viernes, 19 de mayo de 2017

Physics and TV: Genius


A highly recommendable TV series for those who like physics is Genius. This show is on the screen on National Geographic Channel, available on some cable and satellite TV providers. The series tells us the life and work of one of the most brilliant scientists ever: Albert Einstein. It shows us not only the scientist and his crucial works but also his personal life and how the rise of nazism in Germany affected to the most famous Jew of the 20th century. Not only it is a very entertaining program but it is also very educational. It provides a quite comprehensible approach to his paramount contributions, such as his proofs of the existence of molecules, his explanations for the photoelectric effect or the most revolutionary physics ideas ever: the theory of relativity. An absolute "must" for those who like science or TV series.

viernes, 12 de mayo de 2017

Physics and movies: Up



I don't know anyone who dislikes Disney-Pixar's UP. This story of friendship between an elderly man and a boy is very inspiring. The movie deal with a physics principle: buoyancy. The movie tells us how a recently widower man tries to make his wife's dream real by traveling to South America. To do so, he uses his house as a mean of transport by making it float in the air. According to the plot, the house goes up thanks to the buoyancy force produced by thousands of helium balloons. Would that work? A National Geographic TV show tried to recreate the set-off of the house and got the result you can see in the video below.

 

Despite it is a lightweight house specially designed for this experiment, a lot of helium was used. Could something like that be done with an actual house like the ones that people live in? How much helium would be needed? According to an estimation by  www.xatakaciencia.com, a 150-squared-meter house may have a mass of roughly 100 tons. Are you able to estimate the volume of helium that could make a house fly?

Let's do the math.

First, we can get some info from the video. They use 300 balloons. Each of them has a diametre of 8 ft (2.44 m). The reporter says that it was almost freezing, so I will assume they are at STP conditions. We also need additional data, such as helium and air densities:
He: 0.179 kg/m3
Air: 1.295 kg/m3.

How much helium do they use?
Each balloon is a sphere with a radius of 1,22 m. Its volume can be easily calculated: 7.59 m3. All the balloons together add up a volume of 2277 m3. Multiplying by its density we figure out that the mass of helium inside the balloon is 407.5 kg which has a weight of 3994 N.

What buoyancy force can be obtained from that mass of Helium?
The buoyancy force is the weight of the fluid displaced by the balloon. In this case we have to calculate the weight of 2277 m3 of air.
E = 1.295 kg/m3 · 2277 m3 · 9.8 m/s2 = 28897N.

This buoyancy force has to be strong enough to rise not only the house but also the helium itself. The weight of cannot be greater than 28897 N - 3994 = 24903 N, so it has to be lighter than 2541 kg, roughly two and a half tons. To rise an actual house, like the one you may live in, with an estimated mass of 100 tons we would need forty times more Helium, which is 91080 m3. That volume is the equivalent of a sphere with a radius of 28 m. Take the volume of a party balloon (0,91 according to the website a party stuff provider company) into account we conclude that 100000 balloons would be needed. I honestly was expecting an even higher number of balloons. In fact, we would need much more balloons, at least to set the house off. Don't forget the force we have just calculated is the one required to lift the house but, to set off we have to pull it out from its foundations and higher buoyancy force would be required.






jueves, 4 de mayo de 2017

Physics and movies: Titanic

[Spoiler alert: the ship sinks]

In one of my last lessons, a controversy regarding the movie Titanic came up. Just after the sinking of the ship, the two main characters, Jack (Leo Dicaprio) and Rose (Kate Winslet), try to keep themselves alive by laying on a wooden door. After a few attempts, they reach the conclusion that it was impossible because of the fact that the door didn’t have enough buoyancy to hold the two of them. As a consequence, only one them could survive, so Jack decides to let Rose lay on the door while he remains in the water. Finally, he dies due to the low temperature of the seawater and sinks. My female pupils, who consider this scene is one of the most romantic ones ever shot, tell me off when I express my doubts about the buoyancy of the door. Possibly Jack could have survived if Rose had let him up.


I have surfed the net and found some information.
  • According to this frame of the movie and others we can estimate that the dimensions of the door are 2 m · 1 m · 15 cm.
  • Jack (Leo Dicaprio) has a mass of 77 kg
  • Rose (Kate Winslet) has a mass of 63 kg
  • Some kinds of wood were used to build this famous ship. Each of them has a different density:
    • Teak: 980 kg·m-3
    • Oak: 770 kg·m-3
    • Pine: 440 kg·m-3
  • The density of sea water at that low temperature (we can assume it was very close to 0 ºC or even lower) is 1.028 g/cm3.

Exercise:
  • Do the math and calculate the maximum buoyancy force exerted on the door.
  • Figure out the total weight of the system door+Jack+Rose for each of the three types of wood mentioned before.
  • Compare that two forces.
  • What do you think? Did Jack have a chance? Did he die because he romantically decided to sacrifice his life to save Rose’s or just because she was mean?

miércoles, 3 de mayo de 2017

Counting one mole

One mole is the number of molecules in eighty grams of water which is very little water, about three teaspoonfuls. Such a little volume of water contains 6.02·1023 molecules (the Avogadro’s number) which is a huge number of molecules. To picture how big this number is I wonder how long it would take to count all molecules in one mole one by one? One year? One century?… Let’s do some maths. To make the task a little bit easier I will suppose we are able to count ten units per second which is a very fast counting rate. Counting that fast, we would count…
10 molecules in 1 second
600 molecules in 1 minute
36,000 molecules in 1 hour
864,000 molecules in 1 day
315,360,000 molecules in 1 year.

As we have to count from 1 to the Avogadro’s number, we just have to divide it by the number of molecules counted in a year (6.02·1023/ 315,360,000), which leads us to an enormous number of years: 1.9·1015. This number is much more impressive if we don’t use scientific notation: 1,900,000,000,000,000 years, in other words, almost two quadrillion years (in Spanish: mil novecientos billones). Is it that long? Let’s compare it with other long times:
First human-ish beings appeared 4.5 million years ago
Earth exists since 4.5 billion (4.5·109) years ago
The Universe 14 billion (1.4·109) years ago.

The time we would need to count from one to the Avogadro’s number is about 1,364,000 times longer than the age of the Universe. Mind-blowing, isn’t it? To make the task shorter, let’s imagine that all people (7 billion = 7·109) helped us to count, in that case, the counting would be 7 billion times shorter, which is roughly 270,000 years. All the human beings in our planet working together would need two hundred and seventy thousand years to count the number of molecules in a mole.


As you can see the Avogadro’s number is really huge but it is just the number of water molecules in a sip of water.