Math love

[KenWright]

Hi all!

This is a platform for all things math.

Calculating stuff from novels.

Talking about math.

Loving math.

Have fun!!

 

Note: as WuxiaWorld is a platform for novels, I don't think it would be appropriate to specifically ask for advice for your school homework... you might raise it, and I think it would be appropriate for someone to re-direct you to another site.

Let's see how this page goes and evolves, shall we? 

[KenWright]

WolframAlpha

For those who don't know, https://www.wolframalpha.com/ is an amazing site. You can have it do quick calculations or (limited) visualizations to double-check your work.

Also, there's a lot of cool other topics you can ask the engine about!

[KenWright]

List of novels on WuxiaWorld, as of 2023/12/05, ~17h00 UTC+0

Made manually from novelupdates and checking on WW. May have inaccuracies.

I made this after a request on another thread for novel recommendations. I made a list of the novels, and then thought, how can I rank them? 

My personal preference on ranking is given. "Tiers" don't mean much - it was a stepping stone to the "Class" (Rank).

 

WuxiaWorld Novel Rankings (2023-12-05).xlsx

[KenWright]

In Chapter 236 of The Nebula's Civilization, it was asked in the comments how damaged a house-sized mortar shell would be.

For posterity, and easy reference, I have pulled out some of the calculations here. Mind you, it is all fairly rough (very).

Considering that the dinosaurs were wiped out by an asteroid only the size of Mount Everest (check out Life on Our Planet), even a small object given enough speed can be lethal. So a house sized object, say, traveling at 2000 to 4500 km/h, with a mass of 100m by 100m by 100 m at 2000 kg per meter cubed would have the momentum of mass x velocity = 2x10^9 kg x 4500 km / h = 2.5 x 10^12 kg.m/s. 

I am going a bit further than I went in the comments section.

Let D = 2.5 x 10^12 kg.m/s

Random asides

From wikipedia, the asteroid that killed the dinos had estimated energy of 300 zetajoules (3x10^23 joules). Note: that was enough to stuff up the planet for a long time. And the major impacts it had weren't just the initial blast, but the consequences (earthquakes, debris - like meteors (stuff from the ground that got blasted up and then went down again), pressure waves, extreme heat, asphyxiating clouds, climate change). How many cups of coffee could you make with that energy? That would be about 8 x 10^18 cups of coffee (about a billion of 8 billions), or enough coffee (water heating energy) for 10 million years for ALL coffee drinkers on the planet (everyday for 10 million years).

Hmm. Let's say a good cup of coffee of 200 ml is heated from 15 deg C of water to 60 deg C. That's a 45 deg C change. Energy required = m*c*delta T = 0.2 kg * 4200 J/(kgK)*45K = 37.8 x 10^3 joules of energy. 

300 zetajoules = 3 x 10^23 J

How many cups of coffee could you make with 3 x 10^23 J ?

= 3 x 10^23 J / 37.8 x 10^23 

= 7 936 507 936 507 936 507.93...

= 7.9 x 10^18 cups of coffee

Let's just say 8 x 10^18 cups of coffee

 

How many cups of coffee are drunk every day?

"Based on the latest study, there are approximately 1 billion coffee drinkers worldwide and over 2 billion cups of coffee are consumed daily."

https://earthweb.com/how-many-people-drink-coffee/

 

If we could have somehow harnessed the kinetic energy of the asteroid that killed the dinos, how many cups of coffee could it make?

8 x 10^18 cups of coffee

How many people could that feed and for how long?

1 billion people

2 billions cups per day (2 x 10^9)

7.9...x10^18/2x10^9 = 3 968 253 968.253

= 3.96 x 10^9 days

= 10 864 487.25 years

~= 10 million years

 

 

D = 2.5 x 10^12 kg.m/s

That is the momentum that would need to be absorbed. Not to useful to compare to the energy of the dino-killer.

Let's get that to energy.

m = pV = (1000 kg / m3) * (100 m by 100 m by 100 m) = 10^9 kg

v = 4500 km/h = 1250 m/s

E = 0.5mv^2 = 781.250 x 10^12 ~= 8 x 10^14 J

which is about 1 billionth of the dino-killer.

Knowing that the dino-killer killed off more than 75% of all life on the planet (land, sea and air), that's still crazy high.

 

This would still  be very devastating to a city I think, though in the context of fantasy novels, one can (may) expect shields, magic defenses, and that the math itself is not taken too seriously. The worlds under question could very well be said to operate according to different laws of physics than ours.

[KenWright]

Am I the only one posting here...?