We've all heard the myth. Drop a penny from the top of the Empire State Building, it will gain enough velocity to do considerable damage to someone standing on the sidewalk - plunge a hole through their hand, or, in more gruesome versions, their head.
Though at first this thought seems plausible (considering the height of the Empire State Building and the acceleration due to gravity), it's important to realize that - due to other important factors - this myth is busted.
When we first release the penny from the top of this skyscraper, it begins to accelerate downward at 9.8 m/s^2, the acceleration due to gravity. If the only force on this penny were the force of gravity downward, it would continue to accelerate at a constant 9.8m/s^2 until the moment it hit the sidewalk. Since we know the height of the Empire State Building is about 381m, and we also know the acceleration is 9.8 m/s^2 and initial velocity (Vo) is zero, we can calculate the final velocity (Vf) using our kinematics equation: Vf^2 = Vo^2 + 2ax.
Plugging in those numbers, we get that the penny would be traveling about 86.4 m/s just before it struck the sidewalk or person on the sidewalk. For those of you who find it hard to comprehend just how fast this is (because here in the US we say "screw the metric system!" ), this translates to roughly 193 mph. Yeah, that's pretty fast.
But wait! There's more! We forgot to account for one crucial detail, the very detail that makes this myth a bust: drag.
As the penny falls, it experiences another force - the force of drag, or air resistance, acting opposite the force of gravity. For its weight, the penny drags an awful lot of air behind it. As a result, it reaches terminal velocity at only about 25 mph.
So, there you have it. Because of the force of drag/air resistance, tourists below the Empire State Building have nothing to fear from falling pennies.
Hope you enjoyed this blog post!
Until next time,