Importance of Science.

Well so I was wondering how Set Theory in Math would actually relate to daily life. It dawned on me that actually everything in Science helps in our lives and we might actually use it unlike Algebra.

Without science, you would not be reading this. Without science, there would be no computers, no internet, and no blogging.Well, so what you might say. I’m sure you could live without reading this blog post, or indeed any of the other 1.6 million posts made every day (according to Technorati). I’m even sure you could live without computers and the internet in general - after all, only 22% of the world’s population has access to such luxuries. Maybe you’d find it harder to get by without cars, antibiotics and fridges, although these are also unfortunately far from universal worldwide.

But is science only about new inventions, new technology and new medicines? When the Large Hadron Collider was fired up early this year, besides suggesting we were all doomed, many people were asking what the point of it all was. Wouldn’t the money be better spent elsewhere, it was suggested. Who really wants to know about a bunch of stupid particles anyway?
I’d counter this argument with: who wouldn’t want to know? The human mind is inescapably curious. Everybody wants to learn something, be it particle physics, the saxophone, or a comprehensive knowledge of football. Arguably, it is scientific curiosity that has allowed us to rise to our prominent position on planet Earth.

Are Black Holes Real?

The short answer to the question is, "Likely." That means that most astronomers and physicists have good theoretical reasoning to believe that black holes can exist. The problem is that by their very nature, black holes are ... well, they are black. As we shall see below, this is not entirely true; however, for all intents and purposes, evidence for the existence of black holes in the universe is fundamentally of an indirect nature, coming from how black holes influence their surroundings.

What are Black Holes?

Before going further, we first must determine what a black hole is and is not. Black holes do have mass. In fact, it is because they have mass that they can become black holes. So black holes have gravity. But black holes are not cosmic vacuum cleaners. It is true that anything entering a black hole cannot re-emerge again; however, it is not true that black holes are sucking in matter from all over the universe, causing everything to fall into them.
For example, if the Sun were replaced by a black hole of the same mass as our Sun, then it turns out that the Earth's orbit would be largely unchanged (only our planet would become very cold!).

How are Black Holes Made?

The details of how black holes are made are not terribly important to this discussion. What is key is the following idea. Gravity is an attractive force, and only an attractive force. So all bits of mass everywhere are tugging on everything all at once, tugging harder are nearer objects and weaker on the more distant ones. When mass becomes concentrated in a local volume of space, such as the gas in a star, gravity wants to make of that matter come crashing, and crushingly, together. What prevents this from happening? The answer is gas pressure. There is high pressure in the center of this volume of mass, while space itself is a near vacuum, so that there is a huge pressure difference between the gas at the star's center and its outer portion, and this pressure difference resists the tendency of gravity to further compress the gas.
Nice. But to make a long story short, it turns out that when there is enough concentration of mass in the volume, there is no kind of gas pressure that is capable of preventing the crushing effects of gravity, so that all of that mass squeezes together, essentially to a point of matter, a point with small or zero volume but finite mass, and so having essentially infinite density! This is a black hole.

Why is it Black?

An important concept in gravity is that of escape speed. This is the speed necessary for something to move away from a body of mass and never quite fall back. Moving faster than escape speeds ensures that it won't fall back. Moving slower, and the object will execute some form of orbit around the body (possibly only to hit the "ground", or surface of body).
The laws of physics and experimental confirmation indicate that nothing travels faster than the speed of light. Objects with higher and higher masses have larger and larger escape speeds, and there is no limit to this. Black holes, having infinite density, have an infinitely large escape speed. But it turns out that the escape speed value depends on how far an object is from a body of mass. So there is a certain distance from a black hole where the escape speed just equals the speed of light. This is usually represented by a sphere or globe called the "Event Horizon", with a spherical radius given by the Schwarzschild radius which depends on the mass of the black hole. Inside the event horizon, the escape speed is larger than the speed of light, and so nothing can get out if anything ventures this close. Outside the horizon, light that passes by can escape, although it will not travel in a straight line. This means light going into the event horizon (and anything else!) cannot get out, and so that region is necessarily black.
Disturbingly, black holes practice cosmic censorship. There is no telling what happens on the inside. You could go in to look for yourself (but of course you would die), but there would be no way to tell your friends because you could not get back out. Weird.

How Do We Know Black Holes Exist? How Do We Find Them?

Although black holes do not glow, they do have gravity, and so they affect (sometimes drastically) their neighborhood, and we can infer the presence of a black in this way. This is of course indirect, which is not as nice as just seeing the black hole itself, and so can be suspect for the skeptical observer. Yet, it turns out that we often cannot understand what we see from the neighborhood unless a black hole is present, and sometimes this argument can be especially strong when the properties of the neighborhood conform to predictions for how a black hole will affect it.
The theory of stars would claim that massive stars (much more massive than the Sun) will eventually blow up as supernovae, and if there remains a core in excess of around 3 times the Sun's mass, that will collapse under gravity to become a black hole. If this happens in a binary star system, in which one star makes a black hole and the other star manages to survive so that the two continue orbiting one another, then the normal star can in some cases transfer gaseous matter to the black hole (see figure below). As this gas fall toward the black hole, it makes a disk of orbiting gas that slowly dribbles into the black hole. In this process the gas is heated and manages to glow in X-rays. So we cannot see the black hole, but we do see intensely bright X-rays. We also see the one star and can infer the presence of an unseen companion. All of this seems to add up to a black hole.

An especially famous case is the system Cygnus-X1, a binary that has a "missing" companion (we do not see it) but glows brightly in X-rays. The neat thing is that the Hubble Space Telescope has been able to watch as matter dribbles into the black hole. For any normal body, the infalling of gas would cause it to glow more brightly. But because of the odd properties of black holes, such gas as it approaches the event horizon will inevitably grow fainter, and this is what is observed (see figure below).

Another place to find black holes - supermassive ones - seems to be in the heart of galaxies. These monsters are can have anywhere from millions to billions of times the mass of the Sun. The event horizons can be about as large as our solar system. Below are some Hubble images pertaining to a suspected black hole in the heart of the giant galaxy M87. The first image shows the center of the galaxy, and that a jet leads back to its center. The inset of that figure indicates a swirling disk of orbiting gas near the center. The figure below shows how the Hubble can measure the speed of orbiting gas in this disk. It turns out that as these distances from the center (light years), the speeds are so high (hundreds of kilometers per second), that a tremendous amount of mass must exist interior to the disk, a mass of about 100 million Suns, but in a volume that is like the distance from the Sun to the nearest star. The implication of a black hole is based on the idea that it is gravity which makes the gas orbit, and stronger gravity leads to higher speeds. Except for a black hole, no one knows how to cram so much matter into so little volume.

Bimettalic Strips.

Today, we spent quite an large amount on going through excercise 7. One of the main reasons were that it was because some of our classmates were not quite sure how bimetallic strips work and that the diagram given was quite vague. This caused some confusion among the students. So i decided to do a blog entry on bimetallic strips.

Material Expansion Coefficient Aluminium 2.4 x 10-5 K-1 Iron (steel) 1.2 x 10-5 K-1 Copper 1.7 x 10-5 K-1 Brass 1.9 x 10-5 K-1 Glass (pyrex) 3.3 x 10-6 K-1 Concrete 1.2 x 10-5 K-1 Invar <1.3 x 10-6 K-1 Table 1

Figure 1

Volume Expansion of a Solid

The volume of a solid (including metals except for mercury) is slightly dependent on temperature. Let the length L_o be the length of the solid when the temperature is T_o. When the temperature rises the length will change (for most solids the length will increase) Providing the temperature increase is not too great the length of the solid will change by an amount
 

change in L = a * Lo * (T - To)

where the constant a is the thermal expansion coefficient, which accounts for the different solids that could possibly be used.


Uses for Bimetallic strips

Bimetallic strips are made in coils to increase their sensitivity for use in thermostats. One of the many uses for bimetallic strips is in electrical breakers where excessive current through the strip heats it and bends it to trip the switch to interrupt the current.

Sports Science of Football - Project

Since I also like playing football, I decided to do another post on the sport science of Football. This post will be about the Sports Science of A Jabulani, a ball that was much criticized during the 2010 World Cup due to unnatural flight path.



With the 2010 Cup's Jabulani ball (‘to celebrate’ in isiZulu), Adidas claims it has surpassed its own Teamgeist from 2006 in constructing the roundest and most accurate ball ever played. See how it's made inside.
And you thought a ball was just a ball? From the iconic 32 panel black and white Telstar introduced in Mexico City in 1970 to the latest unveiled today for South Africa, the goal for Adidas, naturally, has always been to build a better ball. Soccer players want a ball that feels good on the foot and flies predictably no matter where on the ball it’s struck. Teamgeist achieved its improvements by reducing the number of panels from 32 to just 12, by thermally bonding the panels thereby eliminating inaccurate stitching and by forming the outer panels in 3-D versus making them flat and bending them into shape.

Jabulani, All in One Piece:  Adidas

Jabulani takes another step towards perfection with just eight EVA and TPU panels that provide a 70% larger striking surface due to fewer seams. While the Teamgeist ball was great for strikers, many goal keepers complained that the ball's aerodynamics created a lack of rotation in the air, making its path at times erratic, like a knuckleball. Jabulani attempts to stabilize the flight pattern of the ball through what Adidas is calling ‘aero grooves’, essentially long indentations along the panels. The grooves divide the ball up into additional pseudo-panels but by molding the grooves Adidas can achieve consistent location and shape to achieve optimal flight. The surface of the ball has also been covered with raised nubbins to help with tactile feel on the foot. While Adidas would not provide numerical flight data, it claims that robotic kicking and wind tunnel testing at Loughborough University in England and at its own football lab in Germany show that Jabulani is its most accurate ball. To be sanctioned FIFA Approved, a ball is only subject to a handful of more static tests, which the Jabulani ball obviously meets.
• Circumference: FIFA Standard: 68.5-69.5cm, Jabulani: 69.0 +/- 0.2
• Roundness: Diameter is measured in 16 different locations. FIFA Standard: max 1.5% difference, Jabulani: max 1.0% difference
• Water Absorption: A ball is pressed and rotated in water 250 times: FIFA Standard: max 10% weight increase. Jabulani: 0% weight increase
• Weight: FIFA standard: 420-445 grams, Jabulani: 440 +/- 0.2 grams
• Uniform Rebound: The only dynamic FIFA test, the ball is dropped ten times onto a steel plate from a two meter height. The difference from the lowest to the highest bounce can be no more than 10 cm. Jabulani bounced in a range from 143 to 149 cm.
• Loss of Pressure: Air pressure measured three days after inflation. FIFA Standard: 20% max loss, Jabulani: 10% max loss