The Ladder Problem

I like to solve physics problems. Here is one for you (I just made it up).

A 4 meter ladder leans against a frictionless wall at a 30 degree angle. The mass of the ladder is 10 kg. A human stands 1 meter up the ladder and has a mass of 70 kg. What is the minimum coefficient of static friction between the floor and the ladder so that the ladder doesn’t slip?

Here is the solution-in video form.

But wait! There’s more. Let’s do another problem.

Suppose you have the same ladder and the same human. However, in this case the coefficient of static friction between the ladder and the ground is 0.55. How far up can the human move before the ladder slips?

I like this question because I don’t know how the answer will turn out. That makes it fun. So, let’s do it.

But what kind of problem is this? I’ll make this a multiple choice question. Here are your options.

1. A friction problem.
2. An equilibrium problem.
3. A ladder problem.
4. A work-energy problem.

Your answer? Go ahead and answer. It’s important to think about things like this if you want to become an expert problem solver.