We all know that if you drop a penny from the top of the Empire State Building, it will kill anyone it happens to strike. We think we know it, anyway. Has anyone ever taken the time to examine how much truth there is to this piece of conventional wisdom? Take a look at the physics behind this rumor that has terrified schoolchildren for generations.
There are a few things to consider for us to solve this mystery. The first is the question of whether you could even throw a penny off the top of the Empire State Building. The barricades at the top of the building are designed to make it difficult for anyone or anything to get past them. Assuming you are successful in throwing a penny over them, it isn’t a straight drop from there to the sidewalks below. The design of the building includes a number of tapered reductions in building width, meaning that the penny would have to be hurled outward a significant distance in order for it to fall unimpeded all the way to the ground.
At its fundamental level, the physics behind this question is pretty straight forward. Acceleration due to gravity at sea level is 32 feet/second2 (9.8 meters/second2). The roof height of the Empire State Building is 1,250 feet (381 meters). At that height, the penny would fall for 8.815 seconds before striking the ground at a velocity of 283.6 ft/sec2 (86.44 meters/sec2). If you add in the antenna, the height is 1,454 feet (443.2 m) tall. A penny dropped from that height could be expected to reach a velocity of 305.9 ft/sec2 (93.23 meters/sec2) in the 9.507 seconds it would take for it to hit the ground. You can do your own calculations with this Free Fall Calculator.
At that speed, getting hit by a penny would hurt, and it could do some damage, but it likely wouldn’t be much more than break the skin. Unless you have an eggshell-thin skull, it’s quite unlikely that you’d breathe your last after such an encounter.
That still doesn’t answer our question, however. The above calculations are accurate if there is no atmosphere to hinder the penny’s fall. There is, of course, plenty of atmosphere in New York City. In fact, there is more atmosphere than in most places, given the fact the abundance of air pollution that mixes with the regular air. Because of this, the faster the penny falls, the greater the air resistance it experiences. There is a point at which the drag force equals the gravitational attraction, thus resulting in terminal velocity. The shape of the penny means it has quite a bit of air resistance. It will achieve terminal velocity after only about 50 feet (15 meters) of descent. From there, all the way to the ground, the penny will maintain a fairly-steady 36.67 feet/second (11.8 meters/second).
At that speed, getting hit by a penny would be somewhat akin to having a large flying bug strike you. You would feel it, but it probably wouldn’t even sting.
Feel free to discard your hardhat next time you walk close to the Empire State Building. Any pennies that happen to fall your way will fatten your pocketbook, rather than send you to the grave.
Read more fun facts about money.
Read more fun facts about physics.