ericmazur / PnPbook

Tracking of typos, errors, and improvements for "The Principles and Practice of Physics"
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WaveGen™ failure #100

Open JohnDenker opened 9 years ago

JohnDenker commented 9 years ago

On page II.371 Additional Problem 81 is seriously ill-posed. See item #99 for a discussion of the general issue of ill-posed problems.

Let me outline how I would address the problem according to my own rules https://www.av8n.com/physics/ill-posed.htm which include not taking the question literally, but rather answering the question that _should have been asked_.

  1. I assume the scenario meant to apply to the CEO, not the "founder". In a company of this size, the original founder is almost certainly not the CEO. Different skills are required.
  2. As CEO, the first thing you should do is hire three really good lawyers. You're going to need them.
  3. Then fire everybody in the engineering department. They're incompetent and they're lying to you.
  4. The limitation of tubes no large than 2 meters is bogus. It was obviously stuck in there just to make the problem harder.
  5. The basic WaveGen™ design is not very good. The company that invented it doesn't make such things anymore. For one thing, there are impedance-matching problems between the water and the dynamo. Using a cylindrical volume of air above the water just exacerbates the impedance-matching problems. You'd be much better off using a mechanical float driving a dynamo directly, and storing the energy in a humongous capacitor or perhaps a motor-flywheel-generator.
  6. The claim of 68% efficiency is not credible. A real-world WaveGen™ plant has an efficiency closer to 8% than 68% ... and the design in this scenario is worse, not better. There are several ways in which it is worse:
    • Contrary to the "proof" given on page I.402, waves are generally not purely transverse. In particular, shallow-water waves cannot possibly be transverse. Hint: conservation / continuity. Setting up a reflector of size comparable to the wavelength will convert some of the horizontal motion to vertical motion, but 2 meter diameter pipes forfeit all the horizontal energy, lowering the efficiency.
    • Drilling holes above the waterline is crazy. It makes things in some ways worse and in no ways better.

In summary: This claims to be a rich-context exercise, but it's not. It's an equation-hunting exercise, with a layer of obfuscatory window-dressing. The point of rich-context exercises is that reasoning about the real world is supposed to help make sense of the scenario, but here it is just the reverse.

Here are some possibly-constructive suggestions:

a. As for this question in particular: If you want to ask a real-world question, ask a real real-world question, not a fake real-world question. For example, refer students to various proposals e.g. https://en.wikipedia.org/wiki/Wave_power#List_of_devices and ask them to discuss some important aspect ... perhaps the efficiency of each, with an emphasis on the physics principles that limit the efficiency. If there is something they ought to know about but probably don't (such as the concept of impedance matching) you can make the problem _easier_ by providing hints.

b. More generally, I vehemently object to the idea of taking an easy and unimportant problem and making it _harder_ by adding artificial restrictions (as advocated by e.g. Heller&Heller).