The age old question: If a penny fell from the Empire State Building and hit someone, would it kill them?
Quick answer: No, but it will probably leave a mark.
Everyone knows that you are not supposed to drop stuff, even small stuff like a penny, off tall buildings. But if it wouldn’t kill someone, what will REALLY happen if you drop a penny off the Empire State Building? First, let’s define some key terms that are going to help us understand the situation.
- Acceleration- is the change in the velocity
- Force- an interaction that if unopposed will result in a change in motion. Basically a push or a pull.
- Gravity- is the force constantly pulling down on an object.
- Drag- drag is the force of air resisting motion. In this example, the drag force is going to be pushing back up on the penny increasingly as we increase speed. Think of when you put your arm out a moving car and it gets pushed backwards as you are moving forward.
Alright. Now that we understand the terminology we’ll throw that penny off the building.
Lets break this into steps:
- After you let go of the penny, gravity works its magic, pulling it towards the ground, increasing velocity along the way.
- As the velocity increases so does the force of drag on the penny due to the air not being able to move out of the way fast enough.
- At some point in the fall, the force of gravity will equal the force of drag and the penny will no longer accelerate.
- At this point the penny will fall at a constant velocity until it hits the ground, or an unsuspecting person.
This constant velocity is known as an object’s terminal velocity.
The equation to determine terminal velocity is:
For a penny off the Empire State Building:
Force of Gravity = 9.8 m/s^2 *0.0024kg =0.02352 kgm/s^2
Drag Coefficient = 1.17
Air Density = 1.23 Kg/m^3
Area = 0.00028m/s
Plugging those values in we get about 11m/s as a maximum velocity which works out to be about 24 miles per hour.
This is another way to look at it:
The force of gravity is constant, but as the velocity of the penny increases, the force of drag pushing back up on the penny increases until they equalize. And when they are equal, that is the maximum velocity the penny will move (unless you put another force on the penny like a small rocket engine).
OK, so we know the penny (unaided by rocket propulsion) will hit a maximum speed of about 24 miles per hour. All of this you can find on other websites. You can research about terminal velocity for any number of interesting objects (including humans), but what does that 24 miles-per-hour-penny mean for the innocent bystander on the street?
Here is where this article is unique. I did some research and found a study that specifically looked at the minimal velocities for different weights and bullets necessary to penetrate the skin:
Minimal velocities necessary for perforation of skin by air gun pellets and bullets.
The study was published in the Journal of Forensic Science. They studied different air guns pellets weights and different velocities to see at what velocity they would break the skin.
My favorite quote from the abstract:
“Human lower extremities were used.”
So basically, they found people that would volunteer (or cadavers… they didn’t specify) to be shot with pellets at different velocities until it broke the skin… SCIENCE!
The study found the following results:
A penny weighs about 1 gram so comparably for a pellet, that would be 167.8 miles/hour. Now they say that one of the elements in the pellet study is total pressure exerted on the skin, and a pellet will have a higher pressure (force will be the same but divided over a smaller area as the pellet is smaller). So we would have to assume that the speed necessary for a penny to break skin would need to be higher than that of a pellet.
As a result, if you toss a penny off the top of the Empire State Building it wouldn’t kill, or even break the skin, but I would imagine that a penny traveling at 24 miles per hour might leave a welt.
Further info and links:
Terminal Velocity via NASA