Fermi Questions C

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Re: Fermi Questions C

Postby Unome » December 22nd, 2016, 7:13 pm

Assumption: the human body is mostly water (will round down the length slightly to account for the non-water parts containing heavier elements that aren't proportionally wider).
Approximate human mass of 7E4 grams.
If this is all water, that's about 5E3 moles of water, so about E28 atoms.
Since the average width is probably about 1 nanometer (estimated from DNA width) or E-9 meters, the total length of those atoms is about E19 meters (or E16 kilometers, since that's better for converting).
Convert to light years using 3E8 km per light year, and with the rounding for correction mentioned earlier, E11 light years.
The Milky Way is about E5 light years in radius, so E11 / E5 = E6
FA = 6
[url=http://www.madsci.org/posts/archives/2000-06/962225341.Bc.r.html]Elemental composition of the human body[/url]
Average human mass is 8E4 grams
Running the math, that's 3250 moles of oxygen, 1200 moles of carbon, 8000 moles of hydrogen, and 170 moles of nitrogen (just using those four because the rest are pretty tiny, not much change caused in the length)
Molecules: 1.95E27 oxygen, 7.2E26 carbon, 4.8E27 hydrogen, E26 nitrogen
Using their actual radii of 60, 70, 25, and 65 picometers respectively, 1.17E17 meters oxygen, 5.04E16 meters carbon, 1.2E17 meters hydrogen, 6.5E15 meters nitrogen.
Adding those up, that's a total length of around 5.84E17 meters, or 5.84E14 kilometers (looks like my correction factor wasn't large enough)
Convert to 6.2E4 light years
The most commonly cited estimate of the Milky Way's radius is 5E4 light years, so 1.24 Milky Way diameters, hence:
FA = 1 (wow I was off by a lot)
Over the course of one year, how many skin cells will be produced on a single adult human?

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Re: Fermi Questions C

Postby appleshake123 » December 23rd, 2016, 4:19 am

Assumption: the human body is mostly water (will round down the length slightly to account for the non-water parts containing heavier elements that aren't proportionally wider).
Approximate human mass of 7E4 grams.
If this is all water, that's about 5E3 moles of water, so about E28 atoms.
Since the average width is probably about 1 nanometer (estimated from DNA width) or E-9 meters, the total length of those atoms is about E19 meters (or E16 kilometers, since that's better for converting).
Convert to light years using 3E8 km per light year, and with the rounding for correction mentioned earlier, E11 light years.
The Milky Way is about E5 light years in radius, so E11 / E5 = E6
FA = 6
[url=http://www.madsci.org/posts/archives/2000-06/962225341.Bc.r.html]Elemental composition of the human body[/url]
Average human mass is 8E4 grams
Running the math, that's 3250 moles of oxygen, 1200 moles of carbon, 8000 moles of hydrogen, and 170 moles of nitrogen (just using those four because the rest are pretty tiny, not much change caused in the length)
Molecules: 1.95E27 oxygen, 7.2E26 carbon, 4.8E27 hydrogen, E26 nitrogen
Using their actual radii of 60, 70, 25, and 65 picometers respectively, 1.17E17 meters oxygen, 5.04E16 meters carbon, 1.2E17 meters hydrogen, 6.5E15 meters nitrogen.
Adding those up, that's a total length of around 5.84E17 meters, or 5.84E14 kilometers (looks like my correction factor wasn't large enough)
Convert to 6.2E4 light years
The most commonly cited estimate of the Milky Way's radius is 5E4 light years, so 1.24 Milky Way diameters, hence:
FA = 1 (wow I was off by a lot)
Over the course of one year, how many skin cells will be produced on a single adult human?
I read somewhere that thousands of skin cells die a second. So assuming that the cells get regenerated at a similar rate and that there are 86400s in a day, 365 days, so about e7s in a year, e7s*e3cell/s = E10 =  FA = 10
So according to[url=http://book.bionumbers.org/how-quickly-do-different-cells-in-the-body-replace-themselves/]this website[/url] skin cells replace themselves 10-30 days, or 12 - 36 times a year. There are 36 billion skin cells. so between 432 - 1296 billion a year or FA = 11 or 12
Since I'm unoriginal, what is 262! [EDIT: Brute force got it even if doubles arent large enough]

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Re: Fermi Questions C

Postby raxu » January 23rd, 2017, 2:30 pm

I read somewhere that thousands of skin cells die a second. So assuming that the cells get regenerated at a similar rate and that there are 86400s in a day, 365 days, so about e7s in a year, e7s*e3cell/s = E10 =  FA = 10
So according to[url=http://book.bionumbers.org/how-quickly-do-different-cells-in-the-body-replace-themselves/]this website[/url] skin cells replace themselves 10-30 days, or 12 - 36 times a year. There are 36 billion skin cells. so between 432 - 1296 billion a year or FA = 11 or 12
Since I'm unoriginal, what is 262! [EDIT: Brute force got it even if doubles arent large enough]
At this size we use stirling approximation. sqrt(2pi*262) is about E1, (262/e)^262 is about E524, so I'm going with 525.
Wolfram alpha gives E521.4. The problem is that 262<100e...
In chains (the Imperial Unit), how wide is an Iridium atom?
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Re: Fermi Questions C

Postby Unome » May 21st, 2017, 7:31 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?
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Re: Fermi Questions C

Postby Raleway » May 21st, 2017, 8:04 pm

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
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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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