Nerds rejoice! Math thread.

AshleYy

AshleYy

Member
Just a random math question. :D

For each breath that you take, how many of the air molecules would also been breathed by the patron saint of Physics, Sir Isaac Newton (1642-1727)during his life time, the atmosphere is about 8 km high, and the molecules in the air each occupy a space representing a little cubic box about 3.33*10^-9 m along a side, the earths radius is 6..38*10^6. make any reasonable assumptions for any data needed.

a) 6
b) 6*10^3
c) 6*10^6
d) 6*10^9
e) 6*10^12

PM me for the answer.

Correct answer get's a present! :D
 
Synista

Synista

Member
Okay here we go.....
This is just a theory.

Assume 12 breaths per minute and a tidal volume of 1L.
= 12 liters/minute = .2 liters/second

Newton's age = 46
Assume average rate of intake between 0-20 = 1/2 of adult

No. of molecules Newton breathed
Volume inhaled lifetime = .2 l/s * (46-10)Yrs
V = 4.6x10^8 L

Volume of Earth's atmosphere - (V.e atm) = 4/3 π ((radius(earth+atm))^3 - (radius(earth))^3)
V.e.atm = 4/3 π ((6.378x10^6m)^3 - (6.370x10^6m)^3)
V.e.atm = 4 x10^18 m^3 = 4 x 10^21 L

No. of Molecules per breath
=.001m^3 (this is equal to 1L)/ (3.33x10^-9)^3
= 2.7 x 10^22 Molecules

No. that Newton breathed:
2.7x10^22 * 4.6x10^8 L/4x10^21 L
= 3.11 x10^9 Molecules

Your book probably assumed Isaac Newton had a slightly higher intake of O2 (Approx. ~24L/min)

CHEATER

Assumptions.
 
Vinzyboy23

Vinzyboy23

Member
LexLuthorWrong.png
 
57thEnryu

57thEnryu

Member
in theory its simple, determine how much volume is breathed in and then figure out how many molocules there are based on preasure. I just dont want to do it right now...
 
WildFire

WildFire

Warrior of Linux
This is a Fermi type of problem, and you must supply reasonable numbers to get a rough answer! Answers are 3 orders of magnitude apart, so you can even afford to be sloppy! If each breath of Sir Isaac’s (and ours) is about 1 litre = 10-3 m3, and they are 3 seconds apart, then in 1727-1642=85 years, he will have had 85 x 365 x 24 x 3600 /3 = 8.93 x 108 breaths, for a total volume of 8.93 x 105 m3. We will assume that the air mixes well enough that we do not have to worry about air being breathed twice.
The total volume of the atmosphere is 4 Re2 h, where Re is the Earth’s radius, and h is the height of the atmosphere, giving 4.08 x 1018 m3. The fraction of air molecules ever breathed by the patron saint of Physics is thus 8.93 x 105 / 4.08 x 1018 = 2.19 x 10-13. The number of molecules in each breath of ours is the density 1/(3.3 x 10-9)3 = 2.78 x 1025 m-3, multiplied by the volume of each breath, 10-3 m3, or 2.78 x 1022 molecules. Multiplying by the fraction breathed by Newton, each breath of ours has about 6.08 x 109 molecules also breathed by him (D). Since we have about 9 x 108 breaths, each breath of ours has about 7 molecules also breathed by Isaac Newton.

Seeing as you copied the question, I just had to copy the answer.
 
Synista

Synista

Member
Fireblasto said:
This is a Fermi type of problem, and you must supply reasonable numbers to get a rough answer! Answers are 3 orders of magnitude apart, so you can even afford to be sloppy! If each breath of Sir Isaac’s (and ours) is about 1 litre = 10-3 m3, and they are 3 seconds apart, then in 1727-1642=85 years, he will have had 85 x 365 x 24 x 3600 /3 = 8.93 x 108 breaths, for a total volume of 8.93 x 105 m3. We will assume that the air mixes well enough that we do not have to worry about air being breathed twice.
The total volume of the atmosphere is 4 Re2 h, where Re is the Earth’s radius, and h is the height of the atmosphere, giving 4.08 x 1018 m3. The fraction of air molecules ever breathed by the patron saint of Physics is thus 8.93 x 105 / 4.08 x 1018 = 2.19 x 10-13. The number of molecules in each breath of ours is the density 1/(3.3 x 10-9)3 = 2.78 x 1025 m-3, multiplied by the volume of each breath, 10-3 m3, or 2.78 x 1022 molecules. Multiplying by the fraction breathed by Newton, each breath of ours has about 6.08 x 109 molecules also breathed by him (D). Since we have about 9 x 108 breaths, each breath of ours has about 7 molecules also breathed by Isaac Newton.

Seeing as you copied the question, I just had to copy the answer.
Click to expand...

That's not the point, it's meant to be a fun thread w/out people googling answers...
And plus you already got his age wrong, since 1643 January is when he was born and Died in 1727 on March. so he's 84 before he died. The reason why you can't tell his exact age is because of calender changes, but that's also not the point.

But this is also incorrect, BECAUSE the average life expectancy in 1700-1750 was ~43.13. So obviously one man CANNOT live to approximately almost double that age. Which is why people actually assume he died at 46.

Like my teachers always tell me TRIPLE CHECK before you Ctfl+A > Ctrl+C > Ctrl+V an answer.

But nevertheless, Outlawl got D first :D
 
Propkid

Propkid

Member
There are bazillions of those and I can never remember them fully so I just googled one :]

Three friends have a nice meal together, and the bill is $25

The three friends pay $10 each, which the waiter gives to the Cashier

The Cashier hands back $5 to the Waiter

But the Waiter can't split $5 three ways, so he gives the friends one dollar each and keeps 2 dollars as a tip.

They all paid $10 and got $1 back. $10-$1 = $9

There were three of them 3 X $9 = $27

If they paid $27 and the waiter kept $2: $27+$2=$29

Where did the other dollar go?
 
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