Answer to the Question 03/98

WEIGHING A FLY

The question was:

An open bottle lies on a precise weighing scale. A fly then enters the bottle and flutters around in futile attempt to escape. How will the weight reading of the scale change?

A lazier fly, instead of using its wings to fly, uses a small helium filled balloon in order to remain airborne. What happens if it happens to wander into the same bottle?


The problem has been solved by K. MacArthur (e-mail macarthu@firsttrust.com). The solution is presented below.

Solution:

In the first case, the reading of the scale will increase approximately by the same amount as if the fly was sitting on the bottom of the bottle, i.e. it will increase by the weight of the fly: Since the fly "flutters around" it exerts a force on the air equal to its weight (and the air exerts the same force on the fly), while the air in its turn acts with the same force on the bottom of the bottle.

In the second case the lazy fly + balloon displace an amount (weight) of air which is exactly equal to their weight (that's why it remains airborne) and thus will have no effect on the scale.

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