Modeling a Falling Rope Ladder That Falls Faster Than Free Fall.

Photo: Rhett Allain. Free Body Diagrams

I saw this YouTube short on Vertiasium’s channel. It shows two falling rope ladders. The one on the left hits a table while the one on the right never hits anything. Which one ends up falling faster? The one that hits the table (SPOILER ALERT).

Falling ladders - why does this happen?

So, I THINK that the key to this falling ladder problem has to do with the tilted rungs. When one side of a rung hits the table before the other side does, there is an induced rotational motion. This rotation stretches the string on the opposite side and pulls DOWN on the rung above it.

Here is my sketch of how this works (how I think it works at least).

Notice that I am trying to show the “slackness” in the right string as the bottom rung is hit. Of course, this would only be slack if the middle rung couldn’t rotate — which I’m assuming it won’t because it’s connect to the stuff above it.

Python Model

OK, enough of that. You don’t really know if something will work until you can model it. So, I’m going to build this falling ladder in python. I already have a head start. In this previous post, I modeled the motion of a stick hitting the floor (or table).

Modeling a Bouncing Stick with Python

Now I just need to add two more “sticks” connected by strings. I guess I should go ahead and explain my string-force model. Right? Well, let’s say that a string has some starting length of s_0. I can also find the vector length of this string from the beginning to the end. If the string is stretched (even a tiny bit) then there will be a force pulling in the opposite direction of the string. This would…