## Fermi Questions C

Test your knowledge of various Science Olympiad events.
Unome
Moderator
Posts: 4037
Joined: January 26th, 2014, 12:48 pm
State: GA
Location: somewhere in the sciolyverse

### Re: Fermi Questions C

Tom_MS wrote:According to the shell theorem (essentially Gauss's law), the only mass that matters should be within a spherical shell at the radius being considered.

Vector calculus being useful XD
Userpage
Chattahoochee High School Class of 2018
Georgia Tech Class of 2022

Opinions expressed on this site are not official; the only place for official rules changes and FAQs is soinc.org.

Name
Member
Posts: 275
Joined: January 21st, 2018, 4:41 pm
Division: C
State: NY
Location: Syosset

### Re: Fermi Questions C

Tom_MS wrote:
Name wrote:Wait a screwed up the question. It is E0 but I should've said something like 3000 where the new mass is around E22 and radius is 1000 where the gravitational force is E1 stronger while on the surface

I feel like this is being overthought. According to the shell theorem (essentially Gauss's law), the only mass that matters should be within a spherical shell at the radius being considered. If you do the math, this gives a linearly decreasing force for a linearly decreasing radius. Thus, just taking the ratio of 5/6 (5000 km compared to around 6000 km) gives you fermi 0.

Wait hmm I checked the math and this seems correct. I probably screwed up something while doing the math earlier. The mass is porportional to volume which is radius cubed and is divided by radius squared so the force is linearly decreasing.
South Woods MS (5 medals)/Syosset HS (24 medals)
Favorite Past Events: Microbe, Invasive, Matsci, Fermi
Next Year: Astro, Code, hopefully Orni, and maybe Compound
2018-19 highlights

Tom_MS
Member
Posts: 41
Joined: April 28th, 2015, 11:08 am
State: PA

### Re: Fermi Questions C

PM2017 wrote:What is the 273rd Fibonacci number?
To clarify, 0 will be considered the first Fibonacci number.

Attempt

A proton and electron are initially separated by 1 meter. After being released, they end up colliding due to their coulombic attraction. If the final kinetic energy (right before collision) of the two particles is converted almost entirely into rest mass energy of the particles released, how much mass is formed (kg)?

PM2017
Member
Posts: 483
Joined: January 20th, 2017, 5:02 pm
State: CA

### Re: Fermi Questions C

Hmmm... I sort of made that question so the others would be able to learn the method of approximating fibbonacci numbers... (I'm pretty sure I know what you're doing, but I won't disclose it if you don't want it disclosed.)
2018 Events

2019 Events

--
West High '19
UC Berkeley '23

Name
Member
Posts: 275
Joined: January 21st, 2018, 4:41 pm
Division: C
State: NY
Location: Syosset

### Re: Fermi Questions C

PM2017 wrote:Hmmm... I sort of made that question so the others would be able to learn the method of approximating fibbonacci numbers... (I'm pretty sure I know what you're doing, but I won't disclose it if you don't want it disclosed.)

Uh it's pretty easy to just google
South Woods MS (5 medals)/Syosset HS (24 medals)
Favorite Past Events: Microbe, Invasive, Matsci, Fermi
Next Year: Astro, Code, hopefully Orni, and maybe Compound
2018-19 highlights

whythelongface
Exalted Member
Posts: 326
Joined: March 12th, 2017, 7:42 pm
State: NJ
Location: 705 kilometers overhead

### Re: Fermi Questions C

Name wrote:
PM2017 wrote:Hmmm... I sort of made that question so the others would be able to learn the method of approximating fibbonacci numbers... (I'm pretty sure I know what you're doing, but I won't disclose it if you don't want it disclosed.)

Uh it's pretty easy to just google

It's just Stirling's Approximation of Factorials. It's not exactly a trade secret.
WEST WINDSOR-PLAINSBORO HIGH SCHOOL SOUTH '18
EMORY UNIVERSITY '22
SONT 2017 5th Place Medalist [Microbe Mission]

"One little Sciolyer left all alone,
He went out and hanged himself and then there were none."

Congratulations to WW-P South for winning 14th place at Nationals!

PM2017
Member
Posts: 483
Joined: January 20th, 2017, 5:02 pm
State: CA

### Re: Fermi Questions C

whythelongface wrote:
Name wrote:
PM2017 wrote:Hmmm... I sort of made that question so the others would be able to learn the method of approximating fibbonacci numbers... (I'm pretty sure I know what you're doing, but I won't disclose it if you don't want it disclosed.)

Uh it's pretty easy to just google

It's just Stirling's Approximation of Factorials. It's not exactly a trade secret.

Wait I was thinking of something else... The limit of the ratio between one Fibonacci number and the next is the golden ratio, as you get larger and larger numbers. So you just do (Phi)^(273-1).
2018 Events

2019 Events

--
West High '19
UC Berkeley '23

Unome
Moderator
Posts: 4037
Joined: January 26th, 2014, 12:48 pm
State: GA
Location: somewhere in the sciolyverse

### Re: Fermi Questions C

PM2017 wrote:
whythelongface wrote:
Name wrote:
Uh it's pretty easy to just google

It's just Stirling's Approximation of Factorials. It's not exactly a trade secret.

Wait I was thinking of something else... The limit of the ratio between one Fibonacci number and the next is the golden ratio, as you get larger and larger numbers. So you just do (Phi)^(273-1).

This is how I would do it.
Userpage
Chattahoochee High School Class of 2018
Georgia Tech Class of 2022

Opinions expressed on this site are not official; the only place for official rules changes and FAQs is soinc.org.

whythelongface
Exalted Member
Posts: 326
Joined: March 12th, 2017, 7:42 pm
State: NJ
Location: 705 kilometers overhead

### Re: Fermi Questions C

Unome wrote:
PM2017 wrote:
whythelongface wrote:It's just Stirling's Approximation of Factorials. It's not exactly a trade secret.

Wait I was thinking of something else... The limit of the ratio between one Fibonacci number and the next is the golden ratio, as you get larger and larger numbers. So you just do (Phi)^(273-1).

This is how I would do it.

Oops I appear to have read "fibonacci" as "factorial"

Yes, this seems to be the ideal way of doing it.
WEST WINDSOR-PLAINSBORO HIGH SCHOOL SOUTH '18
EMORY UNIVERSITY '22
SONT 2017 5th Place Medalist [Microbe Mission]

"One little Sciolyer left all alone,
He went out and hanged himself and then there were none."

Congratulations to WW-P South for winning 14th place at Nationals!

Raleway
Exalted Member
Posts: 228
Joined: March 12th, 2017, 7:19 pm
Division: C
State: -

### Re: Fermi Questions C

Time to restart this thread for now... b/c it'll be relevant next year!

With the hot air coming out of Donald Trump's mouth when he says cofveve, how many times would he need to repeat it in order to boil water? Whoever actually solves this (not you whythelongface) correctly gets a cookie!
Last edited by Raleway on May 28th, 2018, 7:37 pm, edited 1 time in total.
Sleep is for the week; one only needs it once a week

God bless Len Joeris | Balsaman

whythelongface
Exalted Member
Posts: 326
Joined: March 12th, 2017, 7:42 pm
State: NJ
Location: 705 kilometers overhead

### Re: Fermi Questions C

Fermi Questions C is for Cookie and Cookie is for me!
WEST WINDSOR-PLAINSBORO HIGH SCHOOL SOUTH '18
EMORY UNIVERSITY '22
SONT 2017 5th Place Medalist [Microbe Mission]

"One little Sciolyer left all alone,
He went out and hanged himself and then there were none."

Congratulations to WW-P South for winning 14th place at Nationals!

NeilMehta
WikiMod
Posts: 318
Joined: August 27th, 2016, 5:27 am
Division: C
State: NY

### Re: Fermi Questions C

Raleway wrote:Time to restart this thread for now... b/c it'll be relevant next year!

With the hot air coming out of Donald Trump's mouth when he says cofveve, how many times would he need to repeat it in order to boil water? Whoever actually solves this (not you whythelongface) correctly gets a cookie!

You should prob specify the amount of water lol and also current temp
i can't feel my arms wtf i think i'm turning into a lamp

voted least likely to sleep 2018, most likely to sleep in class 2017+2018, biggest procrastinator 2018

TheChiScientist
Member
Posts: 649
Joined: March 11th, 2018, 11:25 am
State: IL
Location: Hiding from the college bounty hunters.

### Re: Fermi Questions C

NeilMehta wrote:
Raleway wrote:Time to restart this thread for now... b/c it'll be relevant next year!

With the hot air coming out of Donald Trump's mouth when he says cofveve, how many times would he need to repeat it in order to boil water? Whoever actually solves this (not you whythelongface) correctly gets a cookie!

You should prob specify the amount of water lol and also current temp

This is easy....
5x10^2 (He talks too much)
A Science Olympian from 2015 - 2019
Medal Count:30
Background In

School:Crystal Lake Central High School Wiki
Assassinator #119 and Co-Conspirator in #120
President of The Builder Cult. Builders rise up!

PM2017
Member
Posts: 483
Joined: January 20th, 2017, 5:02 pm
State: CA

### Re: Fermi Questions C

TheChiScientist wrote:
NeilMehta wrote:
Raleway wrote:Time to restart this thread for now... b/c it'll be relevant next year!

With the hot air coming out of Donald Trump's mouth when he says cofveve, how many times would he need to repeat it in order to boil water? Whoever actually solves this (not you whythelongface) correctly gets a cookie!

You should prob specify the amount of water lol and also current temp

This is easy....
5x10^2 (He talks too much)

What process did you use?
Also, next question, please.
2018 Events

2019 Events

--
West High '19
UC Berkeley '23

TheChiScientist
Member
Posts: 649
Joined: March 11th, 2018, 11:25 am
State: IL
Location: Hiding from the college bounty hunters.

### 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 )
A Science Olympian from 2015 - 2019
Medal Count:30
Background In

School:Crystal Lake Central High School Wiki
Assassinator #119 and Co-Conspirator in #120
President of The Builder Cult. Builders rise up!