Fermi Questions C

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

Postby Torterra » Mon Sep 11, 2017 7:33 pm

If she sells all the seashells on all the seashores on earth, how much money will she make?

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whythelongface
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Re: Fermi Questions C

Postby whythelongface » Mon Sep 11, 2017 8:24 pm

Torterra wrote:If she sells all the seashells on all the seashores on earth, how much money will she make?


Depends on what you define as the seashore, as well as what you define as a "shell". Do fragments count? What about the shells of sea urchins, crabs, horseshoe crabs, etc? And how about the shore? Does the intertidal zone count? What about the littoral zone? Also, many shores have layers of sediment stacked on top of each other. How deep can you go and still call it the shore? Depending on your answers, you could be many magnitudes, perhaps even as far off as five magnitudes, off.
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Re: Fermi Questions C

Postby Torterra » Mon Sep 11, 2017 8:50 pm

Sorry, should have clarified. Only shells that are intact and on the surface to an inch deep. Any kind of shell though

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Re: Fermi Questions C

Postby whythelongface » Tue Sep 12, 2017 1:33 am

Business calculations
Assume E4 intact shells of any kind along any stretch of coastline 1m long and 1 inch deep. That makes E7 shells along a 1 km coast. Assume E6 km of oceanic coastline, to get E13 shells.

Shells vary in rarity, going from bare cents to thousands of dollars. Estimate average cost of shell to be around ten cents, or E-1 dollars. Multiplying, we get E12 dollars. She is the world's first trillionaire.

Absolutely sure I got some approximation completely wrong, if not all of them.

Have you, perchance, heard of Sanibel Island, Florida?


If a 6-pack of Monster got converted into pure energy based on its caloric content, how long could it keep a 60-watt lightbulb on for?
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Re: Fermi Questions C

Postby jkang » Tue Sep 12, 2017 4:04 am

whythelongface wrote:If a 6-pack of Monster got converted into pure energy based on its caloric content, how long could it keep a 60-watt lightbulb on for?

Answer
5
~200 Calories in monster (16 oz). 1 Calorie is ~4200 joules, 840000 joules per can, 60 W/6 pack -> ~ 84000 seconds. Putting it in fermi, 5.

If we took all the energy used by phones in the world in a day, how long could we produce the same power as the Sun (seconds)?
Last edited by jkang on Tue Sep 12, 2017 6:26 pm, edited 1 time in total.
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Re: Fermi Questions C

Postby ScottMaurer19 » Tue Sep 12, 2017 11:41 am

whythelongface wrote:
Business calculations
Assume E4 intact shells of any kind along any stretch of coastline 1m long and 1 inch deep. That makes E7 shells along a 1 km coast. Assume E6 km of oceanic coastline, to get E13 shells.

Shells vary in rarity, going from bare cents to thousands of dollars. Estimate average cost of shell to be around ten cents, or E-1 dollars. Multiplying, we get E12 dollars. She is the world's first trillionaire.

Absolutely sure I got some approximation completely wrong, if not all of them.

Have you, perchance, heard of Sanibel Island, Florida?


If a 6-pack of Monster got converted into pure energy based on its caloric content, how long could it keep a 60-watt lightbulb on for?

Sanibel is a great place for finding sea shells by the seashore.
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Re: Fermi Questions C

Postby Raleway » Wed Sep 13, 2017 3:16 am

Guess I'll make another question...

What is the sum of all natural numbers (I'm just kidding- who needs zeta function regularization)

Taking the total amount of sugar the USA consumes in a year and converting it into energy, how far could a model TeslaX go?
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Re: Fermi Questions C

Postby Torterra » Wed Sep 13, 2017 7:24 pm

I'm still kinda new, any feedback would be appreciated.


An abomination called my work
Assume the average American consumes 50g of sugar a day and 40 grams of sugar has 100 calories, giving 1.2E2 calories per person per day. Multiply by 3E8 people in America and 365 days to get 1.3E13 calories in a year. Multiply by 4E3 to get 5E16 joules. Assume a Tesla Model X has 20% efficiency to get 1E16 joules of useable energy. W=F*d. Assume that the force is equal to a force of friction, which is mg*mu, which I assumed to be .01 and a mass of 2000kg, which gives 2E2N of force. Solving for distance gives us an answer of 15, in meters.

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Re: Fermi Questions C

Postby whythelongface » Wed Sep 13, 2017 9:57 pm

I'm new too, but here's one estimation that strikes me as maybe being a bit too small.

A single can of Coke has about 40 grams of sugar, and probably approaches 200 calories. I think that the average American consumes a lot more sugar than just 50 g a day.

Just some friendly feedback.
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Re: Fermi Questions C

Postby Torterra » Thu Sep 14, 2017 12:23 am

Ok, thanks. I just figured that not all the calories in a can of soda come directly from sugar, and also that people eat a healthy amount. I probably am a bit low though.


I'll ask another question.
If an army of 500 industrious beavers wanted to log the entire Amazon rainforest, how long would it take them in days?

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Re: Fermi Questions C

Postby whythelongface » Thu Sep 14, 2017 1:01 am

Answer
Assuming a single beaver doing nothing but logging can clear half of your typical rainforest tree, that's 250 trees a day. There are what, E9 trees in the Amazon?E9/E2 = E7 days.

Edit: There are 7E12 trees in the amazon, so the answer would be E9, maybe?


If I funneled the world's oceans into a cylindrical column of radius 1 meter, what would be the pressure at the bottom, in atmospheres?
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Re: Fermi Questions C

Postby Torterra » Thu Sep 14, 2017 2:42 am

Answer
Radius of the earth is 6E6m. 4pir^2 gives a total surface area of 4.3E14. Assuming the earth is 75% water gives 3.2E14 m^2 of water. Assuming an average depth of 10m gives a volume of 3.2E15 m^3. The volume of a cylinder is pir^2h. Solving this for h gives a height of 1.1E15m. Pressure is equal to density times heigh times g. This gives a pressure of 1.1E16 pa. There are 1E5 pa in one ATM, so the answer is 11

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Re: Fermi Questions C

Postby whythelongface » Thu Sep 14, 2017 3:10 am

Mind you, the average oceanic depth is a lot deeper than 10 m. Continental shelves alone are usually hundreds of meters deep, and the abyssal plains are usually many thousands of meters deep. For example: the Barents Sea, one of the shallower large expanses of water on the planet, is only about 100 meters deep, though it may reach 200 near the deeper parts. In contrast, Challenger Deep, off the Marianas Island Arc, is about 11 kilometers deep.
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Re: Fermi Questions C

Postby Torterra » Thu Sep 14, 2017 4:33 am

Yeah, that's a good point. I think that bumps my answer up by 2 then.

How fast would Santa have to travel to visit every child in the world in one 24-hour period?

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Re: Fermi Questions C

Postby NeilMehta » Thu Sep 14, 2017 3:24 pm

Torterra wrote:Yeah, that's a good point. I think that bumps my answer up by 2 then.

How fast would Santa have to travel to visit every child in the world in one 24-hour period?

attempt
assuming there are E9 children in the world, and children refers to anyone under 18, including teens
24 hours = 1440 min = 86400 seconds = E5 seconds
if he had to visit every single child, he would have E-4 seconds per child
making a blind guess on population density, he would have to travel about E6 meters per second
Final answer: E6 m/s


New question: what is price of every single item in the displays at the NYC Apple Store converted to japanese yen?
Last edited by NeilMehta on Thu Sep 14, 2017 10:09 pm, edited 1 time in total.
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