Fermi Questions C

Test your knowledge of various Science Olympiad events.
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Re: Fermi Questions C

Postby Unome » May 22nd, 2017, 4:54 am

Restarting this in preparation for Fermi I'm return next year.
* Iridium being a metal, it's probably a bit large, let's say 100 picometers (estimating from what I know of microbiology)
* Equals around E-10 meters
*  No idea how much a chain is, I'll take it as a bit longer and multiply by E-1
* Final answer: -11
Wow
Turns out a chain is 20.1168 meters (exactly 22 yards), and an Iridium atom has a Van der Waals radius of 200 pm. Although my estimates for the two values were off, the difference s were nearly identical and cancel out perfectly.
True Answer: -11
Starting with a semi-introductory level question: How many steps could an average person walk in 100 days, assuming no rest and a constant brisk pace?
What's hiding lol
Assuming the "walking pace" is andante or 60 BPM (Haha @Bernard), then a person walks 60 paces in a minute, 3600 in an hour, and 86400 in a day or approx 10^6-. 100 days is 10^2 which then yields 10^8- but rounds to 8
* Final answer: 8
Hoooo
As the average walking pace is 3.1 MPH, and the average stride length between man and woman averaged is approx 28 inches, that averages to around 7015 steps per hour, which multiplied by 24 (to days), 100 (for 100 days) to finally yield 16835657 which is 1.7*10^7

DANG IT haha maybe my approximation was incorrect so sadly I was quite close :(((
True Answer: -7
You didn't post a question ;)
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Re: Fermi Questions C

Postby talkingturtle101 » May 22nd, 2017, 10:58 am

Since no one else seems to actually want to post a question, I got one.
How many people laid end to end would it take to create a line between the Sun and Pluto? Assume there are no obstacles in the way.
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Re: Fermi Questions C

Postby Unome » May 22nd, 2017, 2:13 pm

- Guesstimating orbital distance of 80 AU
- Which is ~E10 km (guesstimated 1.3E8 km per AU)
- So E11 meters
- With a person height of 2 meters, that's 0.5E10
- Knowing that my E11 meters is probably a little high, I round up to E11 people
Fermi Answer: 11
Pluto's semi-major axis with respect to the sun is 39.48 AU (this equals the distance for reasons that exist but which I never figured out). Average human height appears to be around 1.73 meters (it's very hard to get a good number on this). This comes out at 3.4E12 people.
True Answer: 12
How many times would a minivan have to travel between Atlanta and Cincinnati in order to spend as much money on gas as Donald Trump's current net worth? Assume gas is refilled at each end.
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Re: Fermi Questions C

Postby talkingturtle101 » May 23rd, 2017, 8:40 am

- Donald Trump is probably worth $5 billion
- The distance from Cincinnati to Atlanta is around 500 km
- A good car could get 30 mpg, or around 12 kilometers per liter
- Gas is around $2.25 per gallon, but let's say $2 for simplicity. This is around $0.50 per liter.
- We don't have to worry about refueling along the way if I read the question right.
- A kilometer's worth of gas is worth $0.50/12, or $0.04-ish, multiplied by 500 km is $20.
- $5 billion divided by $20 is 250 million trips
- Fermi Answer: 8
- Forbes estimates Trump is worth $3.5 billion as of this February
- It's 742 km from Cincinnati to Atlanta.
- A Honda Odyssey can get 27 mpg on a highway, or 11.48 kmpL.
- AAA says the average gas price is $2.36, or $0.62 per liter.
- This is $0.05 per kilometer, or $38.60 for the whole trip.
- $3.5 billion divided by this is 90,661,976 trips.
- So the actual Fermi Answer is 8.
Next Question: How many pencils would it take to fill a classroom completely?
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Re: Fermi Questions C

Postby Unome » May 23rd, 2017, 10:46 am

- Classroom size is around E3 square feet, multiply that by around 10 ft high to get E4 cubic feet.
- Pencil size is around 1/2 inch by 1/2 inch by 1 foot long, 4 pencils per ft * in^2
- E4 ft^3 = 1.4E6 ft * in^2
- Multipyling that gives E7
Fermi Answer: 7
- A more logical size for a classroom in a typical US high school would be around 700 square feet, according to what information I can find.
- 10 feet appears to be a good standard classroom height, so the total classroom is 7000 cubic feet = 198217926144 cubic millimeters
- Standard pencil size appears to be ~62 mm^2 (calculated from a 6 mm diameter)
- 190 mm length, 11780 cubic millimeters
- Divide to get 1.68E7
True Answer: 7
How close would a supernova have to be to be as bright as the sun?
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Re: Fermi Questions C

Postby appleshake123 » May 23rd, 2017, 12:21 pm

The brightness of a supernova is probably on a magnitude of e6 of the sun or so. Then inverse square law:  L/d^2 = Ls/ds^2; e6 Ls  /d^2 = Ls/1 au; d = e3 au. Fermi answer: 3
Hyperphysics says supernovas can be e10 times brighter than the sun, so my approximation was pretty off. I think the rest of the steps were right, so real fermi answer: 5.
My Ramen cup noodles is in need of some food colouring. How many pens do I need to make some blue/black ink ramen soup?
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Re: Fermi Questions C

Postby Unome » May 23rd, 2017, 1:20 pm

- Guesstimating a concentration of E-5 is sufficient for coloration
- E-1 pens should do it, based on the size of a cup of ramen. This is basically just guessing here.
Fermi Answer: -1
Literally I cannot find anything on the subject of how much ink is needed for it to be visible in water. If anyone knows anything abut this that would be great.
How many times have Science Olympiad competitors built models for Write It Do It while at tournaments in the last ten years?
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Re: Fermi Questions C

Postby Raleway » May 23rd, 2017, 4:14 pm

- Guesstimating a concentration of E-5 is sufficient for coloration
- E-1 pens should do it, based on the size of a cup of ramen. This is basically just guessing here.
Fermi Answer: -1
Literally I cannot find anything on the subject of how much ink is needed for it to be visible in water. If anyone knows anything abut this that would be great.
How many times have Science Olympiad competitors built models for Write It Do It while at tournaments in the last ten years?
I think blue wavelength is approx 475 NM? Might be wrong. I would guess each drop is approx 0.05 mL (I learned this from my dad, a PhD in chemistry so I guess it's right), and if the ramen cup is around 10 CM across, could you try using beer's law??? I don't think that'd be a good approach... Black is a bad color to use because true black is defined as reflecting back absolutely no light. Still clueless :)))

And I would guess approximately 250 regional tournaments, 50 state, and 1 national tournament per year. Knowing the total number of teams in the nation is around 7000 and hopefully it averages out to that for 10 years, and adding on about 50 invitationals (from test bank knowledge from each invitational), that adds up to 351 tournaments a year, or 3000 over ten (estimating drop off from the earlier years). Multiplying by 7000 teams and assuming no DQ teams, then approximately 21000000 builds have been done, or 2.1 * 10^7. Final answer: 7

My question (see I'll post one!): How long would all the music stands in the US be if they were lined up end to end?
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Re: Fermi Questions C

Postby talkingturtle101 » May 23rd, 2017, 6:07 pm

- So say 50 million people in the U.S. can play an instrument (it's probably a lot lower than this).
- Out of those, maybe 5 million own a stand.
- A stand, when fully extended, is about 1.5 meters tall.
- This is 7.5 million meters of stand.
- However, 25 million people probably also use a stand at school or private lessons or someplace.
- This is 37.5 million meters of stand.
- The real number is probably a lot higher than this, but Fermi Answer of 7.
- I can't find any information about how many people own music stands, or how many there are. If someone could please help that would be great.
How many microwaves would you have to run at the same time to make their combined energy use equal to the amount of energy the Sun outputs every second?
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Re: Fermi Questions C

Postby Adi1008 » May 23rd, 2017, 7:32 pm

- So say 50 million people in the U.S. can play an instrument (it's probably a lot lower than this).
- Out of those, maybe 5 million own a stand.
- A stand, when fully extended, is about 1.5 meters tall.
- This is 7.5 million meters of stand.
- However, 25 million people probably also use a stand at school or private lessons or someplace.
- This is 37.5 million meters of stand.
- The real number is probably a lot higher than this, but Fermi Answer of 7.
- I can't find any information about how many people own music stands, or how many there are. If someone could please help that would be great.
How many microwaves would you have to run at the same time to make their combined energy use equal to the amount of energy the Sun outputs every second?
From an OWL question, I remember a 600W microwave. Exponent is 3.
From astronomy, I know that the luminosity of the sun is 3.846E26 W. Exponent is 26.
Dividing gives a Fermi Answer of 23
Google searches give about 1000W for a microwave. The luminosity of the sun is as was stated previously, 3.846E26 W. The actual answer would be 23 (I think)
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