Fermi Questions C

[Entomology]

Seeing as SoCal has replaced Game On with Fermi Questions, I thought I would open a thread to further study for this event. Can a mod make it a topic in the study event forum too or...?

Anyone with any advice? (I'm looking at you, samlan) I looked at the wiki page and this seems like a...mathematical event.

[[NerdyTotoro]]

Seeing as SoCal has replaced Game On with Fermi Questions, I thought I would open a thread to further study for this event. Can a mod make it a topic in the study event forum too or...?

Anyone with any advice? (I'm looking at you, samlan) I looked at the wiki page and this seems like a...mathematical event.

samlan16 is gone though?

[appleshake123]

For help, being knowledgeable on unit conversion and measurements of many things. Also, I was told when estimating, .5-5=10^0, 5-50=10^1 50-500 = 10^2 etc. "Fermi estimates generally work because the estimations of the individual terms are often close to correct, and overestimates and underestimates help cancel each other out."

From what I know of this event, it is quick estimation knowing many conversions and answering using the power of 10. An example from a test this year is, "How many unsharpened pencils would fit between the centre of the milky way and the Sun?" (Example answer: 10^1 = 1, 10^30= 30)

Here's the answer. The Fermi Answer[FA]= 21.
The milky way is about 30kpc wide, Sun is not on the centre, so the distance is probably around 12kpc so 1E4 pc.
A parsec is 3.26 light years(time light travels in a year) 3E0
A day is 86400, or abour 9e5 seconds, so a year is about 9e5*300 or 3E7 s
Light is 3*10^8 m/s or 3E8 m
So a light year is 9E15 meters, about E16
Let's say a pencil is 1/5 a metre, so 5 is E1
E4 pc* E0 ly/pc * E16 m/ly * e1 pencils/ m = E(4+0+16+1)= FA= 21
Actual answer from internet: Distance from milky way to sun is 8kpc which is 9.719e+21 inches. an unsharpened pencil is 7.5 inches, so there are about 1.3 e21 pencils from milky way to sun, so FA= 21 is correct. Another question! What is the surface area of water on earth in yellow school busses?

[jonboyage]

For help, being knowledgeable on unit conversion and measurements of many things. Also, I was told when estimating, .5-5=10^0, 5-50=10^1 50-500 = 10^2 etc. "Fermi estimates generally work because the estimations of the individual terms are often close to correct, and overestimates and underestimates help cancel each other out."

From what I know of this event, it is quick estimation knowing many conversions and answering using the power of 10. An example from a test this year is, "How many unsharpened pencils would fit between the centre of the milky way and the Sun?" (Example answer: 10^1 = 1, 10^30= 30)

Here's the answer. The Fermi Answer[FA]= 21.
The milky way is about 30kpc wide, Sun is not on the centre, so the distance is probably around 12kpc so 1E4 pc.
A parsec is 3.26 light years(time light travels in a year) 3E0
A day is 86400, or abour 9e5 seconds, so a year is about 9e5*300 or 3E7 s
Light is 3*10^8 m/s or 3E8 m
So a light year is 9E15 meters, about E16
Let's say a pencil is 1/5 a metre, so 5 is E1
E4 pc* E0 ly/pc * E16 m/ly * e1 pencils/ m = E(4+0+16+1)= FA= 21
Actual answer from internet: Distance from milky way to sun is 8kpc which is 9.719e+21 inches. an unsharpened pencil is 7.5 inches, so there are about 1.3 e21 pencils from milky way to sun, so FA= 21 is correct. Another question! What is the surface area of water on earth in yellow school busses?

When you say yellow school buses, are you referring to one side of a school bus, or the total surface area of a bus if you were to "unfold" it?

[Unome]

For help, being knowledgeable on unit conversion and measurements of many things. Also, I was told when estimating, .5-5=10^0, 5-50=10^1 50-500 = 10^2 etc. "Fermi estimates generally work because the estimations of the individual terms are often close to correct, and overestimates and underestimates help cancel each other out."

From what I know of this event, it is quick estimation knowing many conversions and answering using the power of 10. An example from a test this year is, "How many unsharpened pencils would fit between the centre of the milky way and the Sun?" (Example answer: 10^1 = 1, 10^30= 30)

Here's the answer. The Fermi Answer[FA]= 21.
The milky way is about 30kpc wide, Sun is not on the centre, so the distance is probably around 12kpc so 1E4 pc.
A parsec is 3.26 light years(time light travels in a year) 3E0
A day is 86400, or abour 9e5 seconds, so a year is about 9e5*300 or 3E7 s
Light is 3*10^8 m/s or 3E8 m
So a light year is 9E15 meters, about E16
Let's say a pencil is 1/5 a metre, so 5 is E1
E4 pc* E0 ly/pc * E16 m/ly * e1 pencils/ m = E(4+0+16+1)= FA= 21
Actual answer from internet: Distance from milky way to sun is 8kpc which is 9.719e+21 inches. an unsharpened pencil is 7.5 inches, so there are about 1.3 e21 pencils from milky way to sun, so FA= 21 is correct. Another question! What is the surface area of water on earth in yellow school busses?

Most likely you mean the top; either way, the difference is probably ~E0.5 or so, in which case the lower number is safer, since I don't know for sure.

Earth radius is around 6000 km
Surface area of earth is around 6000^3 times pi times 4/3 which is around E8
Times 70% which should about bring down the extra from 6^3
Convert to meters so E14
Top of a school bus is around 2 meters by 10 meters, so 2E1
E14/2E1
Fermi Answer = 13

Actual Answer from internet (Click to Show Hidden Text)

Water on earth's surface = 3.61 E14 square meters
Standard school bus = 2.59 meters wide, varies between 31 and 38 feet long; I used 35, so my surface area on the top is 2.769 E1 meters
Fermi Answer from internet = 13 (yay!)

Question: If you accelerated a bullet to 0.01% of the speed of light, how far would it penetrate into a solid wall of arbitrary thickness composed of Kevlar? (assuming that the wall is securely anchored).

[appleshake123]

Question: If you accelerated a bullet to 0.01% of the speed of light, how far would it penetrate into a solid wall of arbitrary thickness composed of Kevlar? (assuming that the wall is securely anchored).

I'm trying (Click to Show Hidden Text)

So I believe I saw somewhere that a bullet travels 1000 ft/s which is about 300 m/s. .01% of the speed of light is about 30000 m/s. I'm just going to assume penetration is linear with velocity, so it will penetrate 100x as far. If 1 cm kevlar can protect against a 300 m/s bullet, then I will say 100 cm, or  FA of 2. I probably used the wrong units though.

How many electrons are there in the universe?

[Unome]

Assuming you mean the observable universe, since the amount of matter in the universe is generally accepted to be infinite (Click to Show Hidden Text)

I think I read somewhere that there are E68 kg of matter in the observable universe (hopefully this is close :? ). I'm just going to assume it's all hydrogen, so E71 g of hydrogen is 6E23 * E71 = 6E94, so I'll go with:
FA=95

From the internet (Click to Show Hidden Text)

It's apparently E53 kg of matter in the observable universe, and the best real answer I can find for the number of electrons is
FA=80

If there was a planet with the same mass as Earth, with a diameter such that the Earth could be inscribed in a rectangular prism, which was itself inscribed in this hypothetical planet, what would be the density of this planet in kilograms per cubic meter?

[appleshake123]

Assuming you mean the observable universe, since the amount of matter in the universe is generally accepted to be infinite (Click to Show Hidden Text)

I think I read somewhere that there are E68 kg of matter in the observable universe (hopefully this is close :? ). I'm just going to assume it's all hydrogen, so E71 g of hydrogen is 6E23 * E71 = 6E94, so I'll go with:
FA=95

From the internet (Click to Show Hidden Text)

It's apparently E53 kg of matter in the observable universe, and the best real answer I can find for the number of electrons is
FA=80

If there was a planet with the same mass as Earth, with a diameter such that the Earth could be inscribed in a rectangular prism, which was itself inscribed in this hypothetical planet, what would be the density of this planet in kilograms per cubic meter?

Assuming the earth is a perfect sphere (Click to Show Hidden Text)

Earth has a radius of 6e6m or a diameter about e7m. If it is inscribed in a prism which is inscribed in another sphere. If I can geometry good, then the diameter of the new planet is sqrt(2)(or about 1.4)* D of earth which is still about e7m. The radius is half of that which still rounds to e7m. Then V = 4/3 * r^3= about e21m, maybe round down later. The density is mass of earth: 6e24/V = e4, round down  so Fa= 3

From the internet (Click to Show Hidden Text)

So I can't geometry, but it shouldn't change the answer too much. A sphere inscribed in a cube has a cube edge length of Diameter(D). A cube inscribed in a circle has a diameter of Dsqrt(3) and a radius of Rsqrt(3). The Earth's radius is 6e6, so the new radius is 1e7. MofEarth/V = Density. (5.97e24)/(4/3*((e7)^3) = 4477.5 or FA = 3.

Within the average high schooler's sleep during the school year, how many periods of radiation of a Cs-133 atom moving between two hyperfine level of the ground state occurs? I probably worded this poorly.

[Unome]

This is from atomic clocks right? (Click to Show Hidden Text)

Let's estimate 6 hours per day, so over ~270 days that's ~E3 hours which is ~E6 seconds. If I remember correctly, the period of transition is something like E-8, so E6 / E-8 = E14
FA=14

From the internet (Click to Show Hidden Text)

Average hours of sleep is 7-7.25 per day
The transition is actually E-10 (I had the right frequency, but I rounded the 9 in the wrong direction to get E-8)
So the answer comes out at 6.7E16 or:
FA=17

How many blades of grass are there over all land area on the Earth classified as grasslands? (idk I couldn't think of anything good)

[jonboyage]

My answer (Click to Show Hidden Text)

Lets assume in one square meter of grasslands there's about 10^3-10^4 blades of grass. I'm going to take a wild guess and say that there is 10^6 km^2 of grasslands on the earth. 10^4(blades/m^2)*10^6(m^2/km^2)*10^6(km^2) would give around 10^16 blades of grass on the Earth.

Internet (Click to Show Hidden Text)

10 blades of grass per square centimeter, 100.000 blades of grass per square meter, 100.000.000.000 blades of grass per square kilometer.
The total surface area of earth is 5.1 * 10^8 km2. The surface of earth is roughly 70.8% water, which means that 29.2% is land. Of these 29.2% approximately 20% is grass.
This means the surface area of all grass areas combined is:
Area_of_grass = 5.1 * 108 km2 * 29.2 % * 20 % = 29 million km2
This amounts to
blades = 1011 blades of grass / km2 * 29 million km2 = 3 * 10^18 blades of grass

Keep in mind that this answer does not take into account that the original question asked for just grasslands, so the actual value could be closer to 10^17

What is the length of all of the atoms in a single average person's body lined up in a single atom-wide line in terms of Milky-Way-radii?