I am thinking about adding another rule to my Perpetual Motion Guidelines. Currently, I only read crazy idea emails if they meet the following:

  • First, the author must have read my guide about emails.
  • Second, the author shows that the machine runs in isolation (no external influences).
  • Third, the machine must be a new idea (not one that has been demonstrated before).
  • Fourth, no conspiracies.

I am considering adding this: If the perpetual motion machine is super-popular, I might look at it even if it doesn’t meet all other criteria. This is where the See-Saw Balance falls. It’s popular enough that I am going to point out how silly it is.

The Machine

The See-Saw Balance uses the very common perpetual motion theme of unbalanced torques. The idea is a mass moves in such a way that the torque making the machine rotate is greater on one side than the other. In this case, the unbalanced torque is created when a ball rolls to one side of the machine but the support is on the other side.

I don’t want to go into the explanation of how it works since a) that’s covered in the video and b) it’s bogus.

Conservation of Energy

There is one particular thing you can calculate such that the total value of this thing in a closed system remains constant. This thing is called energy. If you have a system without adding any energy, then the total energy remains constant. We have demonstrated this many times and you can take it as true (even though science is just about models).

I think it’s safe to assume the See-Saw Balance is supposed to be a closed system (no energy inputs). If this is a true perpetual motion machine, the total energy at one point must be less than or equal to the total energy at a later point. (Yes, the grand idea behind perpetual energy machines is they could be used to as a source of energy.)

Let me draw a diagram of the See-Saw Balance at two different times.

Spring 2016 Sketches key

Looking at the positions of both balls, the added height of the two balls is greater in position 2 than in position 1. Go ahead and measure it from the video; it’s true. This means that going from position 1 to 2, the center of mass of the whole system increases (assuming the wooden apparatus is symmetrical, its center of mass shouldn’t change). Since the center of mass increases, the gravitational potential increases. Just to be clear, let me write this using the Work-Energy Principle (which says the work done on a system is equal to the change in energy). Since this is a closed system (or supposed to be), the work is zero and I can write:

La te xi t 1

Clearly this can’t work. There are a few possibilities that could explain this.

  • The Work-Energy Principle is wrong. OK, this isn’t very likely. We have used this principle for a long time and it always works. It would be crazy to have a stupid wood-and-ball toy prove that energy isn’t conserved.
  • There is some other energy term that should be in the system. Perhaps there is stored spring potential energy or maybe the thing has a battery (probably not).
  • The work isn’t zero. Instead, there could be an energy input into the system. We assumed this was a closed system, but if it isn’t, it isn’t a perpetual motion machine.

My guess is that there is some external energy input. Maybe there are magnets under the table or something. It doesn’t matter how the trick works, only that there is a trick.

Net Torque

But what about the torque? Wouldn’t a configuration like this cause the machine to tip over? No. The problem is with these “cross supports”. Let me draw a simplified model with just one ball.

Spring 2016 Sketches key

If this is released from rest, which way would it tip? According to the See-Saw Balance machine, it would tip to the left since the ball is pushing on the support and the support pushes on the left side. Nice idea, but wrong. Let me draw that same support with the forces acting on it. If you held the board steady, that support would be at rest and not rotating, so the net force and the net torque on the board must be zero. This probably is the diagram a perpetual motion person would draw:

Spring 2016 Sketches key

The ball pushes down on the support and the horizontal board pushes up on the board. This means the support pushes down on the board (because every force has an equal and opposite force) and the board would tip to the left. But wait! Although this shows a net force of zero on the support, the net torque is not zero. The only way for the support to not tip over is with some extra forces. It would probably be something like this:

Spring 2016 Sketches key

At the point where the support meets the board, there have to be two contact forces. On one side of the contact point, the board pushes up on the support and on the other side the board pulls down on the support. Yes, it pushes up more than it pulls down, but the combination of these two forces (at different locations) would produce a torque on the board that makes it rotate to the right. Actually, this would be a great homework question. Show that this support (assume massless support) has the exact same torque as a vertical support.

In the end, the torque on the board doesn’t really depend on the shape of the support but rather the location of the center of mass.

How Does it Work?

If it’s a trick, how does it work? I’m not sure (and I don’t really care that much). However, I do think there is something weird in the way it moves. First, let’s look at the horizontal position of both balls and the structure during one oscillation.

Notice how the two balls stop rolling around one second but the structure doesn’t move right away? That seems odd, but yes, it might just be a measurement problem. I was also going to make a longer plot looking at the difference in ball times and structure times but realized I didn’t really care that much.

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The Physics Behind Another Bogus Perpetual Motion Machine