Last night, the last thing I read on Facebook was “Can a penny
dropped from a skyscraper kill you?” I felt too sleepy to find out! So I slept,
with an assumption that it must! I fascinated fabricating a secret mechanism to
make sure the penny hit the target. I had even prepared a list of subjects in
my mind as I slept in peace! When woke up the authenticity of the assumption
bothered me a lot! So I went on with my following calculations and constrains.
So let us find out would it or would it not kill if we drop a penny from the
top of tallest skyscraper.
My calculation would revolve around the present tallest building in world the
Burj Khalifa in Dubai. It has height of 829.84 m. Since we are considering a
building in Dubai, I would prefer its currency to be used instead of Penny. So
we are considering a coin of 1 AED that weighs 6.40g. (It has an advantage of
its comparative heavy weight over penny!)
Now before calculating let us discuses some basic assumptions that we will keep
in mind.
We are basically comparing the fallen coin with a bullet. However,
if we consider the overall aerodynamic structure of bullet, it includes time of
flight, mass of bullet, shape, calibre, penetration power, directional muzzle
velocity, etc. So, for the purpose of this blog, I would consider only the mass
of coin and rest of the assumptions and aerodynamic specification will be
assumed to be ideal! Note; that it might affect its overall result.
My calculations will be based on SI system of measurements, primary because, I
grew up India and In India they teach us metric system that makes sense unlike
in USA or in interior design course all over the world.
When we drop the coin its initial velocity is 0m/s
It is accelerating towards the ground with an acceleration of
9.8m/s
The height of Burj Khalifa is the distance it would cover
accelerating i.e. 829.84m.
Using Newton’s third equation of motion; v²= u²+2as
Where;
v= final velocity or in our assumption muzzle velocity
u= initial velocity; 0m/s
a=acceleration i.e. 9.8m/s²
s= the height of the building i.e. 829.84m.
From the above data we get; V²=16265 (After rounding off)
This would give the value of muzzle velocity approximately 127m/s
Muzzle velocity of various types of gun range from 120m/s to 1700m/s
So Burj Khalifa is making it work! However, had it been a little shorter or any
other skyscraper across the globe it might not have had worked under the
similar set of constrains!
Hey! Hold your horses! This velocity is not what we will experience in
practice, due to the atmospheric drag. However, after calculating the effective
drag force it will continue to free fall till velocity is as high as 70m/s
(approximately). After attaining this terminal velocity it will not accelerate
further.
Nevertheless by the end, it will be the muzzle energy that would
confirm our calculation. After all is an AED coin drop would match a gunshot is
our prime objective. In the given circumstances, the mass of coin has a great
significance.
Muzzle energy is the kinetic energy of a bullet as it is expelled
from the muzzle of gun. It is a rough indication of the destructive potential
of a gun.
Numeric value of muzzle energy can be calculated
by; E=1/2mv²
Where,
E=energy in joules
M=mass of object, ie coin 6.4g or 0.0064 Kg.
V= terminal velocity of 70m/s
From the above data we get; E=31joules
Well as a matter of fact this is an effective value of energy,
according to Wikipedia muzzle energy levels of different types of firearms vary
from 20- 32,000 joules.
To conclude; Accidental or deliberate dropping of an AED coin from
the top of Burj Khalifa is potentially harmful! Ouch!
Isn't it incredible how gravity can make just a slip of coin
from hand to hold energy of about 52 joules?
A wise man said it so right, “Ah, Gravity, Thou art a Heartless
Bitch!”
