National Science Quiz 2017

Melbourne - 18 JuneAdelaide - 25 June

Questions and solutions

1.If you hang a towel outside on a sunny day after washing it, why does it go stiff?

a. UV light changes the chemical composition of the detergentb. Dust particles blow into the fibresc. Salt crusts are formed due to lack of movement

Answer: cWhen drying a towel by laying it flat or by hanging it on a clothesline (either inside or outside), evaporation of water leaves a crust on the towel consisting of the salts dissolved in the water. (These salts form with elements such as aluminium, calcium, magnesium, and sodium.) This makes the towel feel stiff. In a tumble dryer, the towels are moved consistently, so that the salts cannot dry into a crust, and a lot of the salts will be also shaken off. As a result, towels from the dryer feel softer than those dried by hanging.

When drying towels on the clothesline in the presence of strong winds, we may observe a difference in stiffness between the towel’s top (little movement so more crust forms) and the bottom (strong movement so less crust forms).

2.How are you able to make a water drop sit on top of a water surface indefinitely?

a. By vibrating the waterb. By making the water surface flowc. By heating the water surface

Answer: aWater drops can remain intact near a water surface if a thin layer of air separates them from the surface. Ordinarily, the weight of the drop slowly pushes the air layer away and the drop disappears into the water. By moving the water surface up and down at high speed, the air layer is recharged constantly. As long as this continues (for minutes or even hours) the drop will continue to bounce.

3.What causes champagne bubbles to prickle your tongue?

a. The popping of the bubbles b. The temperature of the bubbles c. A chemical substance in the bubbles

Answer: cThe bubbles in champagne are from carbon dioxide (CO2) released during fermentation. (In soft drinks, the gas is added artificially to produce bubbles.) CO2 reacts with water to form carbonic acid (H2CO3). Our tongue has different types of nerve endings that specialize in detecting environmental factors that may have a harmful effect on us, such as pressure, temperature or chemicals. These receptors, known as "nociceptors", send a small stimulus to the spinal cord nerve cells, which pass the stimuli on to the brain stem. Here the stimuli are perceived as pain. Nociceptors react to carbonic acid. The small bubbles release carbonic acid, thus each bubble on the tongue causes a little sensation of pain. The sensation is known as ``carbonation bite''.

An experiment with drinking fizzy lemonade in a high pressure chamber (3.4 atmospheres, instead of 1 atmosphere) has shown that it is really carbonic acid and not the bursting of the bubbles that causes the prickling sensation. In the high pressure chamber, bubble formation is prevented, but the subjects still felt the same sensation on their tongue. It has been hypothesized, however, that the popping of the bubbles can make the prickle more severe.

Lastly, it has been shown that the temperature of the bubbles has nothing to do with the prickling sensation.

4.A "gravity train" is a proposed rail system where a straight tunnel is built connecting two points on the surface of the Earth. What is the maximum depth of a tunnel for a Melbourne-Adelaide gravity train?

a. 84 metresb. 840 metresc. 8.4 km

Answer: c

Modelling the Earth as a perfect sphere, we get the diagram above, where: B is the surface distance from Melbourne to Adelaide (about 654km), r is the radius of the Earth (about 6300km), A is the distance from the centre of the Earth to the tunnel, and d is the depth of the tunnel

We can solve the problem using values we know (B and r) to derive the values of unknown quantities that will assist us in determining d.

From the diagram we see thatd=r−A

so we need a way to determine A, which is one edge of the shaded right-angled triangle. So, we use trigonometry to get

cos (θ )= Ar or A=r cos (θ ) ,

and we haved=r−r cos (θ )

Therefore, our problem has reduced to finding the angle .θ

The ratio of the arclength B to the total circumference is the same as the ratio of 2θ to the angle of a full circle, which is 2π radians (or 360 degrees). So

2θ (θ isthe unknownangle ,∈radians)2π (angle traced out by a ,̊∈radians) =

B(the known arc length ,∈km)2π r (circumference of the Earth ,∈km)

(Q4 explanation continued)

(The unit “radians” is related to the more familiar “degrees” but is more neat and useful for certain types of problems. Students may have noted a DEG/RAD key on their calculator that converts a value in one unit to the other.)

We rearrange this equation to get the required angle, so

2θ=2π B2π r

=Br ,

leading to

θ= B2 r≈ 0.052rad (2.97 deg).

So using our expression for d this gives:

d=r−r cos ( B2r ).Substituting B ≈ 654 km and r≈ 6300 km, this gives us depth d of approximately 8.4 km, or 8400 m.

5.An aurora is the phenomenon known on Earth as the northern or southern lights. On what planets can aurorae occur?

a. On any planet with an atmosphereb. On any planet with a magnetic fieldc. On planets with oxygen or nitrogen in their atmosphere

Answer: aAn aurora is the result of “gas discharge” (that is, the discharge of energy from gas) in the topmost layers of the atmosphere. This gas discharge is comparable to that which occurs in the operation of neon lamps or fluorescent tubes. Electrons, which originate from the sun, fly into the atmosphere of planets at high speed, thereby passing on energy to gases there.

In particular, when an electron from the sun collides with an electron in a gas atom, energy is transferred from the former to the latter. This may cause a gas electron to be “excited” to a higher energy level. This is an unstable arrangement and when an electron drops back to a lower energy level it releases some or all of the recently acquired energy as electromagnetic radiation. The frequency of this radiation depends on the gas from which it was emitted, as each has characteristic gaps between the electron energy levels. In the case of nitrogen and oxygen (which make up the bulk of our atmosphere), the frequencies fall into the spectrum of visible light.

For example, oxygen emits green light and nitrogen pink; these colours are characteristic of the northern lights on earth. Following excitation, other gases in the atmosphere can emit light in this way, in other colours.

The Earth’s magnetic field lines pass through the Earth’s North and South magnetic poles and extend outwards into space. When an electron from the sun enters the region of field lines near the Earth, its motion is redirected so that it spirals around the field lines, heading in their general direction. It is very likely that at some point the electron will enter the Earth’s atmosphere. Most electrons enter somewhere near one of the magnetic poles as they continue to move in the general direction of field lines.

The magnetic field is thus only responsible for the location, not for the phenomenon itself. On planets like Mars where there is no or only a weak magnetic field, aurorae are also observed. These aurorae are visible from a greater range of locations on the planet surface.

6.You knot together the two ends of a rope. You then pull the rope through a carabiner. With a second carabiner you connect the two ends. You are not allowed to unclip either carabiner and pull the rope out of it.What do you need to do to release the rope?

Answer:The key is to clip one carabiner into the other, thus changing the topology (this is an example of a problem in knot theory). The steps:

7.A magician shuffles a standard deck of 52 playing cards and you pick one at random. They get to ask one question before trying to guess your card. Which of the following questions should they ask to have the best chance of guessing your card correctly?

a. Is it a black card?b. Is it the 2 of spades?c. Either, it makes no difference

Answer: cIt does not matter which question you ask.

Question (a) "Is it a black card?" gives two possibilities. We know that there are 26 red cards and 26 black cards, so any card drawn is one or the other. There is a chance of 26 in 52, or equivalently, one half, that the card is indeed black. So, if the answer to the question is “YES”, then the magician now has a one in 26 chance of correctly guessing your card. By a similar logic, the magician has the same chance of success if the question was answered with “NO”.

Calculating the probability of some event occurring can be complicated. We must account for all of the possible ways the event can occur. In this case, the probability of the magician guessing your card correctly is the sum of the probabilities of the two different ways they could achieve this. By our logic, these ways correspond to whether the unknown card is black or red.

So, summing the probabilities, the magician has a

(1/2) * (1/26) + (1/2) * (1/26) = 1/26

chance of guessing correctly. This is approximately a 4% chance.

Probability of YES answer

Probability of NO answer

Probability of guessing the

correct BLACK card

Probability of guessing the

correct RED card

(Q7 explanation continued)

In the case of Question (b) "Is it the 2 of spades?" the magician has a 1/52 (approximately 2%) chance of getting the right answer immediately. But of course, they have a 51 / 52 chance (roughly 98%) of being wrong. In which case, the magician has to guess from the 51 remaining cards, giving them a 1/51 chance of guessing correctly. Doing a calculation similar to that for question (a), the total chance of guessing the card correctly is

(1/52) * (1/1) + (51/52) * (1/51) = 1/26

Which is the same as the chance of guessing correctly if the magician had asked question (a)!

Note: Any question which restricts the set of possible answers to n choices gives the same result. In the general case where a question may lead to choosing from amongst n possible answers, the overall probability of the magician guessing the card correctly is

(n/52 * 1/n) + ((52-n)/52 * 1/(52-n)) = 1/52 + 1/52 = 1/26

as before.

Probability of YES answer

Probability of NO answer

The card is now known (guess is

certain to be correct)

Probability of guessing the

correct card from 51 options

8.What type of fire must you not try to extinguish with a carbon dioxide extinguisher?

a. Burning gasb. Burning metalc. Burning fat

Answer: bA metal fire results from burning magnesium, zirconium, lithium, potassium or sodium. Let's take magnesium as an example: magnesium fires are extremely bright and hard to quench. Attempting to use carbon dioxide to extinguish the fire is a very bad idea. Magnesium and carbon dioxide react very strongly according to the reaction

Mg + CO2 -> MgO + C.

This is an exothermic (heat releasing) reaction that produces temperatures above 2000 degrees Celsius. This is significant as it causes the fire to burn even more vigorously since the reaction rate increases with temperature.

Water also does not work because magnesium reacts with water to form magnesium oxide and highly explosive hydrogen gas. The way to quench this type of fire is to deprive it of oxygen, such as smothering it with sand, or preferably, to use a so called “dry powder” (an extinguishing agent that works by absorbing the heat as it smothers the fire). Because of its highly flammable nature, magnesium was used in bombs dropped on cities in World War II.

But it is also used in safety flares, and you may have seen the Sydney 2000 Olympic Torch Relay in which a modified torch with Magnesium-based fuel burned underwater near the Great Barrier Reef.

9.You’re driving in a car with a helium balloon, and you turn a corner. What happens to the balloon?

a. It moves to the inside of the cornerb. It moves to the outside of the cornerc. It doesn’t move

Answer: aWhen the car goes around the bend, it acts as a type of centrifuge: the heaviest particles are pushed to the outside under the influence of the centrifugal force, lighter particles remain on the inside. Helium is lighter than air so the air in the car will move towards the outside of the bend, and the helium (in the balloon) will move to the inside.