Thursday, November 15, 2012

Crazy Russians

Apparently, Russians love throwing themselves off of really high things.


Didn't you just wanna say, "jump already!!"? But actually, how on earth did he survive this (yes, he does in fact survive it)? Is this occurrence freak, or if repeated, would he survive again? When you analyze the physics, you'll see that given the circumstances, the daredevil's survival is not entirely due to chance. His seeming thinness (low weight), the high amount of drag, and most importantly, the snow at the bottom, all contributed towards him walking away with his life. The chance portion, here, is that he did not land on his head (and for the purpose of this analysis, he lands either flat on his back or front, with his head making no contact with the ground).

Assumptions:


• Man weighs 75 kg with equipment

• Man is 120 m high (according to video)

• The air is at least 0°C, making p of air at least 1.2922 kg/m3

• The drag constant for a skydiver is 1.2

• The surface area of a typical man is 1.9 m2, but as he is falling, air resistance acts only half of this area, 0.95 m2

• In Russia, the winter snow is probably deep; this would greatly slow the time over which the jumper’s momentum changes (t=0.1s)

• Use 0.8 m2 as area effected upon impact since jumper did not land on his head; assuming no part of his head touches the ground upon impact and that he lands flat on stomach or back

• 170 x 106 = compressive strength of bone

∆KE = -∆PE + WNC

KE2 + PE2 = KE1 + PE1 + WNC                  [PE2 and KE1 go to zero]

½(m)(v22) = m(g)(yo) + Fdcosθ

½(75 kg)(v22) = (75 kg)(9.8 m/s2)(120 m) + (120 m)[½(p)(Cd)(A)(v2)]cos180

37.5(v2) = 88200 + -120(½(1.2922)(1.2)(0.95)(v2))

37.5(v2) = 88200 + -60(1.47(v2))

37.5(v2) = 88200 – 88.2(v2)

125(v2) = 88200

v ~ 26.5 m/s

p = (75 kg)(26.5 m/s) = 2000 kg(m/s)

ΣF = 2000 N/0.1 s = 20,000 N

F/A = stress = 20,000 N/0.8 m2 = 25,000 N

25,000 N < 170 x 106

Based on this analysis, none of the jumper’s bones are crushed by the impact, since the stress experienced by his body as a whole did not exceed the compressive strength of bone. While this in its entirety is likely not true (there may be different values in actual life than what’s used in these calculations, there could be other severe injuries not pertaining to bone fracture, some assumptions may not be realistic, perhaps shear strength for particular bones would have been more appropriate, etc.), it can be seen that it is at least certainly plausible that if there is a good amount of drag force keeping the terminal velocity above that of its actual value and if the person lands in snow to break their fall and if they land in such a way that the force of the impulse is spread over a large area, that falling from such heights is survivable, as is seen by this man. Also remember, that he is wearing pack where the parachute was supposed to deploy from: this too would help break his fall (if he landed on his back).

Here is another just for enjoyment...going with the theme of crazy russians. In lieu of the test tomorrow (which I am NOT prepared for), I am going to forego analysis of this one. Feel free to do the bungee analysis on it though yourself...I know physics analyses are probably your favorite pastime!




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