Bellhead wrote: ↑Sun Aug 02, 2020 8:15 am
I think you're mis-estimating where Maddie's getting
her leverage from. Assuming she had just hit the water in panel 2 and was still moving slightly forward, she would have come to the point where her hips hit the glass at the end of the pool. Given that Karen is below that point, she could hold them both up fairly easily just by holding on and not letting her hips straighten out.
Pull hard enough with her arms at that point, and Karen would whip right around, pivoting on her own feet, landing pretty much right where Maddie started. And
that could be done with a feat of Basitin strength, regardless of size.
The problem is that Maddie in this case doesn't have a purchase point. She's not holding *on* to anything except Karen, and that means that it doesn't matter how strong she is - the laws of mechanics are merciless, strength by itself isn't magic and without a purchase point all that being stronger does is let you pull *yourself* forward just as hard as you pull someone *else* backward. Due to Newton's laws, without a purchase point flipping someone backwards over your head also means flipping yourself forwards. Or, at least, at first glance. Thinking about this more carefully, the complicating factor is actually the presence of the water, which *might* let her pull this off but is *extremely* tricky to model.
I'm going to put on my physics teacher hat for a moment here, because the best way to explain this is with a free body diagram.
Since neither Karen or Maddie are holding on to anything except each other, both of them can be more or less treated as free bodies subject to only a few forces. And what we're mostly interested in here is rotation, so we're really looking for the torques around various pivot points and can neglect the support forces that only act *through* those pivot points. The light blue arrows represent the gravity force on each of them, which are roughly equal in magnitude (since they both weigh about 100 lb) and act downward through their center of masses (which are more or less somewhere in their torsos - exact locations aren't important). The purple arrows represent the forces they exert on each other through their grips, which are by definition equal and opposite due to Newton's 3rd law. The blue and red lines represent the lever arms of each force around their respective pivot points (her foot touching the wall for Karen and her hips touching the edge of the pool for Maddie), the green line outlines the rough position of Maddie's legs since we can't see them, and lastly the yellow lines represent forces between Maddie's legs and the water that I'll talk about in a moment.
The key question here is what the sum of the torques looks like on Maddie, but to figure that out we also have to consider Karen as well. A notable point is that her weight is acting pretty far from the pivot point, so it's exerting a large CCW torque. Maddie's pulling force is also pretty far from the pivot point, though, so it's also exerting a large CW torque. For her to not fall, those torques must be equal, so since the lever arms are roughly equal Maddie is likely pulling her with a force roughly equivalent to her body weight (i.e. pretty hard).
Moving on to Maddie, there are two obvious torques acting on her. First, the torque from the reaction force from her pulling on Karen, which is acting CCW with a pretty strong force and a relatively long lever arm and so exerting a pretty large CCW torque. Second, the torque from her weight, which is actually *also* going to be CCW because she's leaning out and so putting her center of mass beyond the pivot point. This torque is going to be smaller because its lever arm is shorter, but it's still an additional CCW torque. For Maddie to not rotate CCW (i.e. flip forward over the edge of the pool) there must be an equally large CW torque acting on her from somewhere. There are no other forces acting on the top half of her body, so if there's another torque it must come from her legs somewhere, and this is where the question of a purchase point becomes important.
If Maddie were able to brace her feet against something solid, she could exert a backwards force on it with her feet and so have it exert an equal forwards force on her by newton's 3rd law to provide a CW torque. The size of that force (and hence CW torque) would depend on how hard she pushed on it, so her strength would come into play and if she could push hard enough she could balance the CCW torques she's experiencing and not fall. However, Maddie is
not bracing her feet against anything - she's hanging at her waist over the side of the pool (which we know is deep enough at the end to come up to at least mid-torso on several characters), so her legs aren't touching anything except the water and the pool wall. Thus, it doesn't actually *matter* how strong she is, because there's nothing for her to exert a force *on*.
Absent anything to brace against there are only CCW torques on Maddie's body, so she should start to rotate CCW around the edge of the pool. At that point her legs will try to move through the water as she rotates, so they will exert a force on the water to the right and the water will exert an equal force on them to the left by newton's 3rd law (represented by the yellow arrows on the diagram). This does provide a CW torque, which opposes the CCW torques of her weight and the pulling force. However, water isn't a solid. This force is a drag force, so it can't exist unless her legs are *moving* because drag is a function of velocity. Therefore that force cannot be large enough to provide a torque strong enough to keep her from rotating, because if she isn't rotating the velocity of her legs through the water is zero and so there can't be any drag.
As such, Maddie's body *cannot* be in static equilibrium, because if she's stationary there is a net CCW torque on her. What should happen is that as she exerts force on Karen, her body should begin to rotate CCW around the pivot point of the edge of the pool. This rotation will accelerate until her legs are moving through the water fast enough to produce a strong enough drag force for that CW torque to balance the CCW torques, at which point she will rotate CCW at a constant angular speed - at least until her legs break the surface of the water and that torque disappears and she just flips head over heels over the edge of the pool.
However, that's considering it as a more or less static (or, at least, equilibrium) problem. All the reasoning is still valid, but the conclusion we can draw from it is just that the situation must be dynamic and non-equilibrium. Specifically, we know two things - one, that Maddie must be rotating CCW, and two, that Karen is being pulled hard enough to not only hold her up, but reverse her motion and make her rotate CW. The question is then
which happens first - Karen reaching vertical with enough angular velocity to flip her over the edge back into the pool (and dragging Maddie with her), or Maddie's legs breaking the surface of the water and thus removing the CW torque that allows her to actually slow her rotation and keep from flipping over the edge *out* of the pool. This question is a
lot harder to answer. The harder Maddie pulls the quicker Karen's rotation will reverse, but also the quicker that *Maddie's* rotation will increase. In the absence of the water this would more or less completely cancel out because the air drag would be negligible, but drag in water is not only much larger but increases with velocity *faster* than linear (quadratic) for any large object moving at macroscopic speeds. Thus, Maddie pulling harder is still going to make her rotation increase, but not by as much as it will make Karen's rotation increase because the water drag becomes larger faster at higher speeds (relatively - i.e. 2x as much speed means 4x as much drag).
So the question actually becomes "How hard does Maddie have to pull to create enough extra water drag that Karen rotates back up to vertical before Maddie flips out of the pool?", which is unfortunately basically going to be impossible to answer with the information we have. My intuition (and a couple of very ballpark calculations) says "hell no", *especially* considering that both of their initial momenta are in exactly the wrong direction, but actually proving that would require some rigorous calculation (or, more likely, numerical modeling) unlike the simple analysis above. And I've already spent all afternoon on this, so that's about as far as I want to go.