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OfflineAnnom
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Dutch Science Quiz 2010
    #13590512 - 12/06/10 01:18 PM (13 years, 3 months ago)

It's time for the yearly Dutch science quiz, 15 multiple choice questions. It's a quiz posted in newspapers and the internet. The answers are given and demonstrated in a national TV show around christmas.

Wild variety of questions. Some are good food for thought and discussion. I will translate a few and make a poll.
You wind a rope tightly around Earth. Increase its length by 1 m and lift the rope at a one point. How high can you lift the rope?
You may choose only one
A little (toy) boat with pure alcohol floats in a container with water. You empty the alcohol into the water container and place the boat back in the water/alcohol mixture. What happens with the liquid level in the large container?
You may choose only one
You stand on an escalator going up. What happens during the time you also walk up on the escalator?
You may choose only one


Votes accepted from (12/06/10 01:15 PM) to (No end specified)
You must vote before you can view the results of this poll


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InvisibleSalomon
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Re: Dutch Science Quiz 2010 [Re: Annom]
    #13590988 - 12/06/10 02:45 PM (13 years, 3 months ago)

so what are the right answers? can you put them like this?


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OfflineAnnom
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Re: Dutch Science Quiz 2010 [Re: Salomon]
    #13594331 - 12/07/10 02:50 AM (13 years, 3 months ago)

I don't know the answers. They will be made public after christmas.

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OfflineBaby_Hitler
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Re: Dutch Science Quiz 2010 [Re: Salomon]
    #13594492 - 12/07/10 05:02 AM (13 years, 3 months ago)



C=pi *d

d = C/pi

d1 = 13,000,000m/pi

d1 = 4,138,028.5203892787299909778476854.m

d2 = 13,000,001m/pi

d2 = 4,138,028.8386991649137816493854529

d2 - d1 = 0.3183098861837906715377675m


Aaaaaand I just solved the wrong problem because the rope is flexible. But at least we know 12cm is not the right answer. It's more than 32 cm.



The escalator will either slow down or expend more energy when the person begins walking, but level out back to normal when the person stops accelerating, and moves at constant speed. no difference

The sum of the volumes of unmixed water and alcohol are greater than the volume of the two mixed together. decreases



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OfflineSeussA
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Re: Dutch Science Quiz 2010 [Re: Baby_Hitler]
    #13594549 - 12/07/10 05:55 AM (13 years, 3 months ago)


I tried to get an approximation on the first question using an ellipse rather than a circle for the case where the rope is lengthened.  I came up with ~1.5m, which assumes that both ends of the ellipse have the same radius.  Because the end of the ellipsoid that the rope is pulled up from will have a smaller radius than the end being held by the earth, the answer has to be larger than 1.5m.  I tried to calculate the exact circumference of the ellipsoid, but my calculus is pretty rusty and I couldn't work the integral from memory.

The second question is tricky.  I will have to work it out later.  In general, it is a buoyancy/density problem.  The boat, along with the weight of the alcohol, displaces water, increasing the volume of the water from the case with no boat.  If you empty the alcohol from the boat into the water, the boat is lighter, thus it displaces less water, thus the water level decreases.  However, the density of the water has changed with the addition of the alcohol, thus it is a mistake to assume that the boat displaces less water.  I'll have to look up the equations later, but I suspect this will require simultaneous equations to be solved.  If I were to hazard a guess, it would be that the volume remains the same (with the boat displacing less liquid when empty, but there being more liquid total since the alcohol was added to the water).

I haven't had time to think about the third question yet...


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OfflineAnnom
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Re: Dutch Science Quiz 2010 [Re: Seuss]
    #13607027 - 12/09/10 01:25 PM (13 years, 3 months ago)

The first question is 120 m. It's hard to explain without drawing, but here is the relation between the length of the rope and the height. It's a triangle side + arc.

Formula: 0

R is Earth's radius, h the lifted height, L the length of the rope.

Solving using a root finder (or try the 3 answers) gives a height of 0.1214 km. Pretty damn high.

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OfflineBaby_Hitler
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Re: Dutch Science Quiz 2010 [Re: Annom]
    #13687416 - 12/26/10 05:01 PM (13 years, 3 months ago)

bump


--------------------
"America: Fuck yeah!" -- Alexthegreat

“Nothing can now be believed which is seen in a newspaper. Truth itself becomes suspicious by being put into that polluted vehicle. The real extent of this state of misinformation is known only to those who are in situations to confront facts within their knowledge with the lies of the day.”  -- Thomas Jefferson

The greatest sin of mankind is ignorance.

The press takes [Trump] literally, but not seriously; his supporters take him seriously, but not literally. --Salena Zeto (9/23/16)

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OfflineAnnom
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Re: Dutch Science Quiz 2010 [Re: Baby_Hitler]
    #13689512 - 12/27/10 04:27 AM (13 years, 3 months ago)

Answers:

1. 120 m (see my previous post)
2. rises (1 volume unit of alcohol displaces 0.8 volume water, if alcohol and water wouldn't dissolve, this would mean a rise of 0.2 volume units, the solubility doesn't increase density enough to change this)
3. no difference (no acceleration, so no difference in force with standing still, measured over a few steps)

Edited by Annom (12/27/10 09:38 AM)

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OfflineBaby_Hitler
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Re: Dutch Science Quiz 2010 [Re: Annom]
    #13689538 - 12/27/10 04:59 AM (13 years, 3 months ago)

I don't even understand the answer to #2.


--------------------
"America: Fuck yeah!" -- Alexthegreat

“Nothing can now be believed which is seen in a newspaper. Truth itself becomes suspicious by being put into that polluted vehicle. The real extent of this state of misinformation is known only to those who are in situations to confront facts within their knowledge with the lies of the day.”  -- Thomas Jefferson

The greatest sin of mankind is ignorance.

The press takes [Trump] literally, but not seriously; his supporters take him seriously, but not literally. --Salena Zeto (9/23/16)

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OfflineAnnom
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Re: Dutch Science Quiz 2010 [Re: Baby_Hitler]
    #13700366 - 12/29/10 11:28 AM (13 years, 3 months ago)

You can assume the weight and volume of the boat to be zero. The weight/volume of the boat doesn't matter because the boat is in the container before and after emptying, displacing the same water.

So assume a very thin paper boat with alcohol. Alcohol has a lower density than water. The water displaced by the alcohol is thus less than volume of the alcohol; the alcohol level in the (massless) boat is above the waterline. If you empty the alcohol in the water, it will rise with the amount that was above the waterline in the boat, assuming alcohol and water do not dissolve.

You were right that the two mixed have a smaller volume (larger density) than separated, but this is not large enough to beat the effect of the density difference.

We (friend and I) won an archaeology trip to Egypt :smile:

Edited by Annom (12/29/10 11:32 AM)

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