other runner are about the same mass (because, being runners, we're both unnaturally underweight) the other runner is able to accelerate and run faster than me because he is able to apply more force and is therefore subjected to greater net force in a forward direction. And so, once again, I got outkicked (but on the bright side I still took 3rd in the race). This just scratches the surface of the physics of running, so stay tuned for more; but I'll mix it up with some other cooler stuff too. ~That dry, boring running guy

I was always confused by exactly how those worked, I never realized that the air being blown out the little holes was just to reduce the pressure around the ring and therefore get air to flow through the middle

I'm totally with you on the negligible resistance, its just so boring and inapplicable to the world in which we live.

As for the obscure reference to hardware stores, you would have had to been in Physics B last year and even then you might not get it. And to answer that question, if the table was perfectly level you could set an object on the table with no inertia shouldn't move. And any frictionless surface would no doubt be useful in other applications than just holding things.

So I'll get straight to the point. There has been a lot of talk about insanity and it being crucial to the decisions of all of us to take Physics C, and I think there's some truth to that. I too may be a little insane for taking this class but I think that most people think that I'm completely crazy because I genuinely love running (I don't think that makes me crazy though). Sadly that's most of my life but in my free time I try to do some more exciting things like skiing and longboarding as much as possible. With that said, expect a lot of future blog posts on the physics of running and gravity related sports. I'm taking Physics C this year because I aspire to be an engineer of some sort and be involved with something really cool. And the money wouldn't be so bad either. And I'm pretty sure that continuing to learn physics will help me in a college engineering program. Plus I think that physics is more interesting than chemistry and biology... I'm really excited to learn some of the physics of the real world, rather than the laws of some unattainable perfect world that we learned in Physics B because that's boring. And lets be real, if the hardware store that was brought up so many times last year (you know that one that sells mass-less rope, friction-less tables, inclined planes and pulleys, and is likely full of resistance-less air) existed, it would put Lowes and Home Depot out of business in an instant. Interestingly enough, as of now I'm not scared of this class, probably due to false hope or ignorance, so I guess I'm anxious to see how that pans out in a few weeks. Oh and I'm really tired right now so that's why this post may seem like a half- lucid rant. Maybe it's not that simple after all. Foreshadowing?