Occasionally, there are scientific findings that surprise and delight us. One such finding for me is the intriguing properties of a simple two-armed, swing-pan, old-fashion balance. Yes, you can’t hardly find them any more, but I went to an antique shop to get mine. I bought it because I was thinking about a specific problem that I couldn’t decide the correct answer to without experimenting.
The problem goes like this. Suppose that the balance is in horizontal equilibrium without any weights. Next, I add fairly small increments of weight to one side until that side just comes to rest on the table top. Now I place ten times as much weight as was required for the balance to just touch the table in the same pan. Obviously the pan will remain touching the table top since that pan now has the amount of weight that caused it to touch the table plus ten times that weight, but now I add the same ten times amount of weight to the opposite pan. What will happen?
Well my initial thought was that since the pan with extra weight (the amount of weight that caused it to touch the table plus ten times that weight) is touching the table, it won’t move. I couldn’t see how a smaller weight on the opposite side would move the balance. Later, I would learn that about two-thirds out of dozens of people asked this question also thought that the pan on the table wouldn’t move (some of these people are expert scientists and engineers!).
For those who don’t have an old fashion two pan balance –
see these links for a gedanken experiment and further descriptions of a balance gedanken experiment and Simple_Balance_PartI.pdf and Simple_Balance_PartII.pdf.
Although the popular perception is that Archimedes, Galileo and Newton have supplied all the physics we need, there yet remain many intriguing issues to discover.
The fundamental equilibrium of a simple balance leads to some rather surprising findings such as that a fundamental physiological law, often called Weber’s law or the Weber-Fechner law describes how both our senses and a simple balance obey the same law (see – Weber’s Law Modeled by the Mathematical Description of a Beam Balance, Mathematical Biosciences 122: 89-94 (1994)) and that our biological receptors and a simple balance both desensitize (see – Desensitization of a balance with Langmuir binding of weights .
(see – Bio Balance – Reference Library for more references)
The simple physics behind these complex phenomena suggest that we have just begun to truly understand how our own senses work and how they cause us to interact with the universe. This is a journey of self-discovery that we have much farther to travel.
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