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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