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 :-).