Would Thor throwing this woman from the falling car in the below scene seriously injure this women.
Would throwing someone with only their arm for that amount of distance actually rip their arm off?
Here is the video.
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I am going to say yes.
First we need to work out how far the woman fell and by looking at the video she free falls for about 13 sec. The equation for calculating the distance an object falls from rest is,
d = (0.5) * (9.8 m/s2) * (13 sec)2 = 828m
I will guess that she is of average weight and say she weighs 60 kg or about 132 lbs.
The 90-degree arc that the end of the arm makes a length of
L = pi/2 times 100 centimeters. And The energy he exerts must be equal to the potential energy of the weight at 828 meters
E = (Weight * G * Height)
So the equation is as below if Thor was to release at horizontal to the ground,
Force = (60kg * 9.8m/s^2 * 828m) / (pi / 2 / 1m) = 309,956 newtons
And as we can see in the video that Thor releases at the top giving a full arc, we can take out the 2 in the equation effectively halving the force required to reach the required height. So the update value is,
Force = (60kg * 9.8m/s^2 * 828m) / (pi / 1m) = 154,978 newtons
And the answer is
So how much force does it take to rip a human arm off?
According to this web site it will take approximately
30kN - 200kN
The yeild strength of muscle (the closes approximation I can find with a quick google) is about 1-4 MPa or MN/m2.
Assuming an average arm has a diameter of 10 cm, for a cross-sectional area of about 80 cm2.
The the yield force for an "arm" made of muscle (not stronger tendons and ligaments) would be something like 7-30 kN.
So, lets put the force at somewhere between 30 to 200 kN. A wide range, I know, but close enough for government work (as the Royal Executioner of France will attest).
I am going to take a value somewhere in the middle 30kN to 200kN of around 85kN of force needed to rip someones arm.
Which bring us to the conclusion that Thor probably ripped that poor women's arm clean off.
A lot of the calculations and math was not done by me, I am not that smart. But it did take me a few days to get all the data needed to answer this.
Given that Captain America had just failed to rescue the woman a few seconds earlier, (when the bumper came off in his hands) a writer decided to find a way for the Captain to redeem himself. This opportunity can only come if someone can reach the woman but can't fly her back to the Captain easily. So who do we choose?
Not Iron Man: He can fly and could just carry her back.
Not Hulk: He lacks the control to reach the car without destroying it by reaching it.
Not the Vision: He flies by altering his density...
But the writers made a singular mistake. They let the scene go on too long and by the time Thor reaches her she is falling too fast to be safely "thrown backward to the in-need-of-redemption" Captain America.
Such a violent throw necessary to overcome her own falling momentum, and the distance between Cap and the woman should not have relied on him throwing her by the arm because of the fragility of the Human form.
He most assuredly would rip her arm out of the socket no questions need be asked. Too much force for a small part of the Human body to withstand. While such shenanigans might work with Asgardians (having three times the density, and a thousand times the physical strength of a normal Human) on Earth, it would be a recipe for dismemberment, especially since it doesn't take that much force to dislocate a Human shoulder.
The scene could have been mitigated by having him reach into the vehicle take her under his arm, helicopter for a second to remove her falling momentum, tell her to bunch up tight and THEN while in zero g, spin and throw her as a tightly wound ball.
Then the Captain could grab her belt or her hand or whatever was necessary to complete the scene, show his awesome with his one-handed pull up, rubble climbing and the scene is saved. The Captain looks awesome, Thor helps someone rather than just blowing things up with Mjolnir, and a woman is saved WITH all of her limbs intact...
Science and superheroes almost never go well together, but there are simply some scenes that can't be handwaved away. This was one of those scenes that takes anyone with an IQ larger than Shaq's shoe size, right out of the movie. Get it right or just don't do it.
In short: Probably yes.
I know this comes a bit late, but I found this while googling how much force it takes to rip off a human limb, so here you go. Now, what data can we use to determine how much force it takes for an average human limb to rip apart? Well, for one we could use the yield force of the human muscle, but since an arm is not entirely made of muscle that does not seem like a very good approximation to me. BUT we actually know a little bit about what it would take to rip off an arm. After all, quartering was a somewhat common execution method in the middle ages, so we know that we can rip off a limb if we strap a horse to each arm. Now, if you take the mass of a horse as 600kg and approximate that it can accelerate linearly from 0 to 2,77 m/s (30 km/h) in 3s, and take the horse's speed at the time, the ropes connecting the horse to the arm, are fully stretched out as 30 km/h, we get a force of 33,240N acting on the arm.
This is when all the kinetic energy of the horses is used to tear the limb out. It may be important to note that the poor fellas who were unlucky enough to undergo this "treatment" were mostly killed prior to the procedure, so we are talking about dead muscle, whereas the woman in the movie was still quite alive and could flex her muscles, allowing a greater yielding force.
But never the less, taking the approximation for the force enacted on her body by Thor from a previous comment as 154,978N, I would say yes, her arm would definitely be gone.