Penny Wise
To refresh,
A debate was held last night at the Tailgate that if a penny were dropped from a building, a tall one that is, like the Empire State Building, that it would kill someone if it landed on their head. It was stated by the opposing party, those sitting across from me and remaining nameless, that the penny would pick up enough speed to crush or go through a skull. In fact, one even individual stated that it would even come out in a certain spot under the jaw. Below is my research to prove that a penny can not kill a person when dropped from a tall building:
First off, let us start with basic information:
The Empire State Building is 1,250 feet tall. An object dropped off the top would take 8.8 seconds to reach the ground, by which time it would be moving at 193 miles an hour.
The equations to support this:
t =
sqrt ( 2 * 1,250 feet / 32.2 feet/s2 )
=
8.81 seconds
v =
t * 32.2 feet/s2
=
283.7 feet/s
=
193.4 miles per hour
Now here are some notes I found while doing more research:
The mass of pennies has changed with changes in composition. Prior to 1982, pennies weighed 3.1 grams. They got lighter when the alloy was changed from 95% copper/ 5% zinc to copper plated zinc and now weigh 2.5 grams. Terminal velocity increases proportional to the square root of mass. For our calculations, we'll use a 1990 penny.
Gravity accelerates a falling object at 9.81 meters per second (32.2 feet/s).
Coefficient of drag is tricky. If a penny were molded into a sphere we'd use the value "0.5." I've seen various values ranging from 0.36 to 2. Since the penny could also fall on its edge, or flat, or both, the average, 1.18.
As any pilot knows, the density of the air varies with temperature, altitude, and humidity. To keep this simple, we'll assume a temperature of 0°C, which CRC says 1.2929 kg/m3
The area of the object is taken from the part pointed in the direction it falls. If the penny fell flat, its area would be pi * r 2 (where r is the radius). If the penny falls on its edge, the area is 2 * r * d. What's likely to occur is the penny will bobble around a bit. As the area falling towards the earth increases, the terminal velocity decreases. And vice versa.
Now, the equation for terminal velocity goes as follows:
Vterm
=
sqrt (
2 * m * g
c * p * A
)
where:
m
mass of the object
g
acceleration from gravity
c
coefficient of drag
p
density of air
A
Area of the object
So, if we input all the data into the above equation, a penny would reach a maximum speed of 23.6 MPH tumbling through the air when it hit someone on the head below. Clearly there are other factors that would only slow the penny down. These could be things such updrafts, birds or suicide jumpers. I could essentially side arm a penny at someone next to me, that would reach a higher speed of 23.6 mph and obvisoulsy bounce off their head, causing at most a small bruise.
A debate was held last night at the Tailgate that if a penny were dropped from a building, a tall one that is, like the Empire State Building, that it would kill someone if it landed on their head. It was stated by the opposing party, those sitting across from me and remaining nameless, that the penny would pick up enough speed to crush or go through a skull. In fact, one even individual stated that it would even come out in a certain spot under the jaw. Below is my research to prove that a penny can not kill a person when dropped from a tall building:
First off, let us start with basic information:
The Empire State Building is 1,250 feet tall. An object dropped off the top would take 8.8 seconds to reach the ground, by which time it would be moving at 193 miles an hour.
The equations to support this:
t =
sqrt ( 2 * 1,250 feet / 32.2 feet/s2 )
=
8.81 seconds
v =
t * 32.2 feet/s2
=
283.7 feet/s
=
193.4 miles per hour
Now here are some notes I found while doing more research:
The mass of pennies has changed with changes in composition. Prior to 1982, pennies weighed 3.1 grams. They got lighter when the alloy was changed from 95% copper/ 5% zinc to copper plated zinc and now weigh 2.5 grams. Terminal velocity increases proportional to the square root of mass. For our calculations, we'll use a 1990 penny.
Gravity accelerates a falling object at 9.81 meters per second (32.2 feet/s).
Coefficient of drag is tricky. If a penny were molded into a sphere we'd use the value "0.5." I've seen various values ranging from 0.36 to 2. Since the penny could also fall on its edge, or flat, or both, the average, 1.18.
As any pilot knows, the density of the air varies with temperature, altitude, and humidity. To keep this simple, we'll assume a temperature of 0°C, which CRC says 1.2929 kg/m3
The area of the object is taken from the part pointed in the direction it falls. If the penny fell flat, its area would be pi * r 2 (where r is the radius). If the penny falls on its edge, the area is 2 * r * d. What's likely to occur is the penny will bobble around a bit. As the area falling towards the earth increases, the terminal velocity decreases. And vice versa.
Now, the equation for terminal velocity goes as follows:
Vterm
=
sqrt (
2 * m * g
c * p * A
)
where:
m
mass of the object
g
acceleration from gravity
c
coefficient of drag
p
density of air
A
Area of the object
So, if we input all the data into the above equation, a penny would reach a maximum speed of 23.6 MPH tumbling through the air when it hit someone on the head below. Clearly there are other factors that would only slow the penny down. These could be things such updrafts, birds or suicide jumpers. I could essentially side arm a penny at someone next to me, that would reach a higher speed of 23.6 mph and obvisoulsy bounce off their head, causing at most a small bruise.
posted by Z at 12:00 PM
0 comments
