## Posts Tagged ‘Theory’

### Gravity and the human body

September 5, 2013

Our bodies function necessarily under the presence of gravity; how blood pumps, a sense of balance and bone growth are all due to life in a world where gravity is an inescapable reality. Armed with experiments from neuroscientists David Hubel and Torten Wiesel, astronaut Jay Buckey presents a thought experiment: How would our bodies work without the force of gravity?

### If you removed all ships from the sea …

April 2, 2013

How much would the sea level fall if every ship were removed all at once from the Earth’s waters?

Archimedes’ principle tells us that the water displaced by a ship weighs as much as the ship itself. If we can figure out the total weight of all the world’s ships, we can figure out how much water they’re displacing, then divide that volume by the surface area of the ocean to figure out how much the water level would drop.

Weighing ships is confusing. There are a bunch of different measurements of the size of a ship, and many of them, like gross tonnage, are actually measures of the volume of the ship’s rooms and other internal spaces, not its weight.

The UN Conference on Trade and Development publishes estimates of the size of the world shipping fleet.

What the UNCTD publishes is “deadweight tonnage”, which is the maximum weight of the ship’s fuel, cargo, and crew. What we want is “displacement”. Unfortunately, comprehensive numbers for displacement are harder to find.

Fortunately, we can estimate it. Brian Barrass’s book Ship Design and Performance for Masters and Mates gives a table of ratios of deadweight tonnage to displacement for different types of ships.

Extrapolating from the last few years of UNCTD data, and using the coefficients from the book, suggests that the world fleet weighs about 2.15 billion tons when fully loaded.

A ton of water is about a cubic meter. 2.15 billion cubic meters divided by the surface area of the oceans equals about 6 microns (0.006 mm).

So there you go, if every ship were removed all at once from the Earth’s waters the sea level would fall by about six microns—slightly more than the diameter of a strand of spider silk. Learn more here.

### An enormous rain drop

January 19, 2013

What if a rainstorm dropped all of its water in a single giant drop?

We’ll imagine our storm measures 100 kilometers on each side and has a high total precipitable water (TPW) content of 6 centimeters. This means the water in our rainstorm would have a volume of:

100km²×6cm=0.6km³

That water would weigh 600 million tons (which happens to be about the current weight of our species). Normally, a portion of this water would fall, scattered, as rain—at most, 6 centimeters of it.

In this storm, all that water instead condenses into one giant drop, a sphere of water over a kilometer in diameter.

The water would hit the ground moving at over 200 m/s (450 mph). Right under the point of impact, the air is unable to rush out of the way fast enough, and the compression heats it so quickly that the grass would catch fire if it had time.

Fortunately for the grass, this heat lasts only a few milliseconds because it’s doused by the arrival of a lot of cold water. Unfortunately for the grass, the cold water is moving at over half the speed of sound.

The wall of water expands outward kilometer by kilometer, ripping up trees, houses, and topsoil as it goes. The house, porch, and old-timers are obliterated in an instant. Everything within a few kilometers is completely destroyed, leaving a pool of mud down to bedrock. The splash continues outward, demolishing all structures out to distances of 20 or 30 kilometers. At this distance, areas shielded by mountains or ridges are protected, and the flood begins to flow along natural valleys and waterways.

### What if all humans jumped at the same time?

October 10, 2012

What would happen if everyone on earth stood as close to each other as they could and jumped, everyone landing on the ground at the same instant?

The answer … it doesn’t really affect the planet. Earth outweighs us by a factor of over ten trillion. On average, we humans can vertically jump maybe half a meter on a good day. Even if the Earth were rigid and responded instantly, it would be pushed down by less than an atom’s width.

### Speed of light baseball

October 2, 2012

What would happen if you tried to hit a baseball pitched at 90% the speed of light?

The answer turns out to be “a lot of things”, and they all happen very quickly.

The ball is going so fast that everything else is practically stationary. Even the molecules in the air are stationary. Air molecules vibrate back and forth at a few hundred miles per hour, but the ball is moving through them at 600 million miles per hour. This means that as far as the ball is concerned, they’re just hanging there, frozen.

Normally, air would flow around anything moving through it. But the air molecules in front of this ball don’t have time to be jostled out of the way. The ball smacks into them so hard that the atoms in the air molecules actually fuse with the atoms in the ball’s surface. Each collision releases a burst of gamma rays and scattered particles.

These gamma rays and debris expand outward in a bubble centered on the pitcher’s mound. They start to tear apart the molecules in the air, ripping the electrons from the nuclei and turning the air in the stadium into an expanding bubble of incandescent plasma. The wall of this bubble approaches the batter at about the speed of light—only slightly ahead of the ball itself.

Suppose you’re watching from a hilltop outside the city. The first thing you see is a blinding light, far outshining the sun. This gradually fades over the course of a few seconds, and a growing fireball rises into a mushroom cloud. Then, with a great roar, the blast wave arrives, tearing up trees and shredding houses.

Everything within roughly a mile of the park is leveled, and a firestorm engulfs the surrounding city. The baseball diamond is now a sizable crater, centered a few hundred feet behind the former location of the backstop.

### What is fire?

October 17, 2011

Fire is combustion or burning, in which substances combine chemically with oxygen from the air and typically give out bright light, heat, and smoke. See:

### Vestigiality

September 2, 2011

A vestigial trait is a remnant of a trait that used to exist in an organism’s ancestors. The present organism carries some form of this trait but it no longer serves a purpose in the present. An example is the coccyx, or the tailbone in humans. Our ancestors used to have a tail which may have served to help them in movement and in gripping branches when they used to live in trees. This tail structure now exists in humans as a small bone found at the end of the vertebral column called the coccyx.

As another example, when you’re cold or stressed out, your arrector pili are the smooth muscle fibers that contract involuntarily to give you “goose bumps.”

If you’re a furry woodland creature, this can provide insulation (thick, standing fur traps air between the erect hair follicles, helping the animal retain heat), or make you look bigger (which can mean the difference between being eaten and being passed over for less troublesome prey, a particularly good example being a porcupine). Since most humans aren’t hairy enough to fit the “furry woodland creature” bill, our arrector pili provide neither of these benefits. Learn about more human vestigial traits here.

### E = mc²

June 6, 2010

Albert Einstein was a really, really smart guy. He was an amazing thinker and he is probably most well known for this really famous equation:

## E = mc²

But what does “the energy of a body (E) equals its mass (m) times the speed of light (c) squared”, or E = mc² actually mean?

Well basically, it shows that mass can be converted into energy and vice-versa. To appreciate the significance, consider this example:

E is energy in joules, m is mass in kilograms and c is the speed of light in metres per second. Using the equation the energy released by only 1 kilogram of matter

= 1 x 300,000,000 x 300,000,000 joules

= 90,000 million million joules

= energy released by 20,000 kilotons of TNT.

Now the Hiroshima atomic bomb was only a 15-kiloton bomb so 20,000 kilotons is A LOT OF ENERGY to come from only 1 kilogram of matter!

The formula E = mc² made the creation of nuclear weapons possible, something the pacifist Einstein was not particular pleased about. Read more here.

November 6, 2009

A solar eclipse happens when the Moon passes between the Earth and the Sun. It will then block the rays from the sun.

The umbra is the darkest part of the shadow. In astronomy, an observer in the umbra is said to be in the shadows experiencing a total eclipse.

The penumbra is the region in which only a portion of the Moon is obscuring the Sun. An observer in the penumbra experiences a partial eclipse.

### What colour is the green apple?

November 2, 2009

People with colour blindness cannot tell the difference between certain colours, or they may not see colours at all. Most colour blindness is inherited as a genetic condition.

There are far more males who are colour blind than there are females. Between five and eight percent of males, but less than one percent of females, are colour blind.

The most common form of colour blindness is red-green colour blindness. The Ishihara Color Test is the test most often used to diagnose red-green colour deficiencies.

The test consists of a number of coloured plates, called Ishihara plates, each of which contain a circle of dots appearing randomized in colour and size. Within the pattern are dots which form a number visible to those with normal colour vision and invisible, or difficult to see, for those with a red-green color vision defect.

For example, a person with normal colour vision would see the number 74 below, while a person with a red-green color vision defect would see only spots.

Read more here, here, here or here.