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November 25, 2013
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tumblr mwqvjbbIeD1qhyqpto1 500 by Foxy-Noxy
tumblr mwqvjbbIeD1qhyqpto2 500 by Foxy-Noxy


Think for a second about the nearly impossible amount of strength it would take to cut a living vine the thickness of a small tree with something as dull as a window without being able to build any momentum.


Alright, let’s do this.


Applejack exerted a certain amount of psi onto a large vine and broke it. How much psi can Applejack generate without a sweat?


We’ll work in SI units in this exercise.

One pascal (SI unit of pressure) is N / m^2 

  • N = newtons of force applied
  • m^2 = meters squared where pressure is applied.

Let’s first find how many pascals the windowframe first exerts on the vine because of gravity.

N = 9.8 (the gravitational pull of the earth).


A dull window would have a large area exerting force, compared to a sharp, small edge. Various window measurements from Home Depot's website and my house reveals that an average window's edge dimensions are roughly 3/4 inches x 36 inches. An inch is 0.0254 meters.

3/4 * 36 * 0.0254 = 0.6858 meters squared.

m = 0.6858 meters squared.


Let’s calculate.

p = N / m^2

p = 9.8 / 0.6858

p ~= 14.29 pascals

The window exerts 14.29 pascals on the vine naturally.


Let’s assume the vine is made of black oak. The tensile strength of black oak is 6,520 psi (when the oak compresses and crushes). Wolfram|Alpha tells me that that is equal to 44,950,000 pascals. Woah. Let’s subtract the natural gravitational pascals from the overall tensile strength to find out how much Applejack has to exert manually.


44950000 - 14.29 = 44949985.7 pascals

There’s our answer (a lot). But how much is that in psi? Let’s have Google finish it off.


44949985.7 pascals = 6519.44424 pounds per square inch.


Applejack has to exert about 6519.44424 psi of pressure onto the vine. That’s just about the equivalent of twoairplane hydraulic systems.


Applejack for best vine-chopping double-airplane, 2013.


Airplanejack by Foxy-Noxy

I did not math this. Thanks to SgtPiggy for the calculations.





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:iconlupus-ignis:
Lupus-Ignis Featured By Owner Nov 26, 2013  Hobbyist Artist
Crossposted from my reply to Darkflame75's calculation:

Consider that there is no deformation of the window frame. That means that the frame itself was not subjected to a pressure larger than its yield strength, so the vine must be of a softer material than speculated. Since Applejack only has one hoof on the frame, the area that supports whatever force she exerts must be the shadow area of her hoof onto the frame. If we consider the frame to be 19mm broad, and for simplicity's sake have half that area on the inside of the glass, that allows only a segment of her hoof to actually transfer force. A hoof is roughly circular, and if we estimate Applejack's shoe size to be radius r=50mm (no insult intended, miss!), the area of the circular segment that can touch the frame is:

A = (r^2)/2 * (θ-sin(θ)).

θ is equal to 2 * acos((r-h)/r), where h is the length from the glass to the edge of the frame (19mm).
θ = 1,253 rad
A = ((50mm^2)/2) * ((1,253rad)-sin(1,253rad)) = 379mm^2

The maximum force transferred is therefore the yield strength of the frame times the area under the hoof. Since it is the "Golden Oak" library, let us use that material for the frame. Oak has a maximum yield strength of σ = 60 MPa (N/mm^2).
Maximum force is therefore:

F = σ * A = 60 N/mm^2 * 379mm^2 = 22 740 N.

Observation shows that the mare's weight is not enough to cut the vine. Only when she uses her famous earth pony strength does the window slam shut. If we assume that her legs are 0,5m long, her forelegs must muster a moment of:

M= F*L = 22740N * 0,5m = 11370 N*m

For comparison, that is about 15 horsepower seconds. Applejack cuts the vine in roughly one second with her front legs, using her hind legs for bracing, meaning that she utilises her entire body. My conclusion is therefore that Applejack is approximately 15 times as strong as a standard horse
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:iconojamapony:
Ojamapony Featured By Owner Nov 26, 2013
You didn't take friction into account, that window would of already been open, and because of the friction, it wouldn't be putting gravity force on the vine
Also from the way the vine broke, it looks pretty hollow
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:iconmaphisto86:
Maphisto86 Featured By Owner Nov 26, 2013
Here I thought Trekkies over analyzed things. ;P Great maths! :nerd:
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:iconshadowsilverwolf:
ShadowSilverwolf Featured By Owner Nov 26, 2013  Student General Artist
It struck me as how impossible that would be when I saw it.
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:icontediium:
Tediium Featured By Owner Nov 26, 2013  Hobbyist Digital Artist
I love how you've worked this out. I'm like how so many other people have noticed this XD
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:iconkarkovice1:
karkovice1 Featured By Owner Nov 26, 2013

I think there's a far simpler explanation:

 

www.youtube.com/watch?v=NFQCYp… :D

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:iconthe-bloody-bishop:
The-Bloody-Bishop Featured By Owner Nov 26, 2013  Student Writer
Natural Earth Pony strength + Active Apple Farmer lifestyle + Adrenaline Rush = Super Strong Applejack. Huh. I wonder if her superhero persona in "Power Ponies" will have super strength as a superpower? Maybe she'll transform into an Incredible Hulk or The Thing comparison? It would match her coat color. XD
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:iconapple-djaff:
Apple-Djaff Featured By Owner Nov 26, 2013
AJ op plz don't nerf
Reply
:iconphiktorial:
Phiktorial Featured By Owner Nov 26, 2013  Hobbyist Digital Artist
I know that this post is just for fun and that you didn't do the math, but I'd still like to point out some mistakes in the calculations because physics is serious stuff:

- First of all, you shouldn't use symbols of SI units as symbols of quantities like you did when writing N= newtons of force applied, as it can get quite confusing. Instead you should write, for example, F = force applied, A = area where force is applied and pressure = p = F/A.

- Unit conversions: The calculation for the area of the window is wrong, it should be A = 3/4" *36" * (0.0254 m/")^2 = 0.01741932 m^2. Luckily this doesn't really affect the final result.

- Rounding the result: there's no point in writing the result to nine significant figures when the calculations are accurate only to two. The result should be written as 6500 psi.


Sorry about lecturing on a post about cartoon ponies, but you know what happens when someone is wrong on the internet.Sweating a little...
Really fun post though, otherwise I wouldn't have bothered writing all this.
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:iconhyginustus:
Hyginustus Featured By Owner Nov 26, 2013  Student
:icondrugaddictspikeplz::iconsaysplz: nobody cares
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