How much pressure on the skull to kill a person?

[rohanprabhu]

I know it's old already.. but this came up when I was lecturing my mom on the evil effects of urban myths and stuff.. so here it goes..

I'm throwing a 5 rupee coin [Weight: 0.009 kg], from the Empire state building's roof [Height: 381m]. The coin hits a passerby on his head, as in.. vertically i.e. the coin's circumference hits him:

http://img248.imageshack.us/img248/3748/howithitsmo3.jpg

So, the GPE of the coin is: $\textrm{U} = \textrm{mgh} = (0.009 \times 9.8 \times 381) ~J = 33.7~J$. Assuming that the coin hits the head and stops is 0.1s (which I assume is more than what would practically happen) it means that when the coin hits the person, it hits with a velocity:

$$v = \sqrt{\frac{2\textrm{U}}{\textrm{m}}}$$

$$v = 86.54~\textrm{m/s}$$

meaning, it has a momentum of:

$$p = 0.778 ~\textrm{kg} \cdot \textrm{m/s}$$

which was imparted in 0.1s, meaning a total force of:

$$F = \frac{0.778}{0.1} = 7.78~\textrm{kg} \cdot \textrm{m} / \textrm{s}^2$$

I stained the coins circumference with black ink, and placed it on paper, to get the area that the coin would hit. I got a rough rectangle of 0.2cm x 0.5 cm, meaning a total area of $10^{-5}~\textrm{m}^2$.

So, the pressure on the skull at that point would be:

$$P = \frac{7.78}{10^{-5}}~\textrm{Pa} = 7.78 \times 10^{5}~\textrm{Pa}$$

which is like, around 8 times the atmospheric pressure.

So, the question is.. could this kill a person? And, if the time within which the coin stops is like, 10 times less, the pressure is 10 times more. Since, I'm not sure about the interval.. if the coin hits in like 0.01s, the pressure would be 80 times the atmospheric pressure. Could that kill a person?

 

[John Creighto]

I think the coin would stop much faster then 0.1 seconds and if the coin lands on an edge the pressure will also be higher. I have read once in a news group that 90 atmospheres was survivable but you would be barely able to breath. That said I won't volunteer to be your test dummy.

 

[Andy Resnick]

The coin will rapidly reach terminal velocity, which well below 90 m/s. Didn't 'Mythbusters' do an episode on this?

 

[h2oski1326]

The coin will rapidly reach terminal velocity, which well below 90 m/s. Didn't 'Mythbusters' do an episode on this?

yes, the terminal velocity of a penny will be much slower. On the show they determined that the speed would not even be enough to break the skin, but it would hurt.

 

[rohanprabhu]

I think the coin would stop much faster then 0.1 seconds and if the coin lands on an edge the pressure will also be higher. I have read once in a news group that 90 atmospheres was survivable but you would be barely able to breath. That said I won't volunteer to be your test dummy.

90 atmos is not comfortable when you are enclosed in an pressure field of 90 atmos. If the pressure is at a small point on your skin, you won't really feel it as much.

yes, the terminal velocity of a penny will be much slower. On the show they determined that the speed would not even be enough to break the skin, but it would hurt.

righto.. I clearly missed the fact that this experiment was being conducted inside a fluid medium. I assumed no air around me..

 

[mgb_phys]

righto.. I clearly missed the fact that this experiment was being conducted inside a fluid medium. I assumed no air around me..

If you are walking under the Empire State and there is no air around you - falling pennies are the least of your worries!

 

[TVP45]

Surely you've been hit by hail which is more aerodynamic than a farthing and falls farther.

 

[mgb_phys]

Surely you've been hit by hail which is more aerodynamic than a farthing and falls farther.

Hail can get upto quite a speed. Terminal velocity for a sphere in air at hgh speed is roughly V = 90 sqrt( diamter ) m/s
So large 1inch hail can reach 15m/s = 35mph

 

[TVP45]

Yes, hail that size (and bigger) does sometimes kill people. There was an instance somewhere in Asia a few decades back where they had something like 8 cm diameter hail! But, the little stuff under 1 cm hurts but that's all.

 

[John Creighto]

Hail can get upto quite a speed. Terminal velocity for a sphere in air at hgh speed is roughly V = 90 sqrt( diamter ) m/s
So large 1inch hail can reach 15m/s = 35mph

Shouldn't it depend on the density?

 

[Danger]

The hail around here can be pretty nasty. To start with, it's extremely dense, with no air spaces between the ice crystals. If you bust one in two, it looks like an onion inside. There are regularly millions of dollars in hail-damage insurance claims after a big storm (that includes crop damage). The stones break car windshields, severely dent the bodywork, and punch through house siding. Usually about the biggest is smaller than a golf-ball, but it's been known to come in baseball size. You don't want to get pelted with that stuff for long.

 

[mgb_phys]

Shouldn't it depend on the density?

Yes, this assumes sea level air and the density of ice doesn't vary very much - it's just an approximation.