From: Ronald Wong (ronwong@inreach.com)
Date: Mon Jan 27 2003 - 22:52:44 PST
Message-Id: <l03102800ba5aa1c1f0ee@[209.209.18.124]> Date: Mon, 27 Jan 2003 22:52:44 -0800 From: Ronald Wong <ronwong@inreach.com> Subject: Re: Objects Dropped from Tall Buildings
Roy Mayeda said:
>...
>Regarding the danger of airguns, they're covering themselves by
>warning you to be even more careful than necessary to avoid lawsuits.
>Don't get me wrong. If you always follow 100% safe practices, it
>really does cut injuries down to a minimum. However, I seriously
>doubt that an airgun producing typical velocities can even throw
>a projectile 300 meters. Yes, some are quite impressive, but
>there's still that nasty air resistance.
The question was how dangerous would a penny be if it stuck someone after
falling from the top of a tall building.
________________________________________
The airguns were pistols in an ad that I referred to in my reply to
Debbie's original question. They fired pellets with a muzzle velocity of
120 m/s
(by the way - without air friction, a muzzle velocity of 55 m/s
is all that is needed to achieve the maximum range referred to
in the ad)
and this meant that the pellets had about 3.6 J of energy.
As far as harm is concerned it's the energy that is going to do the damage,
not the muzzle velocity of the projectile or it's maximum range.
3.6 joules of energy doesn't seem like much - and compared to that of a
bullet fired from a firearm it isn't - but, to put this into some
perspective, 3.6 joules is equivalent to 2.7 ft-lbs of energy. Drop one of
our heavier physics books on your head from a height of 1 ft and you'll get
a better idea of what we are talking about. Keep in mind that this energy
would be delivered over a very small area (it's equivalent to the
cross-sectional area of the pellet's head).
I would not recommend that you put your head near the end of the barrel of
one of these handguns when it is fired.
Airguns in the form of a rifle have even greater muzzle velocities -
typically 240-340 m/s and the energies are proportionately greater (around
14-29 J).
The gun dealer is right to warn the uninformed - both users as well as
non-users - about his products. At close range, any airgun can be dangerous.
________________________________________
As pointed out in my earlier message, the energy of the penny at the moment
of impact would be about 11 joules if it fell from the top of Chicago's
Sears building (in the absence of air friction). That's about 8.1 ft-lbs of
energy.
Drop a couple of bricks on your head from a height of 1 ft and...
The original question had to do with the penetration of a human skull by
the penny.
For the sake of simplicity, let's say the penny comes to a halt after
penetrating 0.5 inch of the head. This would require an average force of 24
X 8.1-lbs (Work in ft-lbs = force in lbs X distance in feet => 8.1 ft-lbs =
force in lbs X 1/24th of a foot => etc.). That's 190 lbs acting on the
penny and therefore 190 lbs acting on the skull (for every action,...).
Assume that it landed flat on the head of the unfortunate victim. Using
0.75 inches for the diameter of the penny, I get around 0.44 square inches
for the area over which the force acted. Dividing this figure into the
force gaves an average pressure of 440 lbs/in^2.
We are now in a position where we can ask a physiologist whether or not
this is enough pressure for a penny to penetrate the skull.
Alternatively, we can look at it this way: If a fairly heavy athelete (218
lbs) sat on the shoulders of his identical twin who, in turn, sat on a 4 lb
chair which was balanced by one leg on a skull (area of contact with skull,
1.0 in^2), would the chair's leg penetrate the skull?
________________________________________
Fortunately, in the real world, there is air friction.
Using the figures from my original message, you'll see that even at the
maximum terminal velocity - not likely given it's shape - the energy is no
more than 0.24 ft-lb. If the penny landed flat on the head of a person, the
pressure would be about 13 lbs/in^2. I think the skull can handle this
without caving in - it is less than one atmosphere of pressure.
With all due apologies for the use of BPS units in a "scientific"
discussion, I remain irresponsibily yours,
ron wong
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