How fast, in decimeters per hour squared, would a 2017 Volkswagen Beetle, which is currently orbiting the Earth at 700 km altitude, have to be accelerating in order to use as much power as the sun emits?

Re: Fermi Questions C

Posted: September 7th, 2017, 5:02 pm

by WhatScience?

People are actually expected to figure this stuff out....

Re: Fermi Questions C

Posted: September 7th, 2017, 8:38 pm

by whythelongface

People are actually expected to figure this stuff out....

From what I can tell, this is definitely from the more difficult end. Easier ones involve much simpler premises and conditions, i.e. what is the distance, in megaparsecs, that a snail travels in the amount of time it takes Pluto to make a full revolution around the sun or something like that.

Re: Fermi Questions C

Posted: September 7th, 2017, 9:35 pm

by jkang

And we return!

How fast, in decimeters per hour squared, would a 2017 Volkswagen Beetle, which is currently orbiting the Earth at 700 km altitude, have to be accelerating in order to use as much power as the sun emits?

20?
We can say P*t = 1/2m*v^2.
Solving for v, v = sqrt(2P*t/m)
Differentiating wrt t, a = sqrt(P/2mt)
The luminosity of the sun is ~10^26 Watts, and I'd imagine a smaller car like the beetle would weigh a ton, or about 900 kg. Assuming we're trying to get the power output of the beetle to match that of the Sun, we set t = 1 second and find:
sqrt((10^26 kg*m^2/s^3)/(2*900 kg*1 s) ~ sqrt((10^26 kg*m^2/s^3)/(2*10^3 kg*s) ~ sqrt(10^22) ~ 11 m/s^2.
There's 10 meters in a decimeter and 3600 seconds in an hour, so 1 m/s^2 ~ 1e8 dm/s^2.
11 + 8 = 19, and counting all the rounding and numbers I've dropped, the answer might be closer to 20 so I'll go with that. That said, I'd imagine the car would explode long before it got anywhere near this level of acceleration. Also in this analysis I'm basically ignoring the altitude since that's basically the exosphere and unless you wanted me to talk about the car gaining even more potential energy from it falling back down or possibly decreased efficiency in the engine, but that's wayyy too much work beyond the simple algebra I'm willing to do

Re: Fermi Questions C

Posted: September 8th, 2017, 1:01 pm

by NeilMehta

People are actually expected to figure this stuff out....

From what I can tell, this is definitely from the more difficult end. Easier ones involve much simpler premises and conditions, i.e. what is the distance, in megaparsecs, that a snail travels in the amount of time it takes Pluto to make a full revolution around the sun or something like that.

Unome has high standards

Also, new question:
How many copies of Campbell's Biology would it take to cover the state of Texas?

Re: Fermi Questions C

Posted: September 8th, 2017, 4:28 pm

by whythelongface

People are actually expected to figure this stuff out....

From what I can tell, this is definitely from the more difficult end. Easier ones involve much simpler premises and conditions, i.e. what is the distance, in megaparsecs, that a snail travels in the amount of time it takes Pluto to make a full revolution around the sun or something like that.

Unome has high standards

Also, new question:
How many copies of Campbell's Biology would it take to cover the state of Texas?

Let me take a stab:

Campbell's Biology is slightly larger than an 8.5" x 11" sheet of paper, yielding an area of maybe about 5.5E2cm^2.
Assuming the state of Texas is the area of half a square 1000km wide, that's 5E5km^2 or 5E15cm^2.
Dividing, we get a Fermi answer of [b]13[/b].
Google gives me 1.024E13, so it looks like I was correct.

New question:
What is the mass, in kilograms, of a stack of quarters stretching from the sun to the center of the Andromeda galaxy?

Re: Fermi Questions C

Posted: September 8th, 2017, 7:05 pm

by Raleway

C'mon (Fox reference from SSBM weeb I know clarification)
Distance is approx let's say 10^25 m (Adi don't kill me I don't know Astro at all). Each quarter is let's say 1 mm thick, and approximately 6 grams. That's 10^28 quarters times 6 would round it up to 29 as a fermi answer.

Final answer: 29

I'm bad at math let's not try this again

Re: Fermi Questions C

Posted: September 8th, 2017, 7:05 pm

by NeilMehta

From what I can tell, this is definitely from the more difficult end. Easier ones involve much simpler premises and conditions, i.e. what is the distance, in megaparsecs, that a snail travels in the amount of time it takes Pluto to make a full revolution around the sun or something like that.

Unome has high standards

Also, new question:
How many copies of Campbell's Biology would it take to cover the state of Texas?

Let me take a stab:

Campbell's Biology is slightly larger than an 8.5" x 11" sheet of paper, yielding an area of maybe about 5.5E2cm^2.
Assuming the state of Texas is the area of half a square 1000km wide, that's 5E5km^2 or 5E15cm^2.
Dividing, we get a Fermi answer of [b]13[/b].
Google gives me 1.024E13, so it looks like I was correct.

New question:
What is the mass, in kilograms, of a stack of quarters stretching from the sun to the center of the Andromeda galaxy?

I thankfully remember that Andromeda is about 10 million light years away (E7)
I also remember that a light year is E13 km
Quarter in width is just about 1mm, so E6 quarters to make a km and each quarter is E1 grams
Altogether that makes E26

Apparently Andromeda is actually E6 away but quarters are actually E2 grams so they cancel out

New question:
How many paper airplanes woudm it take to equal the mass of one airplane? (use Boeing 777 as an example)

EDIT: raleway posted before me but didn't put a solution or anything so I'll leave my post here for solution plus next question
EDIT 2: spelling

Re: Fermi Questions C

Posted: September 8th, 2017, 7:12 pm

by Raleway

For Neil (Lemme not fail again at units)

Assume one plane is like 1 million pounds. I read on a study of paper that 100 sheets of standard A4 paper weigh exactly 1 pound... so the fermi answer would be 8?

Final Answer: 8

Re: Fermi Questions C

Posted: September 8th, 2017, 7:17 pm

by Raleway

How many times would a violet light (assume perfect light) wrap around the universe if it traveled for Googleplex to the Googleplex lunar months?