θ is equal to 2 * acos((r-h)/r), where h is the length from the glass to the edge of the frame (19mm).
A = ((50mm^2)/2) * ((1,253rad)-sin(1,253rad)) = 379mm^2
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, each of her forelegs must muster a moment of:
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 he utilises her entire body. My conclusion is therefore that Applejack is approximately 15 times as strong as a standard horse.
Now this engineer should really get some sleep. Any blatant mistakes in the above will be blamed the curse that is midnight mathematics.
While we cannot say with certainty how strong the vine is, I doubt that it is much weaker than 6 MPa, or we would see it tear more from the forces the ponies apply to it, so assuming that Applejack is 5 to 15 times as strong as a normal horse would not be unrealistic.
There are different problems I see.
What is your source for the tensile strength of the vine? As long as we don't know what material they are it is pretty difficult to assume any value here. So this is maybe the biggest uncertainty here.
What is your assumption for the 0.2 meters width of the contact area? An estimation from viewing the scene I guess?
But most important, we can't actually calculate AJ's weight with this scene because she doesn't use her entire mass to shut the window. She stands on her hind legs and only applies force with her forelegs. So we could only calculate this force she is able to apply this way. To calculate her mass she would have to stand completely on the vine (or rather stick to the window).
So the idea is nice, but it won't work.
That's why i said at least, she would have to be heavier since she's not on it collegiate
Since they are a creation of Discord the last thing they would do is make sense and follow physics.
She either must have FANTASTIC abdominal muscles or ALL earth ponies are enigmas sans just Pinkie Pie.