Saturday, June 15, 2013

Superman and the Physics of Collapsing Buildings

I saw the new Superman movie this weekend, and I liked it. But it wasn't perfect, and the thing that bothered me the most was the bad physics. I'm not talking about Superman being able to fly or the Kryptonian terraforming machine being able to increase Earth's mass. That kind of thing is expected in a superhero movie. I'm talking about more everyday physics. The most egregious example is skyscrapers falling over.

It happens multiple times in the movie. Superman throws a bad guy (or a bad guy throws Superman) through a skyscraper, part of the building is damaged, it tips and falls over like a tree. You might be wondering what's wrong with that. After all, trees fall down like that. If you build a tower out of Legos and knock it down, it falls down like that. But large buildings don't fall down like trees or Legos. They don't fall over sideways, they simply fall straight down.

So, why do large building fall down? Because gravity pulls them down. It does not pull sideways, so it doesn't tip sideways. But then why do Legos and trees fall sideways? Because there are other forces at work, namely the internal forces holding them together and in the same shape. Gravity is pulling down, but the internal forces prevent the top from simply collapsing into the bottom, so it falls sideways.
Here's a force diagram of a brick in a Lego tower tipping over. Gravity is pulling down. Normal force is pushing at the same angle the building is tipping. The total force is in blue. The vertical components mostly cancel, leaving the total force going mostly sideways.

But why don't large buildings do the same? Don't they have internal forces too? Well, yes, but they don't scale up. As the building gets bigger, it gets heavier, and gravity pulls more strongly. The internal forces of a large building will be stronger than those of a Lego building because it's made with steel rather than plastic, but it will be weaker relative to the force of gravity. The normal force will still be there, causing it to tip just a little bit, but gravity will dominate, so it will fall almost straight down. The top will simply collapse into the bottom, rather than being pushed to the side.

So why does this matter? It's just a movie, right? That's true, but understanding physics and how forces scale can be important. For example, there was a very well known case where some tall buildings fell down unexpectedly. As physics predicts, the buildings fell mostly straight down. (But not entirely. A lot of nearby buildings were hit by debris.) But a lot of people didn't understand the physics, and thought that the fact that the buildings fell down instead of over meant the buildings weren't brought down by airplanes, but rather by controlled demolition, and thus a conspiracy theory was born.