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! :-)