String Bean Physics

This is actually the Physics of string beans, onions, chicken, and their specific sauce from Panda Express. As I let the feeling of freedom from the arrival of Christmas Break, I got dinner with my mom at Panda Express on Saturday night. As I held my three item plate in its bag, I discovered that I couldn't keep the little container holding the string bean chicken from falling over and spilling sauce all over the bag, so I decided to hold it. After a few minutes of holding the rather warm container of food, I thought to myself, "Hey! Physics! Heat!" The small container of food, which was kept hot in its tray was transfering some of this heat to my hand. To start at the beginning of the process: something, probably electricity, heated water in large metal trays, providing the water with heat. This heat is then easily transfered to the metal trays above it, raising its temperature rapidly to a high temperature because metal has a low specific heat, requiring relatively little energy to raise its temperature. This heat is then flows to the food in the metal trays, which was put into a small paper container and given to me. The heat from this food then flowed to my hand, making my hand feel hot. After a while, the food didn't feel so hot anymore. This meant that the system consisting of my hand and the food container was reaching equilibrium, where both the food temperature and my hand's temperature would be the same. However, I'm pretty sure that it didn't, which is a good thing because the food was very hot to begin with, so it probably would have burned my hand, plus the food wouldn't have been very hot anymore :-( . I'm not sure whether this was an isobaric or isochoric process, or neither. I don't think my fingers expanded, but perhaps they did, and I don't think that the pressure inside by fingers increased either, but I don't know. Maybe it did. Scary.....

Physics in Low Brass!

Now, while you might possibly be thinking that low brass instruments usually only serve as metronomes for the rest of the band with very few chances at the melody, that's not entirely true. Although we do find ourselves playing only eighth-notes on down beats more often than the flutes, clarinets, and trumpets do, we often have glory parts of our own (for a good example, listen to "Overture to Colas Breugnon." Go sixteenth-notes!). Or if you want to hear something really different, come to "Merry TubaChristmas," featuring euphoniums(/baritones/me!) and tubas only! I went to a rehearsal for this on Saturday, so along with our awesome lab on Friday, I feel like analyzing the Physics involved in this glorious section of the band.

Now among the various low brass intruments, there are pleny of examples of physics in closed tubes, as our intruments are made of metal tubes and our lips close one end as well as provide sound vibrations. All of these instruments work using the same physics concepts as well. Although the trombone uses a slide instead of valves, as the tuba and baritone do, all three of these instruments legnthen their curly "tube" to create different pitches(however, tuning them to the correct pitches is another story :-) ). Since these instruments are "closed tubes," the harmonics can be calculated using the equation Fn=(2n-1)F1, or (2n-1)(v/2L). For my particular instrument playing the f below middle c, first harmonic present is about 190 Hz, with the other harmonics being twice and three times that. As the valves are pressed, or the slide is lowered, the tube gets longer, increasing L and therefore decreasing the fundamental frequency and all subsequent frequencies, lowering the pitch. But, as we learned in class, these instruments will only let one's lips vibrate at a certain frequency (which explains a lot, especially why I have lots of difficulty "lipping up" my rather flat e flat). When the lip position is tightened to vibrate at the next "open" frequency, the lips vibrate faster, thus resulting in a faster frequency of sound waves and a higher pitch. And over the weekend at TubaChristmas rehersal (an hour and a half of glorious baritone and tuba sound!), I discovered once again that having my lips constantly vibrate at a high frequency is not only difficult to maintain, it hurts! I'm not sure how much it had to do with the frequency and how much had to do with muscle fatigue, but about an hour in I didn't want to play the first part anymore. :-)

Although I'm a devoted baritone player, I have tried trombone as well. Yet in both my attempts to find the correct pitches and listening to our outstanding Band 4 trombonists, I've found that even though the tube of a trombone seems much shorter than the winding ones of a baritone, they have relatively the same sound, as does the small-tubed "valve trombone" I play during Marching Band (except baritones sound prettier. Sorry trombonists, I love my instrument). I wonder if the diameter of the tubes has anything to do with it, because we use the same mouthpieces and our music is interchangable, except for the sound. An interesting question to look into. :-)

By the way, that's me with my baritone in its case and my uncle's trombone, plus the mouthpiece I use for both in my right hand. Isn't my shirt cool? :-)

More Musical Physics!

Talk about a busy musical weekend! Although I know that those in Youth Symphony had it even worse, I had Select Band tryouts early Sunday morning which took at least two and a half hours, and then a Christmas Concert in the evening, plus the Football game on Friday evening (Go Raiders!) and lots of practicing for my tryout. And I didn't realize until a few hours before the concert that I was using Physics with every note I played! Almost every note I play involves at least one of the four valves on my instrument, which consist of a metal rod with holes in it, a metal tube, oil to allow the valve to move, and a spring to return the valve to its unpressed position. When I press the valve, the spring force (-Kx, where x is the distance compressed from the spring's equilibrium point) is equal to the force my finger applies on the top of the valve. Thus the valve has a net force of zero, an acceleration of zero, and in this case a velocity of zero as well since it has reached the bottom of the tube. But when I am not using that valve, the spring force (for I seriously doubt that the spring is ever allowed to reach equilibrium while the valve is in its tube, otherwise the valve may not stay up and play correctly) is equal to the normal force of the valve on the cap keeping it in its tube. This senario is pictured above, with a very bad attempt to draw a spring, even though it was at least my fourth attempt. Since the oil attempts to keep the kinetic friction to a minimum, I wonder what the velocity of the valve is. However, I would need to take a few measurements, such as the greatest and least compression from equilibrium, and experiment to find the force constant of the spring. Perhaps I should do that. It could help answer some questions about why I have difficulty playing fast pieces. But I bet it won't; the instrument is not to blame for my slow fingers. :-)

Happy Halloween, Charlie Brown!

I know it's supposed to be something about "The Great Pumpkin," but I'm officially in Christmas mode now that Thanksgiving has past. I've taken out my Hallmark Christmas singing snowman/dog and snowman at piano people, and marched in the Waikiki Christmas Parade (which was pretty fun, although it started raining and got pretty cold afterward). But this weekend, I noticed a lot of Physics. First of all, the explaination of the title of my entry. For my birthday (which was only a few days before Halloween), my aunt and uncle gave me a bobble-head figure of Charlie Brown trick-or-treating as part of my present (sorry he's sideways, I forgot that I took the picture longways). As I was pondering harmonic motion, I realized, "Hey! Charlie Brown!" Being the type of bobble-head that he is, Charlie Brown's head bounces on a spring. I thought, "If I were to push down on his head, the spring force should accelerate his head back up past the equilibrium point, until it comes to a stop, then accelerates back down in harmonic motion." However, when I actually tried it, the spring was too rigid to allow any noticable displacement along the y axis once it returned to equilibrium. However, if it had been less rigid, the spring should have forced Charlie Brown's head up and past the equilibrium point, then once it reached its amplitude height, it should have accelerated down at the same acceleration as it went up until it passed the equilibrium point and gradually stopped, repeating this process indefinetely (of course, assuming that there is no air resistance or gravity).

However, this wasn't the only Physics I noticed this weekend, and I'm so excited that I must tell everything!!! :-) While I was at the Varsity football game this Saturday, I got myself a shave ice at half-time. As I got to the very bottom where all that was left was melted ice and strawberry syrup, I tried to get my straw (with the spoon side down) all the way to the bottom to get all the liquid, I thought to myself, "Oh no, because I crushed the straw and now there's only a small triangular shaped opening on the bottom, I'm not going to be able to suck out the liquid as fast or as easily." But I was! I suddenly remembered my fluid dynamics Physics chapter, where we learned that V1A1=V2A2, and that pressure decreases as v increases. So the liquid in my straw must be moving much faster at the bottom entering the straw since the area was less, and the pressure must be less as well! Yeah! Physics epiphany! However, this also meant that I was able to drink my remaining shave ice faster, so I soon found myself with none left. Oh well. It was good.

The Physics of Music

Does that sound wierd? Normally you hear about the Mathematics of music, but not Physics. Well, this weekend, I discovered how Physics is truly involved in music, or more specifically, in taking care of and playing my instrument.

I play the baritone (pictured above). If you don't know what that is, it's basically a small tuba (another name for it is "tenor tuba") with a beautiful, mellow sound. I love it :-). However, my valves have been sticking recently, so my dad and I tried to figure out why. This involved taking out the valve, examining the wear patterns, cleaning the tube as well as the valve, and finding out that the bottom of the valve was probably sticking to the spring. After discovering this and cleaning the sticking valves, we put them back in, a simple process which involves valve oil (also pictured above. My valve oil container has a very small opening for the drops of oil to come out of, even smaller than what the top lookes like in the picture. But this bottle alone demonstrates a very important fluid principle. As I squeeze the bottle, the pressure my fingers applied is transfered to the walls is transfered throughouth the fluid. The pressure then pushed the fluid out of the bottle in accordance with the fluid equation of continuity.

However, my valve oil bottle is not the only part of my playing that displays the fluid equation of continuity. My instrument does as well. As I blow into my instrument via the small tube coming off the large bell, the air moves through the different tubes of my instrument, all of which are different sizes. I blow air into the small area tube at a fast rate, and as it travels through the instrument, the diameter of the tube gets larger, until the air comes out of the very large bell at the top. The diameter of the mouthpiece tube is 0.016m, and the diameter of the largest part of the tube that the air probably still completely occupies is about .12m. Thus, by the fluid equation of continuity, which states that V1A1=V2A2, the equation would state that 0.01149(Vbell)=2.01e-4(Vmouthpiece), or that the velocity of the air coming out of the bell is only 1.75% that of the velocity at which it goes in. That sure explains why the air coming out of the bell is barely noticable. Well, now that I know what the increasing diameter of the tube does to the air, I wonder what it does for the sound? Oh well, got to wait a little longer to find that out.

Waiting for Manapua

Have you ever been to Island Manapua around lunchtime? It's packed! Their manapua are the best, and everyone knows it. Good for business, but bad for me because it results in my having to wait a long time in line before getting my lunch/snack, depending how early it is. Well, on Saturday, I found myself in this position, waiting in a long line to get my steamed pork manapua and rice cake. I was just inside the store and right up against the closed door. As I stood there, I began to get tired, so I decided to lean on the door. As I slowly leaned against the door and wondered whether it would swing open and send me falling backwards out the door, I realized "Hey! Static Friction! Torque! Physics!" It was an enlightening moment. There were forces al around me: my weight (mg down!), the friction of the floor on my shoes as well as the friction of the handle of the door (where I was leaning) on my back, keeping me from falling straight down. There were also the normal forces of the floor and handle on me. I have included an approximate Free Body Diagram above. But not only do these forces act on me, I am also applying a torque onto the handle bar, and thus to the door. The torque I applied would be equal to the normal force times the distance I was from the line of hinges on the edge of the door. There was even static friction between the hinges inside themselves, as well as static friction at the other sides of the door with the door posts. It was static friction and torque that allowed me to take a break by leaning on that door. The friction caused the door to stay in place, and my small distance from the hinges kept me from attaining so much torque that I would fall backwards out of the store. That would not have been fun. :-)

Moving Benches

Unfortunately, this week was not quite as Physics filled as last week was, without The Lion King and all. However, I did go to the Homecoming Game with the Marching Band where we were melting in the hot sun along with the rest of the fans, and I took the SAT where one of my extra pencils kept kept getting pushed off the side of my desk as my left elbow (I'm a leftie) brushed over it (Projectile Motion! Vyo=0, Vx, H=height of desk, X=distance from edge of desk/original position: -H=-4.9T^2, X=VxT). But that's not the example I'm about to discuss.

The moment of rotational Physics that I experienced this week (or the first good one that I thought of) was moving benches out on the soccer field during Marching Band on Wednesday. On Tuesday, Mr. Hotoke had thought of the idea that I could stand on a bench to conduct so that everyone could see me better, and so for that day and Wednesday, we had to move the benches about four feet from their original positions. As I started to move the bench on my own on Wednesday, I could only do it one end at a time because dragging didn't work, so I picked up one end and rotated it. Lifting the bench created an axis of rotation at the middle of the leg of the bench farthest from me. As I walked with the bench, my hands were applying a force perpendicular to the bench, as my body stayed in the same orientation (perpendicular) to the bench and I was moving parallel to my body. Therefore, since the force was perpendicular to r, the distance from the axis of rotation to my hands, the equation for the torque as a result of my hands is (tau)=rF. (Sorry, no values again. I was concentrating to hard on Band :-) ) This torque caused the bench's very quick angular acceleration from rest, later keeping it moving at near constant speed, then its deceleration as I set it back down. I then applied the same principles to the opposite side of the bench to place it parallel to its original position. Moving the bench back took the same motions, except in the opposite direction. Four examples of torque! Wow, and they only took about three seconds each. And the benches worked well; I could see everyone, probably everyone could see me as well as ever, and I didn't fall off, despite the fact that a light, movable bench on grass is not the most stable thing to stand on. A pretty good day. :-)

The Circle of Life

So who's seen The Lion King? I went to see it on Thursday night, and it was amazing! This was the first professional musical that I remember seeing, as I've only ever been to the school musicals since I saw Beauty and the Beast at age three, of which I have no memory :-(. By far my favorite scene was the opening, "The Circle of Life." The singing was beautiful and so powerful, and the costumes and props were so interesting. But on to the Physics involved. Multiple times during the play, two animals to appear were two buzzards, props carried on a long pole crossed by a smaller one, with one bird on each end of this smaller pole. As these birds "flew," their carrier would spin them, so they looked like they were circling something, and I thought, "HEY! UNIFORM CIRCULAR MOTION!" Ok, perhaps not quite that enthusiastically because I was more enamored with the play than finding Physics, but it was still cool.

Who would have thought I would find Physics in a brodway play?

The buzzards were probably traveling with a period of about five seconds, and the radius of their circle was probably about 0.5 meters. From these rough estimates, the velocity of these buzzards was v=(2 pi r)/T, or v=(6.28*0.5)/5=0.628m/s. This velocity was applied by their carrier, who was spinning the long pole at a much slower speed than 0.628m/s in order to get that speed for the buzzards. Unfortunately, I don't know the mass of these buzzards, so I can't calculate the centripetal force (F=m*v^2/r) or acceleration (a=v^2/r). I wonder however, what will happen to these figures if I were to analyze the motion of the buzzards while the carrier was turning the pole and walking too? I don't think I know how to do that yet, as it would mean that the axis of the circular motion was not stationary. Oh well, maybe in a few weeks. :-)

Ouch!

Don't worry, nothing is hurting me. That was my reaction to the few examples of Physics that I noticed at this Saturday's Football game at Aloha Stadium. This game was full of many interesting happenings. First there were the two fifteen yard penalties, one on each team, that put us right back where we started, and there were some pretty far thrown flags (none of those "straight to the ground flags," these must have traveled fifteen or twenty yards!). But main examples of Physics that I noticed were the completely inelastic collisions between people, completely inelastic collisions between the ball and the net behind the posts, and the probably inelastic collision between the ball and the soft orange post at the corner of the end zone.

First, the completely inelastic collisions: One of the football players ran towards another player (who may have had the ball, I can't remember), and tackled him. The first player had initial velocity, where as the second player had either none or very little velocity. After the collision, both players went down together, with a common velocity. Their total momentum was the same before and after the collision, although their kinetic energies were definitely different, considering that their uniforms are meant to absorb energy, and I'm sure there was a pretty loud sound as a result. The collision between the extra point kick ball and the net was completely inelastic as well. Ball had initial velocity, whereas the net did not. When they collided, both the ball and the area the ball hit moved with the same velocity. However, the tension on that section of the net by the rest of it caused the net and the ball to come to a stop, leaving weight as the only force acting on the ball (ignoring air resistance), thus allowing it to fall at about -9.8 m/s^2.

And now for the inelastic collision that I tried to diagram above. (Why do I keep forgetting to bring a camera to football games?) I am not sure if the trajectories are correct, but I tried to think about where the ball and post might have gone, and I think they are probably pretty accurate (unless the shape of the football made it go somewhere else). As the ball came in, with it's initial x and y velocities, and hit the post at rest, it transfered some of its momentum to the post, giving it x and y velocity as well. The combined momentum before and after collision of these two objects is the same, but their kinetic energies are very different, as the ground at Aloha Stadium is soft, the post is soft, and they probably let off a dull "phfff" sound. Unfortunately, I had no camera to analyze the motion on Logger Pro, so I can't include exact velocities, angles, or masses(without massing the ball and post, to which I don't have access). That would have made an interesting Physics experiment!

Bumpy, Bumpy Buses

This past Friday was one of the best we'll have all year: it was CLASS DAY! We had no homework due that day, and we got to go to the beach, eat food, and come back to school early. And to get to the beach, we fit the entire grade into a few buses, which took the Juniors, and few Seniors not on Moloka'i, to Bellows. However, these buses did not provide the smoothest rides one can find these days. We felt every single bump, with the large bumps especially noticable. In fact, these large bumps demonstrate........(drumroll....)... Physics!!! And the most noticable form of Physics on these buses was the transfered momentum at every large bump. Every time we went over an extremely large one, the bus would gain y velocity. As this occured, we, the passengers who were sitting on the bus's seats, would get a vertical jolt as the bus's seats collided with us, transfering some momentum to us. Since I am much less massive than the bus, I would continue in the same direction as the bus for the brief moment before gravity brought the bus back down to the ground. Since this would be a relatively elastic collision, the equation for the conservation of kinetic energy would apply, as well as conservation of momentum. The bus would lose very little y velocity to me, whereas I , with my relatively small mass, would gain enough to throw me in the air for a split second before gravity brought me back down. If I knew the amount of time the bus was pushing me into the air and my velocity coming off the seat, I could calculate my impulse (J=F(net)delta t = delta mv), but unfortunately I was too tired to take these measurements. Oh well :-).

Physics Across the Country

Okay, perhaps that's a misleading title. This weekend, I didn't notice Physics all over the country (although I know it's there), but I noticed Physics at a Cross Country meet at Kamehameha this Saturday. For anyone who has run at Kamehameha, or seen the Kamehameha campus and can imagine running a few miles there, you know that it's full of hills. And for anyone who has even tried to walk up a hill, you know... IT'S HARD!!!!!

During warmup for our race, our team walked the course so that we would know where to go as we ran. As we were walking up the first hill, I asked myself, "I wonder how much work we have to do to get up this hill." Then I remembered a hill we had run the year before, when the course was different. That hill was insanely steep! And it went high! Going up that hill resulted in a great change in potential energy (delta mgh). I've included an approximate sky view diagram of the hills, however this representation doesn't do their steepness justice. If I only had a camera! Later on, I considered the work involved in going up those two hills. Knowing that these hills did not have angles from horizontal complementary to each other (I doubt that the friction of the road on our shoes would have allowed that), I started plugging numbers into my calculator, and discovered that the steeper hill actually required less work to rise the same vertical distance. That was certainly a surprise, especially since going up the steep hill leaves you feel like collapsing, whereas the less steep hill only leaves your lungs burning. I wonder how the powers compare. Guess I'll have to time myself on those two hills and perform more calculations. However, I'm too lazy. I'd rather do something that requires less work. And homework doesn't count! :-)

The Physics of Chewy Bars

Okay, maybe not exactly the Physics that goes into Chewy Bars, or the Physics that Chewy Bars perform (if any...), but Physics that I noticed carrying a box of Chewy Bars to Cross Country practice on Friday. I didn't feel like carrying the box under my arm, or infront of me, so I decided to hold on to the top of the box instead. As I was walking along and noticing that my hand was starting to hurt, I thought, "Hey! The only thing keeping the box from slipping out of my hand is....(drumroll, please...) Static Friction!" The maximum static friction force between the box and my squeezing fingers must have been greater than the force needed to keep the box in the air and my hand, otherwise it would have slipped out of my grip. And let me tell you, holding that box was not easy (see my hand straining? Sorry, the picture's a little dark). I could even feel the box sticking to my fingers, with the weight of the box pulling down on my skin. Don't worry, it was nowhere near as creepy as it sounds.

Also, when I lift the box (with my hand in the same place), I do work! I'm moving a mass in the y direction, so my work would be F(delta)y, or mg(delta)y, if I am moving the box at a constant velocity. I am also increasing the potential energy by situating the box at a higher position from the Earth. The PE of the box at any given point would be mgy.

This experience shows that Physics is truly present everywhere, all the time. Who would have thought that I would encounter Physics doing something as simple as holding a box of Chewy Bars? Well, I also realized another thing; if I want to do less work lifting the box, then I have to decrease its mass, decreasing its weight and the force needed to move the box. Oh well, I guess I'll just have to eat one! :-)

Eurus, Notus, and Africanus

Hello fellow Physics students! I bet most of you are wondering, "What in the world is with this title?" But I hope my fellow AP Latin students are wondering, "Why is she reffering to the 'savage winds' that we recently read about in The Aeneid?" Well, I actually have a very interesting reason.
On Saturday, September 22, I attended the Iolani Cross Country Meet at Ford Island, and anyone who was there can testify to the fact that the wind was CRAZY!!!!! Dirt was flying everywhere, and the pop-up tents that housed the girls team were beginning to fly away! As I quickly ran to give my friend a hand in holding one of the tents from collapsing and/or blowing away, I realized, "Hey, there are forces at work here!" Before we began holding the tents against the wind, the wind was providing an x force that was greater than any opposing x forces, causing a strong net force that was threatening to send our tents flying through the air. But the moment one of us (or me in my bad diagram, I was in no position to take a picture even if I had a camera with me at the time) began to pull or push on the tent in the opposite direction to the wind, we evened out the x forces, resulting in a net x force of zero. I have included the Free Body Diagram for the simple forces working on the tent, even though I'm sure there are many more that I'm not aware of, perhaps ones like the wind making its way inside and pushing up on the tent, or othe people pulling on it. For that moment, I was glad the wind was not stronger than it was, but later, as I tried to lean into the wind to see if it would hold me up on its own, I woefully discovered that my weight, applied in the x direction (leaning into the wind) was greater than the force of the wind on my body, causing me to fall flat on my face had I not given up before that point. :-( Oh well. Oh yeah, and about "Eurus, Notus, and Africanus." Those were three of the "savage winds" that, when released, would rip up the earth and sea and send them flying through the sky. I think this was the kind of wind that Vergil was talking about. :-)

Friction, Forces, and Football

Let's see, Physics common in my life... You would not believe that I only just noticed a common example of friction as I was sitting at my computer, doing my Physics homework today. I was sitting in my rolling chair, and I realized "Hey! This chair has forces written all over it!" Not only does its weight, and therefore the normal force exerted by the floor, increase when I sit down on it, but the wheels have massive amounts of friction, and not just from the floor they roll on; the wheels have not exactly been lubricated anytime recently, so the wheel and axle create friction as well! I had never thought about it before. And, according to Newton's second law, the horizontal forces, mainly friction, are the reason that my horizontal push away from my desk does not make the chair travel very far! And then there are the forces that stop the chair quickly, such as the shoes and slippers that live about four feet behind my chair. :-) I feel sorry for them. Oh yeah, and in case you were wondering, that's my stuffed dog. His name is Taffy.
I really noticed a lot of physics this weekend. First on Friday night, I went to the football game at Aloha Stadium as part of the Marching Band, and I vividly noticed the travel pattern of the footbal on kickoffs (emphasized by the traditional trombone gliss following the ball), which was a parabola, as well as the velocity, both x and y. And then there was the Aloha Week Parade on Saturday morning, where I noticed that the normal force of the road on my body seems much increased when I'm marching on my toes, as they quickly started to hurt when I did, with the decreased surface area and all. As a result, my calf muscles are very stiff and sore right now. Oh, well, I'm used to it.

the first few weeks

whew! we've survived the first few weeks, the first test, and three quizzes in AP Physics! First 1D Kinematics, now 2! At first I thought 1D was going to be hard, but now I miss it. 2D has so much to think about! x position, y position, x velocity, y velocity, just velocity, initial velocity, AAAAAAAHHH! my brain is spinning. I keep feeling like I don't have enough information, but I'm sure I do, I'm just not sure what to do with it. Oh well, just have to keep practicing. It's fun though. I'm already seeing physics in daily life. Last year I heard one of my friends from Band say that the only way she got through the beginning of physics was football. I'm going to try her strategy and apply physics to my observations of the football game this Friday. This should be fun!!! :-)