Monday, January 16, 2017

Dropping Pennies from the Empire State Building

You probably heard about the idea of dropping a penny from the Empire State Building and its
probability of doing some damage. The word from various sources is - No, it won't do much of any damage. If it hit you, you might think, "Hey what was that?"

They say (they being those in charge of such things) that a big part of the reason is the flat shape of the penny and the air resistance it would meet. Granted, but what if there is no resistance? Let's try it out.

(Final velocity)2 = (Initial velocity)2 + 2gd is a formula for a free falling object. (Time out - I, for the first time, used html to show exponents. Wow!! Big day for me.)

Mass of penny = 3.1 grams. (I'm going with that, but I saw that it is now 2.5 grams. And I didn't even notice.) Height of Empire State Building is 86.42 meters, and initial velocity of zero. That gives us a final velocity is 86.42 meters per second or 193.32 miles per hour. But as they say, that is a moot point as air resistance is not going to allow it to go that fast. Even if it is going fairly fast, it doesn't weigh very much.

Then I thought, what if you drop a baseball and what would it's impact be? And what would be a measure of its impact. Would we be looking at momentum or kinetic energy? If I had gotten an A instead of a gift B in physics, I might have an answer for that.

Momentum = mass x velocity
Kinetic Energy = mass x (velocity)2

So take the penny's momentum/energy. What would the velocity of the baseball be to have the same impact as the penny?

To make a long story short, I figured if having the same momentum, the baseball would be going 1.488 m/s or 3.329 miles per hour.

If looking at kinetic energy, the baseball's velocity would be 28.275 miles per hour.

Neither speed would hurt a whole bunch. Hopefully no one drops something like an anvil.