PFE002: Perpetual Motion

When deciding how to treat a new paper, there are a number of criteria one uses to determine its crackpot level. That is, there are a lot people out there who try to publish junk under the premise of complicated science. It's the job of actual experts in their field to police this.

An extremely popular crackpot theory that comes up time and again is perpetual motion.

Most of the designs that may seem like perpetual motion rely on energy from the sun, or, more generally, a hidden energy source.

When evaluating a mechanism for perpetual motion (and to figure out where the flaw in the argument must be) I look for a way to get energy out of the system. In the example above, I would likely attach a generator to one of the pulleys to generate electricity. But then something must move the rope to make the pulley move. Clearly, there is a gravitational attraction between the blocks and the earth, and the one on the right has a larger mass, so it moves down causing the system to rotate.

Of course this system is silly, but it demonstrates the process for identifying certain classes of crackpots, an essential part of physics or any hard science.

That's (not really) perpetual motion.

PFE001: Moments

First, a photo story on the importance of moments (don't worry if you don't know what they are yet):

Thanks to the good engineers at Virginia Tech for the content.

Moments of inertia is one of those abstract things learned in kinematics. Understanding things going up and down and friction is easy, but this requires a bit of a step

Formally, a moment of inertia is usually represented by the letter I. For inertia? I'm not really sure. Anyways, here's the formula:$$I=\sum_{i=1}^Nm_ir_i^2$$It is interesting (and relevant to this example) to note that this formula depends on the axis of rotation. This axis isn't always obvious, but here it is along the crane, specifically where it flips over.

There are two reasons that the crane would flip. The first is if the center of mass of the object is outside of the base (anyone who has tried to balance something on end understands this, at least qualitatively). In the third picture, however, the car is out of the water and the crane, while leaning, seems to be doing generally alright.

The other potential problem has to do with applying a force out at a distance. The math here is unnecessary for our purposes, but basically the farther away the car is from the axis of rotation, and the heavier the car weighs in addition to how hard the crane is pulling, needs to be effectively "balanced out" by the rest of the crane. The calculation for this involves the moment of inertia of the whole crane. Needless to say, this is something that any good crane operator should be aware of.

That's moments.