IDEA! Most of us have played in thoes pools of colorful balls as kids. If you understand what I am talking about, mabey you can come up with a thought on my question. If there was a pool of thoes colorful balls, that had an unlimited depth (lets just say), how high up could you jump into it before breaking bones? And to exceed your brain power, how far up would you have to be untill someone died from the "impact"? Now thats a brain teaster. Good Luck.
Ya hafta consider how hard these balls are and how big they are. Then consider the range of brittleness a person's bones can be. Then I think there are other things to consider, which make the whole problem very complicated. . . . I wouldn't know how to solve this problem. Sorry. But it would be interesting to know the answer.
If the depth was infinite, then you'd never actually land, since you'd displace balls into infinity. No, that's not true. Here's how you would go about it. First, find the amount of absortion/resistance in each ball, and between balls. Then compute the point at where a human body breaks when it meets so much resistance, then find the inertia at height x that'd you'd fall to and die.
I'm not sure how much force it takes to break a bone. a big part of it would be the impact angle of the particular bone. The second thing is how much impact can the balls absorb. the density of the balls would increase with depth into the ball pit, so that would effect the ability of it to absorb impact. I'd guess that at 100 feet the chances of fatality would be pretty high. Maybe even at 50. With the right angle, you could snap your neck pretty easy from 10' I'd guess. Makes me wonder at what depth the balls would collapse under the weight of the balls above them. Hey that's sort of how a star works except to complete the analogy, the balls would have to explode. Cool.
It is a very interesting thought. You see poeple jumping into these balls from 15 feet up on TV, Yet you also see poeple leaping into an air bag from almost 1mk up. (I'm Not sure the exact hight, but it is in the world records book. Yes, it also depends on the angle you land into this "pool." Head first...? Feet first? Side ways? Or even some magical angle that lets the human body survive from great hights. But people have amazingly survived from far, far, higher hights, after hitting a cement sidewalk. I really forget the entire story, but i remeber a baby surviving a extreamly high distance becuase his/her dipare exploded on impact. wesmorris you make a good point but think of this. When jumping off a diving board into water, do you feel more force when diving head first, or when you do a belly flop? The same could be said for jumping into a pool of balls... either way, you will injure yourself, but at what point you actully survive? Personaly, with the fact of of the size of the balls are, I would like to go in feet first rather than head first. Drivers gain points in thier sport for less splash on entry. If you are falling to your death, I am sure that would not matter. As far as I know, your legs will be able to withstand more force then when you are in a profesional divers formation.
the same amount of force is going into your body no matter how you land, that is one of the reasons people try te get their shoulders and back hitting the ground first, because if there is more area to take the same force, less damage is being done. but there is also the matter of your vital organs taking a large shock if landing on your shoulders, so legs are a good option if its life or death.
The problem of the infinite depth presents a complex paradox. We assume that the balls are in a state in which they are not falling towards an infinite abyss but are somehow transfixed in one possition as if there was at the bottom of the pile a floor to provide the resistance to hold it all up. But there is no such floor because the pile of balls is infinitely deep. Thats conceptualization problem number 1. The second problem is quite simply the fact that something that is infinitely deep cannot be 'jumped into' because it can't have a surface! Something that is infinite cannot have a 'finite end' it has to stretch towards infinity at both ends to put it figuratively. Of course for this pile of balls there is no such distinction as 'that end' and 'this end'.
At terminal velocity, water might as well be concrete. Start with 9.8 m/s/s ... oh, wait ... even if we don't chide Exsto for the literalism, what would the gravitational influence of such a structure be?
Guys, Forget infinity: there is a natural limit of height. Indeed, you can be sure that if you will hit anything with speed comparable with speed of sound into this "anything", you will effectively hit an absolute rigid body. So, you can imagine what happens if you will hit ball with speed of sound into its material... Even if balls are made of water that speed will be around 1.4 km/sec...
Just thought I would add a couple of thoughts here: Falling through the atmosphere is a lot like falling through a large pool of very small balls. Even though you don't hit the air the same way you would hit a brick wall(at normal velocities) you still experience resistance to the air. Hypothetically, at normal velocities, one could fall indefinitely through air. Obviously, as others have pointed out, the nature of the balls (size, elasticity, friction between them etc... would influence how damaging the fall would be(compare inflateable balls to stone balls). My guess is that you could fall without breaking bones through standard plastic balls, if they are deep enough, unless you fell from orbit or some such hyper-fast collision. As to how someone falls, I thought I would point out that falling on your feet is generally preferrable, because you can exert force against the fall by bending your knees(as a shock absorber). Most people will not fall on their back unless they can't avoid it or theey know its safe. Cheers, Please Register or Log in to view the hidden image!
I used to love playing about in those balls when I was kid too! I remember wishing it was deeper so I could see how deep I could go. lol or something along those lines. I was like that when i was a kid though..always wanting to escape...
