Question about principle of minimum total potential energy

Question

So this question is really basic compared to some others on this website.

I was reading professor povey's perplexing problem, a book on physics problem solving. I came across a problem which is below.

A sewage worker is inside a large underground aqueduct (diameter > a man’s height) of circular cross section, and so smooth that friction is negligibly small. He has a ladder which is the same length as the diameter of the aqueduct. He wishes to inspect something in the roof. He mounts the ladder and continues to climb until he reaches the other end. What happens?

The answer is that as the man starts to climb up a ladder, the ladder will tilt more and more back, until the ladder makes a 360 degree turn, and the man is back to his starting point. The book said that this was a application of principle of minimum total potential energy.

This lead me to wonder about a simple weighing balance scale that we have all seen. Something like this:

Would this simple system be an example of the principle of minimum total potential energy? Since the system is allowed to move, and if you place a weight, the side with the weight will drop. Does the side with the weight drop so that the system can shift to the position with the lowest potential energy? Or am I simply over complicating things?

Answer 1

You are right, but yes, you are slightly over-complicating. Or rather the Professor is.

In both cases there is just a gravitational force and no resistance/friction, so the whole thing (aka center off mass) drops down as far as possible.

For the ladder in the circle, there is however, an unstable equilibrium when the man is right in the middle, on top of the ladder. Also, without friction, he would rotate if he jumped on the ladder. But this should be explained in the book.

Aha, found it. He introduces potential energy with a simple example, because in the next one it is needed and it gets complicated. Nice book.