I know, I know, this blog post is very late! If I’m going to post about a Mythbusters episode, I usually try to do it before the next one airs. But this topic — calculating the circumstances under which a rope will pull a person’s leg — turned out to be pretty complicated. Which of course made it impossible to give up on.

And after days of toil, I think I finally figured it out! If you’re the kind of person who finds complicated physical interactions fascinating, you’re going to love this post. The math isn’t too complicated; if you know what a differential equation is, you’ll be fine, but the physical reasoning is something you could probably spend a while wrapping your head around.

The setup

On the Deadliest Catch-themed Mythbusters episode which came out last week, one of the myths being tested was that if a person steps in a coil of rope, and that rope is attached to a crab pot (trap) that gets dropped over the side of the ship, the rope will be pulled tight enough around the person’s leg that it will drag them overboard, and down to the …

I probably should not have worn my frictionless shoes out last night.

Oddly enough (for the end of March) it’s snowing in State College, which means that the sidewalks are slippery again, which reminded me that I’ve been meaning to follow up my previous post about slippery surfaces with one where I talk about hills.

There were two main points I made in the last post:

1. friction with the ground is what allows you to accelerate (speed up, slow down, or change direction), and
2. friction also helps keep your feet from slipping out from under you when you put them down as you walk.

I used a slightly unrealistic diagram of a foot as a visual aid:

Now compare that to the equivalent diagram for a foot on a hill:

On level ground, without friction, there’s no force pushing you along the ground. But the new diagram shows that that isn’t the case anymore on a hill. With no friction, gravity works to pull you down the slope. So in the absence of friction, you do accelerate — you slip down the hill.

Obviously, this is bad news if you’re trying to walk uphill. Even if …