Physics and its dance arts

Cyd M. Zamot

Ever since I was a little girl I always liked to dance, but more to see the dancing ballet. I always found it interesting, intriguing and curious. Ballet is the art of precision and dance. My curiosity as a child always made me ask how these people (the ballerinas) made jumps and maneuvers so perfectly. As I grew, I understood that for the ballet, more than ability they needed a series of knowledge. But what type of knowledge? They needed to have some physics knowledge.

How do we combine physics and ballet? When I made this big question I didn’t know the answer until I took my first physics class in high school. How do the dancers rotate on its axis? How can they make jumps of over 180 degrees? How can the dancers perfect their techniques just knowing about physics? Those are more questions that I asked myself. I learned that dancers can make those movements so perfect by the laws of gravity, dynamism and energy.

Dancers support their force on a support point which is the floor, balancing their weight; thus having balance, obtaining therefore a uniform circular motion on its axis. But even more; using physics, it is estimated that to maintain this movement (the circular motion) the dancer must have a minimum speed of 2.4m/s and a maximum of 5 m/s to maintain the balance. To make the jump of 180 degrees, the dancers have to open their legs with a force of 10 N. We also have to think about the weight. The weight is the measure of the force that exerts the gravity. Another thing is the shoes that the ballerina is wearing. The ballet slippers are made of a special material that makes the dancers use all its weight exerted a support point because the dancers need to turn over 360 degrees on its axis. 

We can see more concepts of physics in the ballet. Examples include projectile motion, center of mass, kinetic energy and momentum. The projectile motion is any object which projected once continues in motion by its own inertia and is influenced only by the downward force of gravity; it can be seen in the pirouettes of the ballerinas. The center of mass of any homogeneous symmetric object is located on an axis of symmetry, which is classical at the ballet when they supported on a specific point of their body and rotate around its axis of symmetry. Also we see in the ballet the kinetic energy which is the work required to accelerate a body of a given mass from rest to the speed that it has. Last but not least we have the momentum which is the amount of movement, or is the product of body mass and speed at a given instant

I finally answered my biggest question: How do we combine physics and ballet? Physics is combined with ballet because each movement exerts a certain force, which applied to physics would help each of the ballerinas to make better moves and check what steps are wrong.  So finally, what is ballet? For me ballet is de dance of physics. Is the combination of forces, laws another physics things that create a scenic and dance art, the ballet.

Reference:

Giancoli, Douglas C. Physics for Scientists & Engineers with Modern Physics. 4th ed. Vol. 1. Upper Saddle River, N.J: Prentice Hall, 2009. 

http://es.wikipedia.org/wiki/Ballet

http://www.medellin.edu.co/sites/Educativo/Docentes/feriaexplora/Fsica%20y%20Astronoma/La%20F%C3%ADsica%20en%20el%20Ballet.pdf

Black holes a basic component of the universe

Francisco J Vergara Ortiz

When you think about black holes, many things come to your mind, some are the product of movies and television created by Hollywood, others are myths that people say almost every time, that a black hole conversation came up to the table. It is say to be cosmic vacuum cleaners and some people says that they are portals to others universe, or other dimension. Well that’s just myth, assumptions, and theories because no one has ever been in a black hole. But what a black hole really is? How many types of black holes we know and what is the Schwarzschild radius? And if they’re the dark black in a black sky (universe) how we know they exist?

In theory a black hole is so dense that even light can’t escape from it, this happens because of gravity as we learned in general physics every object exert a gravity force into another object, when an object is so dense everything near it radius of gravity will collapse into it by the law of gravity, and that is what a black hole is, a body of mass so dense that even light that is called photon which are mass less can’t escape from it. Also in principle every object can be made into a black hole by reducing that object to cero volume, but conserving its mass and gravitational force, when this happens the object undergoes into gravitational collapse, it attract itself, compressing his mass into a singular point. This black hole will have a gravitational self attraction called the Schwarzschild radius. But the only object that can become a black hole by itself are stars with 10 to 15 times the mass of our sun when they explode (die) they collapse onto itself and forms a stellar black hole, a really little one with only a few tens kilometers of Schwarzschild radius but with three to ten times the mass of our sun.

As we know there are two types of black holes the stellar one that is when a supernova dies and the super massive black holes (SMBHs) this last ones are still a mystery, no one knows how they form, but it’s believed to be the center of almost every galaxy including our milkyway galaxy. (SMBHs), weights up millions or billions times the mass of our sun. But they are really cosmic vacuum cleaners? The answer is no, to be sucked into a black hole you must cross the Schwarzschild radius this radius can be calculated by this equation R=2GM/c^2 where c is the speed of light, M the mass, and G the gravitational constant. If for example a black hole has the mass of our sun, his Schwarzschild radius will be only 3 kilometers, and in order to get sucked in you must be at least 3kilometers from its center. But there are black hole out there with billions times the mass of our sun. At this time the biggest one our scientist have seen is about 18 billion the mass of our sun called (Oj 287), I use this formula to calculate his radius and the result was amazing about 53 billion kilometers, to get and imagination of how big it is if every star where a kilometer it would be 0.18 the number of stars on our galaxy, and to get a direct comparison this radius is about 8 millions the time of our planet radius.

Another fact that I found interesting is the force it exerts on another objects lest take the same black hole and apply the law of universal gravitation by Newton.  If our planet where on the border of the Schwarzschild radius of this monster the force that it will exerts will 5.06845 x 10^27 Newton onto our planet, that’s a lot of force maybe one of the most powerful things in the universe are the black holes, if they are not. They are so powerful that they are what bounds a galaxy and makes them move around it, because they function like stars, like our sun domains our planet system a black hole domains the galaxy.

How do we know they exist, first of all it is impossible to see this stars with the visible spectrum because light cannot escape from it, but for example is there is a normal star near a black hole the black hole will pull matter towards him, in this process of taking matter out of the nearby star or stars, the black hole gains kinetic energy, this energy is so big that the atoms gain millions of Kelvin and when this happens the black hole emits x-ray in the form of jet out to the space. This jets heat up the surrounding and prevents gas to collapse into the center, and that is what we see and know they exist.

We know what are they, how them work, and a lot of things that still are a mystery. But black holes are basic things in the universe, as we learned they are not cosmic vacuum cleaner sucking everything in their way. First and object must cross his Schwarzschild radius, and the x-rays they produce prevent gas from falling inside it. Allowing nearby galaxies to form and growth, after all there is an injured and beneficial part of this, and our sun, our planet, and ourselves seems to be the beneficiary of this far a well monsters.

References

"Black Holes." Imagine The Universe! Home Page. Web. 23 Apr. 2011.             .

"Imagine the Universe News - 10 April 2003." Imagine The Universe! Home Page.         Web. 23 Apr. 2011.              .

"Universe Forum--Black Holes--What Are They?" Center for Astrophysics. Web. 23        Apr. 2011. .

Giancoli, Douglas C. Physics for Scientists and Engineers. Fourth ed. Upper Saddle                     River, N.J: Pearson/Prentice Hall, 2008. 140-41. Print.

Giancoli, Douglas C. Physics for Scientists and Engineers. Upper Saddle River, N.J:             Pearson/Prentice Hall, 2008. 1208-209. Print.