One of my biggest dreams was to visit NYC. I was excited when I finally had the opportunity to explore the city on my own. A friend of mine recommended me to see the Empire State Building. The skyscraper is one of the landmarks of the city. There are many rumors and stories that people tell, but one of them was quite remarkable.
“When someone drops a penny off the Empire State Building and it hits you, you will die from the impact!”
After hearing this I was afraid and stayed well clear off the pavements around the famous building. I didn’t want to die because of a penny!
What do you think? Fact or fiction? Let’s find out!
Long live science!
We need to understand what happens with a penny when it’s dropped off the building. The roof of the Empire State Building has a height of 381 meters. A common penny has a weight of 1-2 gram. First of all we want to calculate the time it takes until the penny hits the sidewalk and in addition to that we want to know the velocity and force that acts upon the object the penny hits.
Since we know the building is 381 m high and the acceleration of gravity is 9.8 m/s/s we can calculate the time of free fall (note that we ignore the air resistance).
We use this simple formula to calculate the time the penny travels. All variables are known except the time, t. After transforming the equation we know the exact time.
So it takes around 8.81 seconds from the top of the building to the ground. We use another formula to calculate the terminal velocity.
Inserting the known values and transforming we know that the penny will hit with sidewalk with a velocity of 80 meters per second. The impulse that acts on the body that is hit is: p = m*v. Since we know the mass m and velocity v we can calculate the impulse p (0.08 Newton per seconds)
Is it fatal?
No, simply no. It would hurt for a few seconds but nothing serious will happen to you at all. There are many facts we need to consider. First of all our calculations ignore the air resistance. Because our penny is small and has a low weight the air resistance plays a huge role. It slows the coins terminal velocity (maximum speed). Furthermore, the force upon impact is tiny due to the weight. A bullet from a gun (9 mm, Glock) reaches a terminal velocity of 350-450 m/s and has a weight of 7.5 g, nothing a penny can reach even closely. Because of the flat shape of the coin the air resistance is very high and reduces its speed to approximately 11 m/s. However, take care. If someone throws a pen it can shoot down like an arrow and become a deadly projectile - it might pierce you
To summarize: A coin is too small, flat, has a low velocity and is cushioned by the air. It wouldn’t even reach the ground since there is a mesh that catches the coin.
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