Fermi Questions C

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

More or less the average word per tweet plus the theoretical "hot" air coming out at which rate it would take to make about 1 ml or water to reach 100C.
A morbid question....
How many nuclear ICBMs would it take to "nuke" the entire world. (Assume you're using UGM-133A Trident II D-5 W88/Mk5 missiles and blasting every single square cm of the world )
Your 3 seems kinda low

Uh my solution to the cofveve assuming the same thing and water at room temp. Takes around 2.5E3 joules of energy for water to reach 100 degrees C and boil. One breathe is 500 ml, you can say cofveve around 10 times before breathing again so 50 ml. 50 ml weighs around 5E-5 kg. Specific heat of air is around 1 kj/kg (?) So 5E-2 joules in a cofveve. 2.5E3/5E-2 is 5E4. I'll round up because assuming normal breathing you probably would say cofveve less times so 5?

When doing Fermi questions here it'll be nice if you can explain the step by step process of how to obtain your answer so others can understand. Just saying a answer doesn't really do anything.
There's about E8km of land on earth. I'll assume that's a nuke and could probably destroy a  city which is E2 km of land so assuming ideal land destruction 6
so from some quick googling/Wikipedia I can't find the power of the wepon you specified so I'll assume a 1 megaton of tnt. That destroys 100 square miles not km. The surface area of land is around 1.5E8/256 is about 6E5 or 6
If you assumed 6E5 1 megaton wepons are used to destroy the world, assuming perfect energy conversation, what is the volume of a object that can be converted by fission into the amount of energy to destroy the world assuming a density of earth in cubic meters.
Last edited by Name on May 29th, 2018, 7:29 pm, edited 1 time in total.
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Name
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Re: Fermi Questions C

Oops thought I was editing. Please delete. Sorry.
South Woods MS/Syosset HS
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"The more cheese, the more holes. The more holes the less cheese. Therefore the more cheese, the less cheese."

PM2017
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Re: Fermi Questions C

If you assumed 6E5 1 megaton wepons are used to destroy the world, assuming perfect energy conversation, what is the volume of a object that can be converted by fission into the amount of energy to destroy the world assuming a density of earth in cubic meters.
Well, fission has a mass to energy efficiency of about 0.03%, so it takes about 3000 times as much mass (and therefore volume) than would be necessary. I'll come back to this fact later. 1 ton of tnt is 4e9 joules, one megaton would be 4e15, and times 6e5 would be 24e20, or 2.4e21 J. m = 3/c^2 ---> m = 2.4e21/(9e16). M ~2e4 kg. On my cheatsheet I had the density of the earth, which I remember was about e3.5 kg/m^3 (so 5500 kg/m^3). V, therefore is m/d = 20000/5500 which is about 4 (non fermi meters cubed). Now, times the 3000 from earlier, gives 12000, or fermi answer of [b]5.[/b]
I'll edit with the real solution later, when I have time.

Question: If, in a distant galaxy, there is a direct linear correlation between number of humanoids and surface area of the inhabited planet, and the Earth just so happens to fit the model perfectly, what is the gravitational force between a planet with 10 trillion humanoids, and a humanoid on the surafce of the planet, that has a mass of 100 kg? Give your answer in newtons. Assume all habitable planets have the same density as the earth.
Last edited by PM2017 on May 30th, 2018, 11:41 am, edited 1 time in total.
West High '19
UC Berkeley '23

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Name
Member Posts: 299
Joined: January 21st, 2018, 4:41 pm
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State: NY
Location: Syosset

Re: Fermi Questions C

If you assumed 6E5 1 megaton wepons are used to destroy the world, assuming perfect energy conversation, what is the volume of a object that can be converted by fission into the amount of energy to destroy the world assuming a density of earth in cubic meters.
Well, fission has a mass to energy efficiency of about 0.03%, so it takes about 3000 times as much mass (and therefore volume) than would be necessary. I'll come back to this fact later. 1 ton of tnt is 4e9 joules, one megaton would be 4e15, and times 6e5 would be 24e20, or 2.4e21 J. m = 3/c^2 ---> m = 2.4e21/(9e16). M ~2e4 kg. On my cheatsheet I had the density of the earth, which I remember was about e3.5 kg/m^3 (so 5500 kg/m^3). V, therefore is m/d = 20000/5500 which is about 4 (non fermi meters cubed). Now, times the 3000 from earlier, gives 12000, or fermi answer of [b]5.[/b]
I'll edit with the real solution later, when I have time.
12000 is 4? Also I said assuming perfect energy conversation so no need to multiply by 3000, and the answer would be 0. I'll do the question later when I have time/or if someone else does it before me

Edit: in your question what's the distance between the planets?
South Woods MS/Syosset HS
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Events!: Astro, Code, hopefully Fossils

"The more cheese, the more holes. The more holes the less cheese. Therefore the more cheese, the less cheese."

PM2017
Member Posts: 491
Joined: January 20th, 2017, 5:02 pm
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Re: Fermi Questions C

If you assumed 6E5 1 megaton wepons are used to destroy the world, assuming perfect energy conversation, what is the volume of a object that can be converted by fission into the amount of energy to destroy the world assuming a density of earth in cubic meters.
Well, fission has a mass to energy efficiency of about 0.03%, so it takes about 3000 times as much mass (and therefore volume) than would be necessary. I'll come back to this fact later. 1 ton of tnt is 4e9 joules, one megaton would be 4e15, and times 6e5 would be 24e20, or 2.4e21 J. m = 3/c^2 ---> m = 2.4e21/(9e16). M ~2e4 kg. On my cheatsheet I had the density of the earth, which I remember was about e3.5 kg/m^3 (so 5500 kg/m^3). V, therefore is m/d = 20000/5500 which is about 4 (non fermi meters cubed). Now, times the 3000 from earlier, gives 12000, or fermi answer of [b]5.[/b]
I'll edit with the real solution later, when I have time.
12000 is 4? Also I said assuming perfect energy conversation so no need to multiply by 3000, and the answer would be 0. I'll do the question later when I have time/or if someone else does it before me

Edit: in your question what's the distance between the planets?
right, I mistyped that.

also, if you re-read the question, its the force of gravitational between a humanoid (100kg) on the surface of the planet and the planet itself.
West High '19
UC Berkeley '23

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whythelongface
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Re: Fermi Questions C

A Trident D5 has a significantly larger yield than one megaton TNT equivalent. If I remember properly, it should be able to destroy land on the scale of E4 square kilometers
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Re: Fermi Questions C

Question: If, in a distant galaxy, there is a direct linear correlation between number of humanoids and surface area of the inhabited planet, and the Earth just so happens to fit the model perfectly, what is the gravitational force between a planet with 10 trillion humanoids, and a humanoid on the surafce of the planet, that has a mass of 100 kg? Give your answer in newtons. Assume all habitable planets have the same density as the earth.
Gravitational acceleration is 9.8 m/s^2 or around 1E1. There are around 8 billion people on Earth. 10 trillion / 8 billion is around 1E3 (if we're using the short system for trillion). Ratio of surface areas is around 1E3. Ratio of radii is around 3E1. Ratio of volumes is around 27E3 or 3E4. Ratio of masses is then around 3E4. 1E1*100*3E4/3E1=1E6. Fermi answer: 6.

Edit: Need to divide by 3E1 again. Fermi answer: 4
9.8 m/s^2 * sqrt(10 trillion humanoids/7.442 billion humanoids) * 100 kg = 3.6E4.
How many drops of 0.1 M HCl would it take to turn Lake Victoria to a pH of 3?
Last edited by UTF-8 U+6211 U+662F on July 2nd, 2018, 7:32 pm, edited 3 times in total.

Name
Member Posts: 299
Joined: January 21st, 2018, 4:41 pm
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Location: Syosset

Re: Fermi Questions C

Gravitational acceleration is 9.8 m/s^2 or around 1E1. There are around 8 billion people on Earth. 10 trillion / 8 billion is around 1E3 (if we're using the short system for trillion). Ratio of surface areas is around 1E3. Ratio of radii is around 3E1. Ratio of volumes is around 27E3 or 3E4. Ratio of masses is then around 3E4. 1E1*100*3E4/3E1=1E6. Fermi answer: 6.
Radius is squared so 1E6 is divided by 3E1 again so final answer I think is 3E4 or 4
South Woods MS/Syosset HS
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UTF-8 U+6211 U+662F
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Re: Fermi Questions C

Gravitational acceleration is 9.8 m/s^2 or around 1E1. There are around 8 billion people on Earth. 10 trillion / 8 billion is around 1E3 (if we're using the short system for trillion). Ratio of surface areas is around 1E3. Ratio of radii is around 3E1. Ratio of volumes is around 27E3 or 3E4. Ratio of masses is then around 3E4. 1E1*100*3E4/3E1=1E6. Fermi answer: 6.
Radius is squared so 1E6 is divided by 3E1 again so final answer I think is 3E4 or 4
Oh yeah, my bad (this does not bode well for my upcoming physics exam)

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Re: Fermi Questions C

How many drops of 0.1 M HCl would it take to turn Lake Victoria to a pH of 3?
Just reminding everyone this is here.