Fermi Questions Marathon

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quizbowl
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Fermi Questions Marathon

Postby quizbowl » September 5th, 2011, 1:34 pm

Would anyone be up for a fermi questions marathon? Like the rocks and minerals and forestry marathons going on?
That sounds like a great idea, as long as you explain your thought process.
Until this gets moved to the Study Events forum, this can stay here. Remember to be specific in the units you use, and try to show all work (or at least how you got to the answer). Remember: no calculators or use of internet!

Here's a good start:

If all of the water in your body turned into pure energy, how many miles could you drive if all of the energy converted could be used to power the average electric car?
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Re: Fermi Questions Marathon

Postby Schrodingerscat » September 5th, 2011, 1:53 pm

we will start with a 70kg human, containing approximately 70% water, so a rough estimate will be 5E1 kg of water.
E=MC^2 or E=5E1*9E16
E=4E18 Joules
I am not quite sure how much energy is in a gallon of gasoline, but I will go with about E15, giving 4E3 gallons of gasoline.
I am also not precisely sure about a modern electric car, but I predict its somewhere between 5E1-and 1E2 mpg, would give between 2E5-4E5 miles.
Therefore, my estimate is E5 miles.

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Re: Fermi Questions Marathon

Postby quizbowl » September 5th, 2011, 1:58 pm

we will start with a 70kg human, containing approximately 70% water, so a rough estimate will be 5E1 kg of water.
E=MC^2 or E=5E1*9E16
E=4E18 Joules
I am not quite sure how much energy is in a gallon of gasoline, but I will go with about E15, giving 4E3 gallons of gasoline.
I am also not precisely sure about a modern electric car, but I predict its somewhere between 5E1-and 1E2 mpg, would give between 2E5-4E5 miles.
Therefore, my estimate is E5 miles.
You calculated the number of joules correctly, but you overestimated the amount of energy in a gallon of gasoline - it's usually about 1E8 joules/gallon.
2010: 5th in NYS
2011: 4th in NYS
2012: 3rd in NYS
<quizbowl> ey kid ya want some shortbread
<EASTstroudsburg13> I don't know why, but I just can't bring myself to delete this post.

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Re: Fermi Questions Marathon

Postby Schrodingerscat » September 5th, 2011, 2:06 pm

Then I would change my estimate to E12 miles. How does this one work, my turn to post one?

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Re: Fermi Questions Marathon

Postby harryk » September 5th, 2011, 2:16 pm

Then I would change my estimate to E12 miles. How does this one work, my turn to post one?
I think so
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Re: Fermi Questions Marathon

Postby Schrodingerscat » September 5th, 2011, 2:31 pm

How many years does it take for 0.3 micrograms of Americium-241 to decay into a single atom?

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Re: Fermi Questions Marathon

Postby hmcginny » September 5th, 2011, 2:47 pm

so .3 micrograms is 3E-7 grams, and if its americium-241 then you have around 1E-9 moles of it, which would then be 1E14 atoms. half life decay of americium is... no idea, lets call it E2 years though. and then it has to go through a ton of half-life periods, 2^50 is close to E14 i think, so lets say 50ish half-lifes. so E4 as a final answer, with E2 years per half life and +E2 half lifes so E4. hope that makes some sense.

and my question is:

How many droplets of water are there in all of the bodies of water in the world?
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Re: Fermi Questions Marathon

Postby harryk » September 5th, 2011, 3:10 pm

Surface area of a sphere is 4pir^2 and the radius of the earth is about 4000mi so that's about 250000000cm
e1*+e9 =+e10 sq cm
And the earths surface is roughly 2/3 water so
+e-1*+e10 = e10
I'm gonna make a guess and say that the average depth is 3mi so that's about 480000cm so
-e6*e10 = -e16

Going with the elementary school approximation that one drop equals one mL, my answer will be e16

Q: How many jelly beans could you fit into a typical school bus?
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Re: Fermi Questions Marathon

Postby Schrodingerscat » September 5th, 2011, 3:42 pm

May be significantly off, but I am guessing about 5x15x3m inside the school bus. that would be 225 cubic meters.

A jelly bean I would estimate is a fraction of a sphere with a diameter of 1 cm. so E-2^3=E-6 and will reduce to E-7 for some uncertainty.

2E2/E-7=2E9
Therefore I will guess E9 jellybeans.

My question:
If every carbon atom in an apple were put in a straight line, how many times would they stretch from the Earth to the Moon?

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Re: Fermi Questions Marathon

Postby hmcginny » September 5th, 2011, 4:34 pm

harryk: the internet says there are 1E24 milliliters of water on the earth, and a drop of water is 1/20th of a milliliter. so its E25, but your thought process makes total sense.

schrodingerscat: so the apple question, lets say an apple weighs 100 grams, of that maybe 85% is water. lets say then there are 10 grams of sugars, which are each like 40% carbon by mass. thats 4 grams of carbon, or 1/3 mole of carbon or 1E23 atoms. diameter of an atom is like 3E-10 meters so 3E13 meters of atoms. distance from earth to moon is like E8 meters so E5. though that doesn't seem reasonably possible... but i guess so.
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