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Wednesday, 10 October 2012

Does a Flying Bird Weigh Anything?

Does a Flying Bird Weigh Anything? ... Suppose that a bird weighing one pound is flying around in a five-pound cage. If you hung the cage on a spring balance,  would the scales record the weight of the cage alone, or the weight of the cage plus the bird? 

There is a story connected with this problem. Some years ago, a graduate student in physics at a large university decided to have some fun at the expense of two of his professors. A newspaper reporter was made a party to the scheme, and was persuaded to call each of the two professors on the telephone in order to ask his expert opinion on a scientific question.

Professor A was asked the following question: If a one-pound bird is flying in a five-pound cage made of thin wire, how much will the combination weigh? "Five pounds," Professor A told the reporter.

Professor B was then called, and a similar, but slightly different question was put to him: If a one-pound bird is flying in a five-pound cage made entirely of glass, how much will the combination weigh? "Six pounds," replied Professor B without hesitation.

The next day, much to the embarrassment of the two prominent professors, headlines appeared in the local paper: UNIVERSITY PROFS DISAGREE ON SCIENTIFIC QUESTION. A carefully misworded account of the questions and answers followed, with the words wire and glass omitted. No doubt everyone would agree that the bird and cage together would weigh six pounds, provided the bird were sitting stationary on its perch. But which of the professors was right in the case of the flying bird? The answer is that they were both right.  Since the bird is not falling, it must be supported by something. That something is the air. Because of the flapping of the bird's wings, the air pushes up on the bird with a force of one pound. The bird must then push down on the air with an equal and opposite force. This downward force of one pound is transmitted through the air to the first solid surface available. Since the wire cage would not have solid walls or floor, the air would push down, not on the cage, but on the ground below. Therefore, as Professor A said, the wire cage plus bird would weigh only five pounds. On the other hand, the glass cage would be impermeable to air, and in this case the weight of the bird must be borne by the cage. Professor B was absolutely correct when he said that the scales would then read six pounds. There is a moral to this story about the bird in the cage. It illustrates the necessity for precise statement in a scientific problem. 

From PHYSICS TELLS WHY, An Explanation of Some Common Physical Phenomena