Clearly. John Gardner makes the point in On Writing that teachers don't teach the books that are the best, they teach the books that make their point as easily and clearly as possible. Scientific experimentation at the undergraduate level is intended to illustrate the bright spots, not the gray areas and convection is fucking awful. It didn't surprise me to spend a month saying "no this is hard" only to be told "no it doesn't exist" on that basis; what did surprise me was the surety with which the argument was made.It is a great problem, though. It's deceptive.
It's one of those problems where my intuition is an immediate 'yes', but I'm gonna think it over. There's a wonderful book by W. Kruczek Moment Pędu w 20 Doświadczeniach (The Angular Momentum in 20 Experiments) that's aimed at Polish highschoolers. The goal of the book was to make the topic more intuitive. I don't have it, but I'm going to scan relevant pages next time I'm in the library and translate as best as I can.Which is 100% useful if you want to build a bicycle but 0% satisfying if you want a deeper, intuitive answer of why the world works.
It's one of the many reasons I hate Kate Wagner. And my boss's degree was in interior design. I'm sure you've experienced this firsthand in working in Acoustics - overconfident assholes with physics degrees who think they know everything there is to know because they know the words "turbulence" "fourier transform" and "decibel" and a couple oversimplified models.
She's a shithead that didn't pay attention in class and couldn't get a job with the same meaningless degree my boss decided to get through distance learning, despite the fact that a year into it she discovered she usually spent her time arguing with her professor about math.
I'm sure I'm guilty of it, too, but in the spirit of dunking: Not actually a physics problem (but even if it were, I'm sure it could only be solved numerically when you actually try to use physiologically meaningful assumptions about the brain, which is very complicatedly anisotropic). It's a medical problem, and can't be modeled theoretically. If it could, then it would be easy to engineer a concussion-proof helmet, which apparently can't be done. A concussion isn't actually a physical phenomenon, it's a medical definition, which basically boils down to: 1. Have you been hit on the head recently? 2. If yes, are you experiencing headache, dizziness, amnesia, etc, etc. If yes, Congrats! you have a concussion. I have no doubt you can solve the problem if a spherical object of mass M and spring constant K bumps into another rigid spherical object filled with a fluid of mass m and sheer strength V while traveling at speed V, do you reach a threshold compression of C? Unfortunately, that's not what a concussion is, and nobody actually really knows what causes one. There's definitely some interesting physics there, but as far as i know, no one has figured it out satisfactorily. One of the most popular animal models of traumatic brain injury (it's also in fashion these days to refer to concussion as a mild TBI) is call the "lateral fluid percussion" model. In this model, you open up the animal's skull and use a tube to direct a compression wave of about a couple atmospheres (I think...can't remember the exact number off the top of my head) to the direct top of the brain. The injury it creates is a very focal lesion far from the site of the blast, but always in the same spot (lateral to the blast, hence the name). I suppose that suggests that it creates a travelling wave that bounces around the brain and two or more of the rebounds create a superposition at the site of the lesion, but I'm not really sure about that. I suggested it once in a meeting with a bunch of TBI experts and they just looked at me blankly then kept talking about something else (because they basically don't know anything about physics--I know about enough to be dangerous). There's something really important there, but no one really know what yet, because the actual cause of injury in a concussion isn't known. The most popular speculations right now are that it either shears some axons ("diffuse axonal injury") or some micro blood vessels (causing very small "petechial hemorrhages"--small enough that they can't be resolved on a CT). Obviously each has a very different cross section and physical properties, so modeling either is different..or maybe both or neither are relevant. Anyway, nice arguing about something else for a change :DIt may seem like I'm dunking on half of Hubski here including myself...
Can "headers" in soccer/football cause concussions, based on the maximum force delivered to the players head when it collides with the ball? You can actually solve it with just calculus if you make the right assumptions...
Anytime I see the title "neuropsychologist" I turn away in disgust! But I'm mostly just needling you about physics supremacy here, so don't take me too seriously (even though in reality I do know a shit load about this topic). I have no idea what the regulations around a soccer ball are, but obviously even with a given material this is going to change with the inflation of the ball. My guess is that if you really wanted to calculate the force, you have to account for the vibration of the ball, since obviously that's going to greatly affect the conservation of momentum. Given that if you drop a soccer ball just to see how much energy is lost to the world during a collision, it's probably greater than 50%. I don't know, but that's where my gut goes. But the much bigger problem is the shape of the head, which matters a lot, and also the strength of one's neck muscles, which also matter a lot. The latter because obviously the g force experienced by a head is going to be dependent, ultimately, on how fast the head is whipped about. Stronger neck muscles are going to limit that. It's one of the hypotheses for why women soccer players appear to have more concussions than men. The former, because the chance of getting a concussion varies pretty significantly depending where on the head the force is applied and in what direction. Man now that I'm thinking about it, you could make a really good qualifying exam question around this.the spring constant of a soccer ball doesn't tend to be a regulated quantity that's published anywhere
Is that similar to, different from, or complimentary of the diagrams and videos that show the cause of a concussion of the brain just bouncing back and forth in the skull?There's definitely some interesting physics there, but as far as i know, no one has figured it out satisfactorily. One of the most popular animal models of traumatic brain injury (it's also in fashion these days to refer to concussion as a mild TBI) is call the "lateral fluid percussion" model. In this model, you open up the animal's skull and use a tube to direct a compression wave of about a couple atmospheres (I think...can't remember the exact number off the top of my head) to the direct top of the brain. The injury it creates is a very focal lesion far from the site of the blast, but always in the same spot (lateral to the blast, hence the name). I suppose that suggests that it creates a travelling wave that bounces around the brain and two or more of the rebounds create a superposition at the site of the lesion, but I'm not really sure about that.
I guess it falls under the old adage that all models are wrong, but some are useful. Showing a cartoon of a brain rattling around in the soft space between the brain and the skull sort of gets the point across that some applied force is the genesis of the injury. Beyond that it's sort of worthless. When you think about the types of injuries that can result from a blow, it's starts getting complicated, because they could be compression, torsional, shear, etc. It all depends where on the head the force was applied and with what impulse, etc. For example, it's really easy to get a concussion from getting elbowed in the chin. You see it in sports all the time where a harmless looking bump on the chin keeps a guy sidelined for weeks. On the other hand, it's probably a lot harder to get concussed if you get hit in an area of your skull that is thick and also doesn't lead to a severe torque on your neck. Applied force is a prerequisite, but it's not even close to the whole story. In fact it's a small part when you look how many times people get hit in the head really hard and don't suffer a concussion or TBI. I've had two in my life and I've been playing ice hockey for more than 30 years. Force is a starting point, not an ending point.